From 8cc1cd86c7244668778c868c87580b309aea4170 Mon Sep 17 00:00:00 2001 From: Joachim Breitner Date: Mon, 30 Sep 2024 14:32:47 +0200 Subject: [PATCH] Massive generation of refutations via polynomials over Z/nZ (#19) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Massive generation of refutations via polynomials over cyclic groups * Use compact syntax to good effect * Use compact syntax, actually commit files * Add counterexamples as separate lib * Do not generate empty files * Remove debugging check * Make DecideBang tactic compiled * Fix bad formula mangling * Introduce decideFin! tactic to avoid type inference overhead. 2.5× times faster! * linter.unusedVariables false * Build counter-examples not parallel * Remove example, now that we can commit the files * Docstring and other cosmetics * Import more refutations * Only include magmas with <5 elements for now * Try to use native decide * Try to balance the large conjunction * Hidingt the inst in a top-level declaration does not help * Revert * Use Magma file, mild refactoring * Memoize monoid op * Typos * Put AllEquations into a namespace for now * Move DecideBang back into main library * SmallMagmas file * Different examples * Move to Generated * Prune counter-examples based on implications * Prune much more * Include more magmas * Remove dead code * Also prune based on covering * Set equational_result --- .gitattributes | 3 + equational_theories/Generated.lean | 1 + equational_theories/Generated/FinitePoly.lean | 132 + .../Generated/FinitePoly/Refutation108.lean | 23 + .../Generated/FinitePoly/Refutation112.lean | 23 + .../Generated/FinitePoly/Refutation114.lean | 23 + .../Generated/FinitePoly/Refutation116.lean | 23 + .../Generated/FinitePoly/Refutation120.lean | 23 + .../Generated/FinitePoly/Refutation126.lean | 23 + .../Generated/FinitePoly/Refutation128.lean | 23 + .../Generated/FinitePoly/Refutation132.lean | 23 + .../Generated/FinitePoly/Refutation138.lean | 23 + .../Generated/FinitePoly/Refutation14.lean | 23 + .../Generated/FinitePoly/Refutation144.lean | 23 + .../Generated/FinitePoly/Refutation146.lean | 23 + .../Generated/FinitePoly/Refutation150.lean | 23 + .../Generated/FinitePoly/Refutation152.lean | 23 + .../Generated/FinitePoly/Refutation154.lean | 23 + .../Generated/FinitePoly/Refutation172.lean | 23 + .../Generated/FinitePoly/Refutation174.lean | 23 + .../Generated/FinitePoly/Refutation176.lean | 23 + .../Generated/FinitePoly/Refutation178.lean | 23 + .../Generated/FinitePoly/Refutation18.lean | 23 + .../Generated/FinitePoly/Refutation184.lean | 23 + .../Generated/FinitePoly/Refutation190.lean | 23 + .../Generated/FinitePoly/Refutation194.lean | 23 + .../Generated/FinitePoly/Refutation196.lean | 23 + .../Generated/FinitePoly/Refutation198.lean | 23 + .../Generated/FinitePoly/Refutation20.lean | 23 + .../Generated/FinitePoly/Refutation200.lean | 23 + .../Generated/FinitePoly/Refutation206.lean | 23 + .../Generated/FinitePoly/Refutation208.lean | 23 + .../Generated/FinitePoly/Refutation212.lean | 23 + .../Generated/FinitePoly/Refutation214.lean | 23 + .../Generated/FinitePoly/Refutation216.lean | 23 + .../Generated/FinitePoly/Refutation218.lean | 23 + .../Generated/FinitePoly/Refutation220.lean | 23 + .../Generated/FinitePoly/Refutation226.lean | 23 + .../Generated/FinitePoly/Refutation232.lean | 23 + .../Generated/FinitePoly/Refutation234.lean | 23 + .../Generated/FinitePoly/Refutation236.lean | 23 + .../Generated/FinitePoly/Refutation238.lean | 23 + .../Generated/FinitePoly/Refutation24.lean | 23 + .../Generated/FinitePoly/Refutation246.lean | 23 + .../Generated/FinitePoly/Refutation250.lean | 23 + .../Generated/FinitePoly/Refutation26.lean | 23 + .../Generated/FinitePoly/Refutation262.lean | 23 + .../Generated/FinitePoly/Refutation264.lean | 23 + .../Generated/FinitePoly/Refutation268.lean | 23 + .../Generated/FinitePoly/Refutation270.lean | 23 + .../Generated/FinitePoly/Refutation272.lean | 23 + .../Generated/FinitePoly/Refutation280.lean | 23 + .../Generated/FinitePoly/Refutation284.lean | 23 + .../Generated/FinitePoly/Refutation286.lean | 23 + .../Generated/FinitePoly/Refutation290.lean | 23 + .../Generated/FinitePoly/Refutation302.lean | 23 + .../Generated/FinitePoly/Refutation312.lean | 23 + .../Generated/FinitePoly/Refutation314.lean | 23 + .../Generated/FinitePoly/Refutation316.lean | 23 + .../Generated/FinitePoly/Refutation318.lean | 23 + .../Generated/FinitePoly/Refutation32.lean | 23 + .../Generated/FinitePoly/Refutation320.lean | 23 + .../Generated/FinitePoly/Refutation326.lean | 23 + .../Generated/FinitePoly/Refutation328.lean | 23 + .../Generated/FinitePoly/Refutation330.lean | 23 + .../Generated/FinitePoly/Refutation34.lean | 23 + .../Generated/FinitePoly/Refutation340.lean | 23 + .../Generated/FinitePoly/Refutation342.lean | 23 + .../Generated/FinitePoly/Refutation344.lean | 23 + .../Generated/FinitePoly/Refutation346.lean | 23 + .../Generated/FinitePoly/Refutation352.lean | 23 + .../Generated/FinitePoly/Refutation356.lean | 23 + .../Generated/FinitePoly/Refutation364.lean | 23 + .../Generated/FinitePoly/Refutation366.lean | 23 + .../Generated/FinitePoly/Refutation370.lean | 23 + .../Generated/FinitePoly/Refutation374.lean | 23 + .../Generated/FinitePoly/Refutation380.lean | 23 + .../Generated/FinitePoly/Refutation386.lean | 23 + .../Generated/FinitePoly/Refutation388.lean | 23 + .../Generated/FinitePoly/Refutation390.lean | 23 + .../Generated/FinitePoly/Refutation394.lean | 23 + .../Generated/FinitePoly/Refutation40.lean | 23 + .../Generated/FinitePoly/Refutation400.lean | 23 + .../Generated/FinitePoly/Refutation402.lean | 23 + .../Generated/FinitePoly/Refutation404.lean | 23 + .../Generated/FinitePoly/Refutation406.lean | 23 + .../Generated/FinitePoly/Refutation408.lean | 23 + .../Generated/FinitePoly/Refutation410.lean | 23 + .../Generated/FinitePoly/Refutation418.lean | 23 + .../Generated/FinitePoly/Refutation420.lean | 23 + .../Generated/FinitePoly/Refutation422.lean | 23 + .../Generated/FinitePoly/Refutation424.lean | 23 + .../Generated/FinitePoly/Refutation426.lean | 23 + .../Generated/FinitePoly/Refutation432.lean | 23 + .../Generated/FinitePoly/Refutation444.lean | 23 + .../Generated/FinitePoly/Refutation454.lean | 23 + .../Generated/FinitePoly/Refutation46.lean | 23 + .../Generated/FinitePoly/Refutation470.lean | 23 + .../Generated/FinitePoly/Refutation472.lean | 23 + .../Generated/FinitePoly/Refutation474.lean | 23 + .../Generated/FinitePoly/Refutation476.lean | 23 + .../Generated/FinitePoly/Refutation482.lean | 23 + .../Generated/FinitePoly/Refutation488.lean | 23 + .../Generated/FinitePoly/Refutation492.lean | 23 + .../Generated/FinitePoly/Refutation50.lean | 23 + .../Generated/FinitePoly/Refutation502.lean | 23 + .../Generated/FinitePoly/Refutation532.lean | 23 + .../Generated/FinitePoly/Refutation550.lean | 23 + .../Generated/FinitePoly/Refutation56.lean | 23 + .../Generated/FinitePoly/Refutation568.lean | 23 + .../Generated/FinitePoly/Refutation6.lean | 23 + .../Generated/FinitePoly/Refutation60.lean | 23 + .../Generated/FinitePoly/Refutation620.lean | 23 + .../Generated/FinitePoly/Refutation622.lean | 23 + .../Generated/FinitePoly/Refutation636.lean | 23 + .../Generated/FinitePoly/Refutation656.lean | 23 + .../Generated/FinitePoly/Refutation66.lean | 23 + .../Generated/FinitePoly/Refutation664.lean | 23 + .../Generated/FinitePoly/Refutation672.lean | 23 + .../Generated/FinitePoly/Refutation674.lean | 23 + .../Generated/FinitePoly/Refutation676.lean | 23 + .../Generated/FinitePoly/Refutation68.lean | 23 + .../Generated/FinitePoly/Refutation682.lean | 23 + .../Generated/FinitePoly/Refutation690.lean | 23 + .../Generated/FinitePoly/Refutation72.lean | 23 + .../Generated/FinitePoly/Refutation74.lean | 23 + .../Generated/FinitePoly/Refutation78.lean | 23 + .../Generated/FinitePoly/Refutation8.lean | 23 + .../Generated/FinitePoly/Refutation82.lean | 23 + .../Generated/FinitePoly/Refutation84.lean | 23 + .../Generated/FinitePoly/Refutation88.lean | 23 + .../Generated/FinitePoly/Refutation90.lean | 23 + .../Generated/FinitePoly/Refutation92.lean | 23 + .../Generated/FinitePoly/Refutation94.lean | 23 + .../Generated/FinitePoly/Refutation96.lean | 23 + .../src/finite_poly_generate_lean.py | 170 + .../src/finite_poly_refutations.txt | 700 + .../FinitePoly/src/implications.json | 35279 ++++++++++++++++ 138 files changed, 39321 insertions(+) create mode 100644 equational_theories/Generated/FinitePoly.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation108.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation112.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation114.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation116.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation120.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation126.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation128.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation132.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation138.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation14.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation144.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation146.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation150.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation152.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation154.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation172.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation174.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation176.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation178.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation18.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation184.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation190.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation194.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation196.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation198.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation20.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation200.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation206.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation208.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation212.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation214.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation216.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation218.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation220.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation226.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation232.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation234.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation236.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation238.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation24.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation246.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation250.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation26.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation262.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation264.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation268.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation270.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation272.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation280.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation284.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation286.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation290.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation302.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation312.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation314.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation316.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation318.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation32.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation320.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation326.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation328.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation330.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation34.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation340.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation342.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation344.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation346.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation352.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation356.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation364.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation366.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation370.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation374.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation380.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation386.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation388.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation390.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation394.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation40.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation400.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation402.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation404.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation406.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation408.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation410.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation418.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation420.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation422.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation424.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation426.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation432.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation444.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation454.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation46.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation470.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation472.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation474.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation476.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation482.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation488.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation492.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation50.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation502.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation532.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation550.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation56.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation568.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation6.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation60.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation620.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation622.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation636.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation656.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation66.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation664.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation672.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation674.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation676.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation68.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation682.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation690.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation72.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation74.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation78.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation8.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation82.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation84.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation88.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation90.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation92.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation94.lean create mode 100644 equational_theories/Generated/FinitePoly/Refutation96.lean create mode 100644 equational_theories/Generated/FinitePoly/src/finite_poly_generate_lean.py create mode 100644 equational_theories/Generated/FinitePoly/src/finite_poly_refutations.txt create mode 100644 equational_theories/Generated/FinitePoly/src/implications.json diff --git a/.gitattributes b/.gitattributes index b273dfbe..82f8f4f9 100644 --- a/.gitattributes +++ b/.gitattributes @@ -2,3 +2,6 @@ equational_theories/Generated/TrivialBruteforce/theorems/Apply.lean linguist-gen equational_theories/Generated/TrivialBruteforce/theorems/RewriteGoal.lean linguist-generated equational_theories/Generated/TrivialBruteforce/theorems/RewriteHypothesis.lean linguist-generated equational_theories/Generated/TrivialBruteforce/theorems/RewriteHypothesisAndGoal.lean linguist-generated + +equational_theories/FinitePoly/Refutation*.lean linguist-generated +equational_theories/FinitePoly.lean linguist-generated diff --git a/equational_theories/Generated.lean b/equational_theories/Generated.lean index b59da261..135f9e68 100644 --- a/equational_theories/Generated.lean +++ b/equational_theories/Generated.lean @@ -2,3 +2,4 @@ import equational_theories.Generated.SimpleRewrites import equational_theories.Generated.Constant import equational_theories.Generated.Singleton import equational_theories.Generated.TrivialBruteforce +import equational_theories.Generated.FinitePoly diff --git a/equational_theories/Generated/FinitePoly.lean b/equational_theories/Generated/FinitePoly.lean new file mode 100644 index 00000000..d42c75cf --- /dev/null +++ b/equational_theories/Generated/FinitePoly.lean @@ -0,0 +1,132 @@ +import equational_theories.Generated.FinitePoly.Refutation6 +import equational_theories.Generated.FinitePoly.Refutation8 +import equational_theories.Generated.FinitePoly.Refutation14 +import equational_theories.Generated.FinitePoly.Refutation18 +import equational_theories.Generated.FinitePoly.Refutation20 +import equational_theories.Generated.FinitePoly.Refutation24 +import equational_theories.Generated.FinitePoly.Refutation26 +import equational_theories.Generated.FinitePoly.Refutation32 +import equational_theories.Generated.FinitePoly.Refutation34 +import equational_theories.Generated.FinitePoly.Refutation40 +import equational_theories.Generated.FinitePoly.Refutation46 +import equational_theories.Generated.FinitePoly.Refutation50 +import equational_theories.Generated.FinitePoly.Refutation56 +import equational_theories.Generated.FinitePoly.Refutation60 +import equational_theories.Generated.FinitePoly.Refutation66 +import equational_theories.Generated.FinitePoly.Refutation68 +import equational_theories.Generated.FinitePoly.Refutation72 +import equational_theories.Generated.FinitePoly.Refutation74 +import equational_theories.Generated.FinitePoly.Refutation78 +import equational_theories.Generated.FinitePoly.Refutation82 +import equational_theories.Generated.FinitePoly.Refutation84 +import equational_theories.Generated.FinitePoly.Refutation88 +import equational_theories.Generated.FinitePoly.Refutation90 +import equational_theories.Generated.FinitePoly.Refutation92 +import equational_theories.Generated.FinitePoly.Refutation94 +import equational_theories.Generated.FinitePoly.Refutation96 +import equational_theories.Generated.FinitePoly.Refutation108 +import equational_theories.Generated.FinitePoly.Refutation112 +import equational_theories.Generated.FinitePoly.Refutation114 +import equational_theories.Generated.FinitePoly.Refutation116 +import equational_theories.Generated.FinitePoly.Refutation120 +import equational_theories.Generated.FinitePoly.Refutation126 +import equational_theories.Generated.FinitePoly.Refutation128 +import equational_theories.Generated.FinitePoly.Refutation132 +import equational_theories.Generated.FinitePoly.Refutation138 +import equational_theories.Generated.FinitePoly.Refutation144 +import equational_theories.Generated.FinitePoly.Refutation146 +import equational_theories.Generated.FinitePoly.Refutation150 +import equational_theories.Generated.FinitePoly.Refutation152 +import equational_theories.Generated.FinitePoly.Refutation154 +import equational_theories.Generated.FinitePoly.Refutation172 +import equational_theories.Generated.FinitePoly.Refutation174 +import equational_theories.Generated.FinitePoly.Refutation176 +import equational_theories.Generated.FinitePoly.Refutation178 +import equational_theories.Generated.FinitePoly.Refutation184 +import equational_theories.Generated.FinitePoly.Refutation190 +import equational_theories.Generated.FinitePoly.Refutation194 +import equational_theories.Generated.FinitePoly.Refutation196 +import equational_theories.Generated.FinitePoly.Refutation198 +import equational_theories.Generated.FinitePoly.Refutation200 +import equational_theories.Generated.FinitePoly.Refutation206 +import equational_theories.Generated.FinitePoly.Refutation208 +import equational_theories.Generated.FinitePoly.Refutation212 +import equational_theories.Generated.FinitePoly.Refutation214 +import equational_theories.Generated.FinitePoly.Refutation216 +import equational_theories.Generated.FinitePoly.Refutation218 +import equational_theories.Generated.FinitePoly.Refutation220 +import equational_theories.Generated.FinitePoly.Refutation226 +import equational_theories.Generated.FinitePoly.Refutation232 +import equational_theories.Generated.FinitePoly.Refutation234 +import equational_theories.Generated.FinitePoly.Refutation236 +import equational_theories.Generated.FinitePoly.Refutation238 +import equational_theories.Generated.FinitePoly.Refutation246 +import equational_theories.Generated.FinitePoly.Refutation250 +import equational_theories.Generated.FinitePoly.Refutation262 +import equational_theories.Generated.FinitePoly.Refutation264 +import equational_theories.Generated.FinitePoly.Refutation268 +import equational_theories.Generated.FinitePoly.Refutation270 +import equational_theories.Generated.FinitePoly.Refutation272 +import equational_theories.Generated.FinitePoly.Refutation280 +import equational_theories.Generated.FinitePoly.Refutation284 +import equational_theories.Generated.FinitePoly.Refutation286 +import equational_theories.Generated.FinitePoly.Refutation290 +import equational_theories.Generated.FinitePoly.Refutation302 +import equational_theories.Generated.FinitePoly.Refutation312 +import equational_theories.Generated.FinitePoly.Refutation314 +import equational_theories.Generated.FinitePoly.Refutation316 +import equational_theories.Generated.FinitePoly.Refutation318 +import equational_theories.Generated.FinitePoly.Refutation320 +import equational_theories.Generated.FinitePoly.Refutation326 +import equational_theories.Generated.FinitePoly.Refutation328 +import equational_theories.Generated.FinitePoly.Refutation330 +import equational_theories.Generated.FinitePoly.Refutation340 +import equational_theories.Generated.FinitePoly.Refutation342 +import equational_theories.Generated.FinitePoly.Refutation344 +import equational_theories.Generated.FinitePoly.Refutation346 +import equational_theories.Generated.FinitePoly.Refutation352 +import equational_theories.Generated.FinitePoly.Refutation356 +import equational_theories.Generated.FinitePoly.Refutation364 +import equational_theories.Generated.FinitePoly.Refutation366 +import equational_theories.Generated.FinitePoly.Refutation370 +import equational_theories.Generated.FinitePoly.Refutation374 +import equational_theories.Generated.FinitePoly.Refutation380 +import equational_theories.Generated.FinitePoly.Refutation386 +import equational_theories.Generated.FinitePoly.Refutation388 +import equational_theories.Generated.FinitePoly.Refutation390 +import equational_theories.Generated.FinitePoly.Refutation394 +import equational_theories.Generated.FinitePoly.Refutation400 +import equational_theories.Generated.FinitePoly.Refutation402 +import equational_theories.Generated.FinitePoly.Refutation404 +import equational_theories.Generated.FinitePoly.Refutation406 +import equational_theories.Generated.FinitePoly.Refutation408 +import equational_theories.Generated.FinitePoly.Refutation410 +import equational_theories.Generated.FinitePoly.Refutation418 +import equational_theories.Generated.FinitePoly.Refutation420 +import equational_theories.Generated.FinitePoly.Refutation422 +import equational_theories.Generated.FinitePoly.Refutation424 +import equational_theories.Generated.FinitePoly.Refutation426 +import equational_theories.Generated.FinitePoly.Refutation432 +import equational_theories.Generated.FinitePoly.Refutation444 +import equational_theories.Generated.FinitePoly.Refutation454 +import equational_theories.Generated.FinitePoly.Refutation470 +import equational_theories.Generated.FinitePoly.Refutation472 +import equational_theories.Generated.FinitePoly.Refutation474 +import equational_theories.Generated.FinitePoly.Refutation476 +import equational_theories.Generated.FinitePoly.Refutation482 +import equational_theories.Generated.FinitePoly.Refutation488 +import equational_theories.Generated.FinitePoly.Refutation492 +import equational_theories.Generated.FinitePoly.Refutation502 +import equational_theories.Generated.FinitePoly.Refutation532 +import equational_theories.Generated.FinitePoly.Refutation550 +import equational_theories.Generated.FinitePoly.Refutation568 +import equational_theories.Generated.FinitePoly.Refutation620 +import equational_theories.Generated.FinitePoly.Refutation622 +import equational_theories.Generated.FinitePoly.Refutation636 +import equational_theories.Generated.FinitePoly.Refutation656 +import equational_theories.Generated.FinitePoly.Refutation664 +import equational_theories.Generated.FinitePoly.Refutation672 +import equational_theories.Generated.FinitePoly.Refutation674 +import equational_theories.Generated.FinitePoly.Refutation676 +import equational_theories.Generated.FinitePoly.Refutation682 +import equational_theories.Generated.FinitePoly.Refutation690 diff --git a/equational_theories/Generated/FinitePoly/Refutation108.lean b/equational_theories/Generated/FinitePoly/Refutation108.lean new file mode 100644 index 00000000..3b163a30 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation108.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 0 * x + 0 * y + 0 * x * y) % 2' (0, 7, 10, 13, 15, 22, 25, 28, 30, 39, 42, 410, 413, 416, 418, 426, 428, 435, 439, 443, 451, 454, 463, 465, 472, 476, 480, 488, 491, 499, 503, 507, 510, 512, 521, 527, 542, 545, 555, 561, 571, 574, 613, 616, 619, 621, 629, 631, 638, 642, 646, 654, 657, 666, 668, 675, 679, 683, 691, 694, 702, 706, 710, 713, 715, 724, 730, 745, 748, 758, 764, 774, 777, 816, 819, 822, 824, 832, 834, 841, 845, 849, 857, 860, 869, 871, 878, 882, 886, 894, 897, 905, 909, 913, 916, 918, 927, 933, 948, 951, 961, 967, 977, 980, 1019, 1022, 1025, 1027, 1035, 1037, 1044, 1048, 1052, 1060, 1063, 1072, 1074, 1081, 1085, 1089, 1097, 1100, 1108, 1112, 1116, 1119, 1121, 1130, 1136, 1151, 1154, 1164, 1170, 1180, 1183, 1222, 1225, 1228, 1230, 1238, 1240, 1247, 1251, 1255, 1263, 1266, 1275, 1277, 1284, 1288, 1292, 1300, 1303, 1311, 1315, 1319, 1322, 1324, 1333, 1339, 1354, 1357, 1367, 1373, 1383, 1386, 1425, 1428, 1431, 1433, 1441, 1443, 1450, 1454, 1458, 1466, 1469, 1478, 1480, 1487, 1491, 1495, 1503, 1506, 1514, 1518, 1522, 1525, 1527, 1536, 1542, 1557, 1560, 1570, 1576, 1586, 1589, 1628, 1631, 1634, 1636, 1644, 1646, 1653, 1657, 1661, 1669, 1672, 1681, 1683, 1690, 1694, 1698, 1706, 1709, 1717, 1721, 1725, 1728, 1730, 1739, 1745, 1760, 1763, 1773, 1779, 1789, 1792, 1831, 1834, 1837, 1839, 1847, 1849, 1856, 1860, 1864, 1872, 1875, 1884, 1886, 1893, 1897, 1901, 1909, 1912, 1920, 1924, 1928, 1931, 1933, 1942, 1948, 1963, 1966, 1976, 1982, 1992, 1995, 2034, 2037, 2040, 2042, 2050, 2052, 2059, 2063, 2067, 2075, 2078, 2087, 2089, 2096, 2100, 2104, 2112, 2115, 2123, 2127, 2131, 2134, 2136, 2145, 2151, 2166, 2169, 2179, 2185, 2195, 2198, 2237, 2240, 2243, 2245, 2253, 2255, 2262, 2266, 2270, 2278, 2281, 2290, 2292, 2299, 2303, 2307, 2315, 2318, 2326, 2330, 2334, 2337, 2339, 2348, 2354, 2369, 2372, 2382, 2388, 2398, 2401, 2440, 2443, 2446, 2448, 2456, 2458, 2465, 2469, 2473, 2481, 2484, 2493, 2495, 2502, 2506, 2510, 2518, 2521, 2529, 2533, 2537, 2540, 2542, 2551, 2557, 2572, 2575, 2585, 2591, 2601, 2604, 2643, 2646, 2649, 2651, 2659, 2661, 2668, 2672, 2676, 2684, 2687, 2696, 2698, 2705, 2709, 2713, 2721, 2724, 2732, 2736, 2740, 2743, 2745, 2754, 2760, 2775, 2778, 2788, 2794, 2804, 2807, 2846, 2849, 2852, 2854, 2862, 2864, 2871, 2875, 2879, 2887, 2890, 2899, 2901, 2908, 2912, 2916, 2924, 2927, 2935, 2939, 2943, 2946, 2948, 2957, 2963, 2978, 2981, 2991, 2997, 3007, 3010, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3102, 3104, 3111, 3115, 3119, 3127, 3130, 3138, 3142, 3146, 3149, 3151, 3160, 3166, 3181, 3184, 3194, 3200, 3210, 3213, 3252, 3255, 3258, 3260, 3268, 3270, 3277, 3281, 3285, 3293, 3296, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3341, 3345, 3349, 3352, 3354, 3363, 3369, 3384, 3387, 3397, 3403, 3413, 3416, 3455, 3458, 3461, 3463, 3471, 3473, 3480, 3484, 3488, 3496, 3499, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3544, 3548, 3552, 3555, 3557, 3566, 3572, 3587, 3590, 3600, 3606, 3616, 3619, 3658, 3661, 3664, 3666, 3674, 3676, 3683, 3687, 3691, 3699, 3702, 3711, 3713, 3720, 3724, 3728, 3736, 3739, 3747, 3751, 3755, 3758, 3760, 3769, 3775, 3790, 3793, 3803, 3809, 3819, 3822, 3861, 3864, 3867, 3869, 3877, 3879, 3886, 3890, 3894, 3902, 3905, 3914, 3916, 3923, 3927, 3931, 3939, 3942, 3950, 3954, 3958, 3961, 3963, 3972, 3978, 3993, 3996, 4006, 4012, 4022, 4025, 4064, 4067, 4070, 4072, 4080, 4082, 4089, 4093, 4097, 4105, 4108, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4153, 4157, 4161, 4164, 4166, 4175, 4181, 4196, 4199, 4209, 4215, 4225, 4228, 4269, 4272, 4274, 4282, 4289, 4296, 4304, 4306, 4319, 4324, 4331, 4340, 4357, 4361, 4363, 4368, 4379, 4382, 4385, 4387, 4395, 4397, 4404, 4408, 4412, 4420, 4423, 4432, 4434, 4441, 4445, 4449, 4457, 4460, 4468, 4472, 4476, 4479, 4481, 4490, 4496, 4511, 4514, 4524, 4530, 4540, 4543, 4584, 4587, 4589, 4597, 4604, 4611, 4619, 4621, 4634, 4639, 4646, 4655, 4672, 4676, 4678, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² % 2» : Magma (Fin 2) where + op := memoFinOp fun x y => x*x + y*y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² % 2» : + ∃ (G : Type) (_ : Magma G), Facts G [11, 26, 29, 43, 452, 455, 481, 492, 508, 522, 543, 546, 556, 572, 647, 655, 658, 684, 692, 695, 711, 725, 749, 759, 775, 861, 887, 895, 898, 914, 928, 949, 952, 962, 978, 1053, 1061, 1090, 1098, 1101, 1117, 1131, 1152, 1165, 1181, 1256, 1264, 1267, 1293, 1301, 1304, 1320, 1334, 1355, 1358, 1368, 1384, 1459, 1467, 1470, 1496, 1504, 1507, 1523, 1537, 1561, 1571, 1587, 1670, 1673, 1699, 1710, 1726, 1740, 1761, 1764, 1774, 1790, 1876, 1902, 1910, 1913, 1929, 1943, 1964, 1967, 1993, 2068, 2076, 2079, 2105, 2113, 2116, 2132, 2146, 2170, 2180, 2196, 2271, 2279, 2282, 2308, 2316, 2319, 2335, 2349, 2370, 2373, 2383, 2399, 2474, 2482, 2511, 2519, 2522, 2538, 2552, 2573, 2586, 2602, 2677, 2685, 2688, 2714, 2722, 2725, 2741, 2755, 2776, 2779, 2789, 2805, 2880, 2888, 2891, 2917, 2925, 2928, 2944, 2958, 2982, 2992, 3008, 3091, 3120, 3128, 3131, 3147, 3161, 3182, 3185, 3211, 3286, 3294, 3297, 3350, 3364, 3370, 3385, 3398, 3404, 3417, 3489, 3497, 3500, 3553, 3567, 3573, 3601, 3607, 3620, 3692, 3703, 3737, 3756, 3770, 3776, 3791, 3804, 3810, 3823, 3895, 3903, 3906, 3932, 3940, 3959, 3973, 3979, 4007, 4013, 4026, 4098, 4106, 4109, 4143, 4162, 4176, 4182, 4197, 4210, 4216, 4229, 4297, 4305, 4325, 4413, 4421, 4450, 4458, 4461, 4477, 4491, 4497, 4612, 4620, 4640] [2, 3, 9, 10, 13, 24, 25, 28, 38, 39, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 416, 420, 426, 430, 437, 439, 463, 467, 474, 476, 501, 503, 510, 615, 616, 619, 623, 629, 633, 640, 642, 666, 670, 677, 679, 704, 706, 713, 818, 819, 822, 826, 832, 836, 843, 845, 869, 873, 880, 882, 907, 909, 916, 1021, 1022, 1025, 1029, 1035, 1039, 1046, 1048, 1072, 1076, 1083, 1085, 1110, 1112, 1119, 1224, 1225, 1228, 1232, 1238, 1242, 1249, 1251, 1275, 1279, 1286, 1288, 1313, 1315, 1322, 1427, 1428, 1431, 1435, 1441, 1445, 1452, 1454, 1478, 1482, 1489, 1491, 1516, 1518, 1525, 1630, 1631, 1634, 1638, 1644, 1648, 1655, 1657, 1681, 1685, 1692, 1694, 1719, 1721, 1728, 1833, 1834, 1837, 1841, 1847, 1851, 1858, 1860, 1884, 1888, 1895, 1897, 1922, 1924, 1931, 2036, 2037, 2040, 2044, 2050, 2054, 2061, 2063, 2087, 2091, 2098, 2100, 2125, 2127, 2134, 2239, 2240, 2243, 2247, 2253, 2257, 2264, 2266, 2290, 2294, 2301, 2303, 2328, 2330, 2337, 2442, 2443, 2446, 2450, 2456, 2460, 2467, 2469, 2493, 2497, 2504, 2506, 2531, 2533, 2540, 2645, 2646, 2649, 2653, 2659, 2663, 2670, 2672, 2696, 2700, 2707, 2709, 2734, 2736, 2743, 2848, 2849, 2852, 2856, 2862, 2866, 2873, 2875, 2899, 2903, 2910, 2912, 2937, 2939, 2946, 3051, 3052, 3055, 3059, 3065, 3069, 3076, 3078, 3102, 3106, 3113, 3115, 3140, 3142, 3149, 3254, 3255, 3258, 3262, 3268, 3272, 3279, 3281, 3309, 3316, 3318, 3337, 3343, 3345, 3352, 3457, 3458, 3461, 3465, 3471, 3475, 3482, 3484, 3512, 3519, 3521, 3543, 3546, 3548, 3555, 3660, 3661, 3664, 3668, 3674, 3678, 3685, 3687, 3715, 3722, 3724, 3749, 3751, 3758, 3863, 3864, 3867, 3871, 3877, 3881, 3888, 3890, 3918, 3925, 3927, 3952, 3954, 3961, 4055, 4066, 4067, 4070, 4074, 4080, 4084, 4091, 4093, 4121, 4128, 4130, 4155, 4157, 4164, 4258, 4268, 4269, 4272, 4276, 4284, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4385, 4399, 4406, 4408, 4436, 4443, 4445, 4470, 4472, 4479, 4539, 4547, 4571, 4583, 4584, 4587, 4591, 4599, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 2, «FinitePoly x² + y² % 2», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation112.lean b/equational_theories/Generated/FinitePoly/Refutation112.lean new file mode 100644 index 00000000..3e73ba52 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation112.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 4' (0, 22, 23, 24, 25, 26, 37, 41, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 1425, 1426, 1427, 1428, 1429, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 2237, 2238, 2239, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 2490, 2491, 3049, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 3100, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x + 2 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x + 2 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [27, 158, 162, 163, 164, 207, 210, 213, 216, 1477, 1680, 1883, 2289, 2492, 3064, 3074, 3084, 3088, 3092, 3096, 3097, 3098, 3099, 3100, 4153, 4359, 4360, 4674, 4675] [2, 3, 8, 28, 29, 31, 39, 40, 43, 47, 99, 166, 167, 169, 170, 176, 177, 179, 218, 219, 221, 222, 228, 229, 231, 255, 312, 313, 315, 316, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2644, 2847, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3862, 4055, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4587, 4588, 4590, 4591, 4605, 4606, 4608, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 2 * y² + x + 2 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation114.lean b/equational_theories/Generated/FinitePoly/Refutation114.lean new file mode 100644 index 00000000..9ab7a29f --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation114.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 0 * y**2 + 1 * x + 1 * y + 3 * x * y) % 4' (0, 22, 30, 39, 1628, 1636, 1717, 1730, 1745, 2237, 2245, 2292, 2440, 2465, 2495, 2542, 2604, 2643, 2651, 2661, 2705, 2732, 2745, 2760, 2794, 3049, 3057, 3138, 3151, 3166, 3455, 3463, 3471, 3484, 3499, 3508, 3521, 3536, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3711, 3758, 3819, 4064, 4067, 4089, 4093, 4097, 4117, 4130, 4164, 4225, 4269, 4340, 4589, 4621) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + x + y + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + x + y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + x + y + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [31, 1637, 1718, 1731, 2246, 2293, 2466, 2496, 2543, 2652, 2662, 2706, 2733, 2746, 3058, 3139, 3152, 3500, 3509, 3692, 4098, 4165, 4341, 4590] [2, 3, 8, 24, 25, 26, 28, 29, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2239, 2240, 2241, 2243, 2244, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2467, 2469, 2470, 2493, 2494, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2645, 2646, 2647, 2649, 2650, 2653, 2659, 2660, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2707, 2709, 2710, 2734, 2736, 2737, 2743, 2744, 2847, 3051, 3052, 3053, 3055, 3056, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3140, 3142, 3143, 3149, 3150, 3253, 3337, 3457, 3458, 3459, 3461, 3462, 3465, 3471, 3474, 3475, 3481, 3482, 3484, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3761, 3862, 4055, 4066, 4067, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4167, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + x + y + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation116.lean b/equational_theories/Generated/FinitePoly/Refutation116.lean new file mode 100644 index 00000000..6e598a35 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation116.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 1 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 7, 410, 1019, 1034, 1037, 1222, 1250, 1831, 3252, 3317, 3318, 3861, 3914, 4064, 4092, 4130, 4590) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + y² + y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + y*y + y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + y² + y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [8, 1035, 1038, 1251, 3318, 3862, 4093, 4131, 4591] [2, 3, 9, 10, 11, 13, 14, 16, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 614, 817, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1036, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + y² + y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation120.lean b/equational_theories/Generated/FinitePoly/Refutation120.lean new file mode 100644 index 00000000..7a405035 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation120.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 10, 98, 107, 254, 263, 410, 413, 435, 439, 443, 816, 819, 822, 834, 841, 845, 849, 857, 1019, 1022, 1027, 1035, 1044, 1048, 1052, 1063, 1831, 1834, 1856, 1860, 1864, 3252, 3255, 3314, 3318, 3322, 3658, 3661, 3720, 3724, 3728, 3861, 3869, 3914, 3927, 3942, 4269, 4340, 4597, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * y*y + x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [11, 108, 264, 414, 436, 440, 820, 842, 1028, 1036, 1053, 1835, 1857, 1861, 3256, 3315, 3659, 3870, 3928, 4270] [2, 3, 9, 10, 13, 14, 16, 23, 38, 39, 40, 43, 47, 100, 101, 102, 104, 105, 107, 114, 115, 117, 118, 124, 125, 127, 151, 203, 256, 257, 258, 260, 261, 263, 270, 271, 273, 274, 280, 281, 283, 307, 331, 359, 407, 412, 413, 416, 417, 419, 420, 426, 427, 429, 430, 437, 439, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 614, 818, 819, 822, 825, 826, 832, 833, 836, 843, 845, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1025, 1026, 1029, 1035, 1038, 1039, 1046, 1048, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1223, 1426, 1629, 1833, 1834, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3660, 3661, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3722, 3724, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4065, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * y² + x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation126.lean b/equational_theories/Generated/FinitePoly/Refutation126.lean new file mode 100644 index 00000000..ef0d19b5 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation126.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 15, 410, 418, 435, 465, 499, 512, 527, 574, 816, 1019, 1044, 1074, 1121, 1183, 1222, 1324, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1920, 1933, 1948, 2034, 2136, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3658, 3861, 3886, 3914, 3961, 4022, 4064, 4117, 4274, 4306) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 419, 436, 466, 500, 513, 817, 1045, 1075, 1122, 1325, 1629, 1840, 1921, 1934, 2137, 3261, 3659, 3887, 3962, 4118, 4275] [2, 3, 9, 10, 11, 13, 14, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 429, 430, 437, 439, 440, 463, 464, 467, 473, 474, 476, 477, 501, 503, 504, 510, 511, 614, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1426, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1922, 1924, 1925, 1931, 1932, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3271, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3355, 3456, 3543, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation128.lean b/equational_theories/Generated/FinitePoly/Refutation128.lean new file mode 100644 index 00000000..7b7ab448 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation128.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 1 * x + 0 * y + 1 * x * y) % 4' (0, 98, 104, 106, 410, 1222, 1223, 1224, 1227, 1238, 1240, 1241, 1242, 1244, 1247, 1248, 1249, 1250, 1253, 1258, 1261, 1831, 1860, 3658, 3661, 3723, 3861, 3869, 3924, 4597, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x + x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x + x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [105, 107, 411, 1243, 1245, 1250, 1254, 1259, 1262, 1861, 3662, 3724, 3870, 3925] [2, 3, 8, 23, 38, 39, 40, 43, 47, 100, 101, 102, 104, 108, 114, 115, 117, 118, 124, 125, 127, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 614, 817, 1020, 1226, 1229, 1231, 1232, 1238, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3660, 3661, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 2 * y² + x + x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation132.lean b/equational_theories/Generated/FinitePoly/Refutation132.lean new file mode 100644 index 00000000..5ca8eeea --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation132.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 0 * x + 2 * y + 1 * x * y) % 3' (0, 254, 306, 1628, 1730, 2846, 3252, 3305, 3455, 3658, 4319, 4361) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [255, 307, 1731, 2847, 3306, 3456, 3659, 4362] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2238, 2441, 2644, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation138.lean b/equational_theories/Generated/FinitePoly/Refutation138.lean new file mode 100644 index 00000000..eebed861 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation138.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 1 * x + 0 * y + 1 * x * y) % 3' (0, 98, 103, 1019, 1037, 1222, 1227, 1237, 1247, 1257, 3252, 3315, 4586, 4665) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [104, 1038, 1223, 3316, 4666] [2, 3, 8, 23, 38, 39, 40, 43, 47, 100, 101, 102, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1229, 1231, 1232, 1239, 1241, 1242, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y² + x + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation14.lean b/equational_theories/Generated/FinitePoly/Refutation14.lean new file mode 100644 index 00000000..aa9443f4 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation14.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 2 * y + 0 * x * y) % 4' (0, 22, 25, 150, 151, 158, 159, 160, 202, 204, 208, 211, 214, 306, 307, 324, 325, 326, 1425, 1426, 1427, 1428, 1429, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1628, 1629, 1630, 1631, 1632, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1831, 1832, 1836, 1837, 1838, 1849, 1850, 1851, 1859, 1860, 1861, 1870, 1871, 1872, 1873, 2237, 2239, 2242, 2245, 2248, 2253, 2256, 2259, 2263, 2266, 2269, 2273, 2277, 2281, 2285, 2440, 2442, 2445, 2448, 2451, 2456, 2459, 2462, 2466, 2469, 2472, 2476, 2480, 2484, 2488, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4267, 4281, 4313, 4314, 4338, 4356, 4584, 4597, 4655, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x + 2 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x + 2 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 26, 161, 215, 327, 1453, 1456, 1457, 1458, 1459, 1663, 1874, 2254, 2257, 2264, 2267, 2489, 3053, 3058, 3066, 3075, 3091, 3315, 3318, 3460, 3520, 3523, 3524, 3525, 4073, 4143, 4315, 4339, 4585, 4673] [2, 3, 8, 24, 25, 28, 29, 31, 38, 39, 40, 43, 47, 99, 153, 154, 156, 157, 166, 167, 169, 170, 176, 177, 179, 204, 206, 208, 211, 218, 219, 221, 222, 228, 229, 231, 255, 309, 310, 312, 313, 315, 316, 323, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1834, 1835, 1840, 1841, 1847, 1848, 1857, 1858, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2239, 2241, 2244, 2247, 2253, 2256, 2263, 2266, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2444, 2447, 2450, 2456, 2459, 2466, 2469, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2644, 2847, 3051, 3052, 3055, 3059, 3065, 3069, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3862, 4055, 4066, 4067, 4070, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x + 2 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation144.lean b/equational_theories/Generated/FinitePoly/Refutation144.lean new file mode 100644 index 00000000..e14e6f45 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation144.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 1 * x + 2 * y + 1 * x * y) % 3' (0, 39, 3252, 3255, 3277, 3281, 3285, 3658, 3661, 3663, 3664, 3667, 3671, 3673, 3676, 3677, 3681, 3683, 3687, 3691, 3693, 3698, 3699, 3703, 3708, 3711, 3748, 3758, 3819, 4064, 4067, 4089, 4093, 4097, 4269, 4320, 4340, 4589, 4621, 4657) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + x + 2 * y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + x + 2 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + x + 2 * y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3286, 3709, 3749, 3820, 4098, 4321, 4341, 4622, 4658] [2, 3, 8, 23, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3660, 3661, 3667, 3675, 3685, 3687, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3751, 3752, 3758, 3761, 3769, 3786, 3862, 4055, 4066, 4067, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + x + 2 * y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation146.lean b/equational_theories/Generated/FinitePoly/Refutation146.lean new file mode 100644 index 00000000..13dfc118 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation146.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 2 * x + 1 * y + 1 * x * y) % 3' (0, 39, 3252, 3255, 3277, 3281, 3285, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 3720, 3723, 3724, 3728, 4064, 4067, 4089, 4093, 4097, 4269, 4292, 4340, 4589, 4621, 4635) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 2 * x + y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + 2 * x + y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 2 * x + y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3286, 3693, 3724, 3729, 4098, 4293, 4341, 4622, 4636] [2, 3, 8, 23, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3664, 3667, 3668, 3674, 3675, 3678, 3712, 3714, 3715, 3722, 3726, 3727, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4066, 4067, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + 2 * x + y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation150.lean b/equational_theories/Generated/FinitePoly/Refutation150.lean new file mode 100644 index 00000000..9b11d6e2 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation150.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 3 * y + 3 * x * y) % 4' (0, 202, 210, 220, 1628, 1730, 2237, 2242, 2245, 2252, 2255, 2265, 2276, 2280, 2289, 2292, 2302, 2313, 2317, 2329, 2367, 2371, 3049, 3455, 3463, 3518, 3658, 3683, 3748, 4319, 4361) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + 3 * y + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x + 3 * y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + 3 * y + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [211, 221, 2277, 2281, 2314, 2318, 2368, 2372, 3050, 3464, 3519, 3684, 3749, 4362] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 204, 205, 206, 208, 209, 212, 218, 219, 222, 228, 229, 231, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2239, 2240, 2241, 2244, 2247, 2254, 2257, 2263, 2264, 2267, 2291, 2294, 2300, 2301, 2304, 2327, 2328, 2331, 2337, 2338, 2340, 2441, 2644, 2847, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3253, 3337, 3457, 3458, 3459, 3461, 3462, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x + 3 * y + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation152.lean b/equational_theories/Generated/FinitePoly/Refutation152.lean new file mode 100644 index 00000000..3fc225c9 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation152.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 10, 15, 39, 254, 263, 270, 272, 279, 410, 413, 418, 426, 435, 439, 443, 454, 465, 473, 499, 503, 507, 512, 527, 542, 574, 816, 819, 822, 834, 841, 845, 849, 857, 869, 881, 905, 909, 913, 916, 927, 951, 977, 1019, 1022, 1027, 1035, 1044, 1048, 1052, 1063, 1074, 1082, 1108, 1112, 1116, 1121, 1136, 1151, 1183, 1628, 1634, 1636, 1644, 1646, 1657, 1669, 1672, 1684, 1690, 1717, 1728, 1730, 1739, 1745, 1773, 1779, 1831, 1834, 1839, 1847, 1856, 1860, 1864, 1875, 1886, 1894, 1920, 1924, 1928, 1933, 1948, 1963, 1995, 2440, 2443, 2446, 2458, 2465, 2469, 2473, 2481, 2493, 2505, 2529, 2533, 2537, 2540, 2551, 2575, 2601, 3252, 3255, 3260, 3268, 3277, 3281, 3285, 3296, 3305, 3314, 3318, 3322, 3333, 3344, 3352, 3397, 3413, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3713, 3720, 3724, 3728, 3736, 3748, 3760, 3809, 3822, 3861, 3864, 3869, 3877, 3886, 3890, 3894, 3905, 3914, 3923, 3927, 3931, 3942, 3953, 3961, 4006, 4022, 4269, 4274, 4289, 4296, 4306, 4320, 4340, 4368, 4587, 4589, 4597, 4619, 4621, 4646, 4657, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [11, 16, 264, 271, 273, 280, 436, 455, 474, 508, 513, 543, 882, 914, 928, 952, 978, 1053, 1083, 1117, 1137, 1152, 1670, 1673, 1685, 1740, 1746, 1774, 1876, 1895, 1929, 1964, 1996, 2474, 2482, 2506, 2538, 2552, 2576, 2602, 3286, 3297, 3345, 3398, 3692, 3737, 3749, 3810, 3823, 3895, 3906, 3932, 3954, 4007, 4297, 4321, 4369, 4620, 4622, 4647, 4658] [2, 3, 9, 10, 13, 14, 23, 38, 39, 43, 47, 99, 151, 203, 256, 257, 258, 260, 261, 263, 270, 274, 281, 283, 307, 331, 359, 407, 412, 413, 416, 417, 420, 426, 429, 430, 437, 439, 463, 464, 467, 473, 476, 477, 501, 503, 510, 511, 614, 818, 819, 822, 825, 826, 832, 833, 836, 843, 845, 869, 872, 873, 879, 880, 883, 907, 909, 916, 919, 1021, 1022, 1025, 1026, 1029, 1035, 1038, 1039, 1046, 1048, 1072, 1073, 1076, 1082, 1085, 1086, 1110, 1112, 1119, 1120, 1223, 1426, 1630, 1631, 1632, 1634, 1638, 1644, 1648, 1654, 1655, 1657, 1681, 1682, 1684, 1692, 1694, 1695, 1719, 1721, 1722, 1728, 1833, 1834, 1837, 1838, 1841, 1847, 1850, 1851, 1858, 1860, 1884, 1885, 1888, 1894, 1897, 1898, 1922, 1924, 1931, 1932, 2035, 2238, 2442, 2443, 2446, 2449, 2450, 2456, 2457, 2460, 2467, 2469, 2493, 2496, 2497, 2503, 2504, 2507, 2531, 2533, 2540, 2543, 2644, 2847, 3050, 3254, 3255, 3258, 3259, 3262, 3268, 3271, 3272, 3279, 3281, 3308, 3309, 3316, 3318, 3337, 3342, 3343, 3346, 3352, 3355, 3456, 3543, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3712, 3715, 3722, 3724, 3748, 3751, 3752, 3758, 3759, 3863, 3864, 3867, 3868, 3871, 3877, 3880, 3881, 3888, 3890, 3917, 3918, 3925, 3927, 3951, 3952, 3955, 3961, 3964, 4055, 4065, 4258, 4268, 4269, 4272, 4273, 4276, 4283, 4284, 4291, 4293, 4314, 4320, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4683, 4688] := + ⟨Fin 3, «FinitePoly x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation154.lean b/equational_theories/Generated/FinitePoly/Refutation154.lean new file mode 100644 index 00000000..9f26367b --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation154.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 0 * x + 0 * y + 2 * x * y) % 4' (0, 306, 307, 324, 325, 326, 358, 360, 374, 377, 380, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3658, 3659, 3663, 3664, 3665, 3713, 3714, 3715, 3723, 3724, 3725, 3734, 3735, 3736, 3737, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4066, 4069, 4072, 4075, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4267, 4281, 4313, 4314, 4338, 4356, 4379, 4381, 4394, 4397, 4400, 4432, 4435, 4438, 4469, 4472, 4475, 4506, 4510, 4514, 4518, 4583, 4598, 4601, 4630, 4654, 4674) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + 2 * y*y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [327, 381, 3315, 3318, 3460, 3520, 3523, 3524, 3525, 3526, 3738, 3915, 3918, 3925, 3928, 4076, 4124, 4134, 4138, 4142, 4146, 4519, 4602] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 309, 310, 312, 313, 315, 316, 323, 331, 332, 333, 335, 336, 360, 362, 364, 365, 367, 368, 374, 377, 384, 385, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3661, 3662, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3721, 3722, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3865, 3868, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4068, 4071, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4127, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4381, 4383, 4385, 4386, 4388, 4396, 4399, 4405, 4406, 4408, 4435, 4442, 4443, 4445, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4585, 4587, 4588, 4590, 4591, 4598, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + 2 * y² + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation172.lean b/equational_theories/Generated/FinitePoly/Refutation172.lean new file mode 100644 index 00000000..03855191 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation172.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 7, 15, 22, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 638, 675, 702, 816, 834, 871, 905, 1019, 1044, 1074, 1081, 1108, 1121, 1183, 1222, 1311, 1324, 1425, 1433, 1480, 1487, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1849, 1886, 1920, 1933, 1948, 2034, 2089, 2136, 2237, 2262, 2299, 2326, 2440, 2458, 2529, 2643, 2698, 2705, 2846, 2935, 3049, 3067, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3480, 3521, 3548, 3658, 3676, 3724, 3758, 3861, 3886, 3914, 3927, 3954, 3961, 4022, 4064, 4117, 4130, 4274, 4306, 4319, 4361, 4379, 4408, 4441, 4472) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 23, 419, 436, 466, 500, 562, 639, 676, 703, 835, 872, 906, 1045, 1075, 1082, 1109, 1122, 1312, 1325, 1434, 1481, 1488, 1840, 1850, 1887, 1921, 1934, 2090, 2137, 2263, 2300, 2327, 2459, 2530, 2699, 2706, 2936, 3068, 3261, 3388, 3481, 3549, 3677, 3725, 3759, 3887, 3928, 3955, 3962, 4362, 4409, 4442, 4473] [2, 3, 9, 10, 11, 13, 14, 24, 25, 26, 28, 31, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 430, 437, 439, 440, 463, 464, 467, 474, 476, 477, 501, 503, 504, 510, 511, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 640, 642, 643, 666, 667, 669, 670, 677, 679, 680, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 836, 842, 843, 845, 846, 869, 870, 873, 879, 880, 882, 883, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1083, 1085, 1086, 1110, 1112, 1113, 1119, 1120, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1313, 1315, 1316, 1322, 1323, 1427, 1428, 1429, 1431, 1432, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1482, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1847, 1848, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1888, 1894, 1895, 1897, 1898, 1922, 1924, 1925, 1931, 1932, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2301, 2303, 2304, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2700, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3352, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3748, 3749, 3751, 3752, 3758, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3961, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4443, 4445, 4470, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation174.lean b/equational_theories/Generated/FinitePoly/Refutation174.lean new file mode 100644 index 00000000..5b55677f --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation174.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 2 * y**2 + 1 * x + 3 * y + 1 * x * y) % 4' (0, 22, 1628, 1730, 2237, 2440, 2643, 2705, 2745, 3049, 3455, 3508, 3521, 4064, 4117, 4130, 4164) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 2 * y² + x + 3 * y + x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + 2 * y*y + x + 3 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 2 * y² + x + 3 * y + x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [23, 1731, 2238, 2706, 2746, 3509, 4165] [2, 3, 8, 24, 25, 26, 28, 29, 31, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2847, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3253, 3337, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3862, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + 2 * y² + x + 3 * y + x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation176.lean b/equational_theories/Generated/FinitePoly/Refutation176.lean new file mode 100644 index 00000000..bee6d27c --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation176.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 0 * x + 1 * y + 2 * x * y) % 3' (0, 202, 204, 2237, 2239, 2242, 2245, 2248, 2440, 2458, 4064, 4127, 4267, 4281) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + y + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + y + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [205, 2238, 2459, 4128, 4282] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 204, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2239, 2241, 2244, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + y + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation178.lean b/equational_theories/Generated/FinitePoly/Refutation178.lean new file mode 100644 index 00000000..fe6957ae --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation178.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 3 * y**2 + 0 * x + 2 * y + 3 * x * y) % 4' (0, 3252, 3257, 3261, 3305, 4275) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 3 * y² + 2 * y + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 3 * y*y + 2 * y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 3 * y² + 2 * y + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [3258, 3262, 3306, 4276] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3259, 3261, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 3 * y² + 2 * y + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation18.lean b/equational_theories/Generated/FinitePoly/Refutation18.lean new file mode 100644 index 00000000..bc93a237 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation18.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 1 * y**2 + 2 * x + 0 * y + 3 * x * y) % 4' (0, 39, 306, 309, 311, 315, 319, 322, 3252, 3255, 3257, 3261, 3265, 3267, 3271, 3275, 3277, 3281, 3285, 3287, 3292, 3297, 3302, 3305, 3658, 3661, 3663, 3664, 3667, 3671, 3673, 3676, 3677, 3681, 3683, 3687, 3691, 3693, 3698, 3699, 3703, 3708, 4269, 4271, 4275, 4279, 4340, 4342, 4345, 4350, 4354, 4589, 4621) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + y² + 2 * x + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + y*y + 2 * x + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + y² + 2 * x + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 320, 323, 3303, 3662, 3668, 3678, 3700, 4346, 4622] [2, 3, 8, 23, 38, 39, 43, 47, 99, 151, 203, 255, 308, 309, 313, 315, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3259, 3261, 3269, 3271, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3660, 3661, 3667, 3675, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4273, 4275, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + y² + 2 * x + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation184.lean b/equational_theories/Generated/FinitePoly/Refutation184.lean new file mode 100644 index 00000000..1fb14261 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation184.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 3 * x + 1 * y + 0 * x * y) % 4' (0, 7, 13, 15, 22, 25, 28, 42, 410, 416, 418, 435, 463, 465, 476, 488, 491, 499, 510, 512, 521, 527, 571, 574, 613, 616, 619, 629, 668, 675, 679, 683, 691, 702, 706, 710, 713, 724, 745, 758, 1019, 1035, 1037, 1044, 1072, 1074, 1081, 1112, 1119, 1121, 1151, 1154, 1164, 1170, 1180, 1183, 1222, 1225, 1230, 1240, 1275, 1284, 1288, 1292, 1303, 1311, 1315, 1319, 1324, 1339, 1357, 1373, 1425, 1431, 1433, 1441, 1443, 1454, 1466, 1469, 1478, 1480, 1491, 1503, 1506, 1518, 1557, 1560, 1628, 1631, 1634, 1646, 1653, 1657, 1661, 1669, 1683, 1690, 1694, 1698, 1706, 1730, 1779, 1792, 1831, 1837, 1839, 1847, 1849, 1860, 1872, 1875, 1893, 1920, 1931, 1933, 1942, 1948, 1976, 1982, 2034, 2050, 2052, 2059, 2087, 2089, 2096, 2127, 2134, 2136, 2166, 2169, 2179, 2185, 2195, 2198, 2237, 2240, 2243, 2255, 2262, 2266, 2270, 2278, 2290, 2326, 2330, 2334, 2337, 2348, 2372, 2398, 2440, 2446, 2448, 2456, 2458, 2469, 2481, 2484, 2493, 2495, 2506, 2518, 2521, 2533, 2572, 2575, 2846, 2849, 2852, 2862, 2901, 2908, 2912, 2916, 2924, 2935, 2939, 2943, 2946, 2957, 2978, 2991, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3102, 3111, 3115, 3119, 3130, 3149, 3194, 3210, 3252, 3258, 3260, 3277, 3305, 3307, 3318, 3330, 3333, 3341, 3352, 3354, 3363, 3369, 3413, 3416, 3455, 3458, 3461, 3471, 3510, 3517, 3521, 3525, 3533, 3544, 3548, 3552, 3555, 3566, 3587, 3600, 3861, 3877, 3879, 3886, 3914, 3916, 3923, 3954, 3961, 3963, 3993, 3996, 4006, 4012, 4022, 4025, 4064, 4067, 4072, 4082, 4117, 4126, 4130, 4134, 4145, 4153, 4157, 4161, 4166, 4181, 4199, 4215, 4272, 4274, 4282, 4304, 4306, 4331, 4357, 4379, 4382, 4385, 4397, 4404, 4408, 4412, 4420, 4434, 4441, 4445, 4449, 4457, 4481, 4530, 4543, 4584, 4587, 4634, 4639, 4646, 4655, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + 3 * x + y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * y*y + 3 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + 3 * x + y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 26, 29, 43, 466, 492, 513, 522, 572, 684, 692, 711, 725, 759, 1152, 1165, 1171, 1181, 1293, 1304, 1320, 1340, 1358, 1374, 1467, 1470, 1504, 1507, 1561, 1670, 1699, 1793, 1876, 1943, 1983, 2170, 2180, 2186, 2196, 2199, 2271, 2279, 2335, 2349, 2373, 2399, 2482, 2519, 2522, 2573, 2917, 2925, 2944, 2958, 2992, 3066, 3079, 3120, 3131, 3211, 3364, 3370, 3417, 3553, 3567, 3601, 4007, 4013, 4026, 4162, 4182, 4216, 4305, 4358, 4413, 4421, 4450, 4458, 4544, 4640] [9, 10, 11, 13, 24, 25, 28, 31, 40, 412, 413, 414, 416, 420, 426, 427, 429, 430, 437, 439, 440, 463, 467, 473, 474, 476, 501, 503, 504, 510, 615, 616, 619, 622, 623, 629, 632, 633, 639, 640, 642, 643, 666, 667, 670, 677, 679, 704, 706, 713, 716, 817, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1039, 1046, 1048, 1049, 1072, 1076, 1083, 1085, 1086, 1109, 1110, 1112, 1119, 1224, 1225, 1228, 1229, 1232, 1238, 1239, 1242, 1248, 1249, 1251, 1252, 1275, 1278, 1279, 1286, 1288, 1313, 1315, 1322, 1323, 1427, 1428, 1429, 1431, 1435, 1441, 1445, 1451, 1452, 1454, 1478, 1482, 1488, 1489, 1491, 1515, 1516, 1518, 1525, 1526, 1528, 1637, 1645, 1682, 1718, 1722, 1729, 1835, 1857, 1885, 1887, 1898, 1925, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2054, 2061, 2063, 2064, 2087, 2091, 2098, 2100, 2101, 2124, 2125, 2127, 2134, 2239, 2240, 2243, 2246, 2247, 2253, 2254, 2257, 2264, 2266, 2290, 2293, 2294, 2300, 2301, 2303, 2304, 2328, 2330, 2337, 2340, 2444, 2466, 2503, 2506, 2530, 2541, 2543, 2644, 2848, 2849, 2852, 2855, 2856, 2862, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2903, 2910, 2912, 2937, 2939, 2946, 2949, 3051, 3052, 3055, 3056, 3059, 3065, 3068, 3069, 3076, 3078, 3102, 3105, 3106, 3113, 3115, 3139, 3140, 3142, 3143, 3149, 3152, 3256, 3269, 3271, 3315, 3346, 3457, 3458, 3461, 3464, 3465, 3471, 3474, 3475, 3481, 3482, 3484, 3509, 3512, 3519, 3521, 3546, 3548, 3555, 3558, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3881, 3888, 3890, 3918, 3925, 3927, 3928, 3951, 3952, 3954, 3961, 4071, 4081, 4090, 4120, 4165, 4270, 4290, 4320, 4381, 4382, 4385, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4590, 4598, 4605] := + ⟨Fin 4, «FinitePoly 2 * y² + 3 * x + y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation190.lean b/equational_theories/Generated/FinitePoly/Refutation190.lean new file mode 100644 index 00000000..30630314 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation190.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 410, 418, 428, 435, 613, 621, 816, 841, 1019, 1831, 3252, 3260, 3305, 3318, 3333, 3455, 3463, 3508, 3521, 3536, 3658, 3683, 3861, 3914, 4589, 4621) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [8, 419, 429, 436, 622, 842, 3334, 3537, 3684, 3862, 4622] [2, 3, 9, 10, 11, 13, 14, 16, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 430, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 617, 619, 620, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1223, 1426, 1629, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y² + x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation194.lean b/equational_theories/Generated/FinitePoly/Refutation194.lean new file mode 100644 index 00000000..ce985f24 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation194.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 2 * x + 0 * y + 1 * x * y) % 4' (0, 39, 358, 359, 366, 367, 368, 377, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 4064, 4065, 4066, 4067, 4068, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4130, 4269, 4340, 4582, 4589, 4590, 4591, 4596, 4607, 4608, 4621, 4622) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * x + x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + 2 * x + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * x + x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [369, 378, 3684, 3685, 3687, 4099, 4341, 4609] [8, 99, 361, 362, 364, 365, 374, 375, 377, 384, 385, 411, 817, 1020, 1223, 1832, 3253, 3721, 3724, 3725, 3862, 4070, 4071, 4073, 4081, 4083, 4084, 4269, 4293, 4314, 4584, 4588, 4598, 4606, 4636] := + ⟨Fin 4, «FinitePoly x² + 2 * x + x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation196.lean b/equational_theories/Generated/FinitePoly/Refutation196.lean new file mode 100644 index 00000000..2fd757ab --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation196.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 4 * x + 1 * y + 3 * x * y) % 5' (0, 816, 3252, 3861) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + 4 * x + y + 3 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => y*y + 4 * x + y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + 4 * x + y + 3 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [817, 3253] [8, 43, 411, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1020, 1223, 1629, 1832, 2035, 3261, 3278, 3306, 3319, 3353, 3456, 3659, 3887, 3915, 3962, 4065, 4275, 4283, 4290, 4320, 4380, 4598, 4605, 4635] := + ⟨Fin 5, «FinitePoly y² + 4 * x + y + 3 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation198.lean b/equational_theories/Generated/FinitePoly/Refutation198.lean new file mode 100644 index 00000000..59e98769 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation198.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 46, 98, 1019, 1222, 1425, 1628, 3658, 3723, 3724, 4379) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [47, 99, 1020, 1223, 1426, 1629, 3724, 3725, 4380] [2, 3, 8, 23, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation20.lean b/equational_theories/Generated/FinitePoly/Refutation20.lean new file mode 100644 index 00000000..3ba3deae --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation20.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 2 * y**2 + 1 * x + 0 * y + 3 * x * y) % 4' (0, 2, 7, 22, 46, 98, 150, 202, 254, 306, 325, 358, 374, 377, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3318, 3455, 3521, 3658, 3714, 3721, 3724, 3861, 3914, 3927, 4064, 4117, 4120, 4130, 4379, 4469, 4472, 4598) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 2 * y² + x + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + 2 * y*y + x + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 2 * y² + x + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3, 307, 378, 3456, 3725, 3928, 4121, 4473, 4599] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3724, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + 2 * y² + x + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation200.lean b/equational_theories/Generated/FinitePoly/Refutation200.lean new file mode 100644 index 00000000..6eada1da --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation200.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 3 * x + 1 * y + 3 * x * y) % 4' (0, 3252, 3455, 3658, 3861, 4064, 4319, 4361, 4379, 4404, 4434, 4479) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x + y + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x + y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x + y + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [3253, 4065, 4362, 4405, 4435, 4480] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4406, 4408, 4433, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x + y + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation206.lean b/equational_theories/Generated/FinitePoly/Refutation206.lean new file mode 100644 index 00000000..e8e15212 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation206.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 0 * x + 3 * y + 0 * x * y) % 4' (0, 7, 15, 98, 103, 116, 126, 137, 150, 158, 165, 178, 193, 358, 363, 374, 384, 394, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 1019, 1024, 1034, 1044, 1054, 1074, 1084, 1095, 1111, 1121, 1132, 1149, 1166, 1183, 1201, 1222, 1227, 1237, 1247, 1257, 1277, 1287, 1298, 1314, 1324, 1335, 1352, 1369, 1386, 1404, 1628, 1633, 1646, 1656, 1667, 1680, 1690, 1700, 1720, 1730, 1741, 1762, 1779, 1796, 1815, 1831, 1839, 1846, 1859, 1874, 1883, 1896, 1911, 1920, 1933, 1948, 1957, 1978, 1999, 2023, 2034, 2042, 2049, 2062, 2077, 2086, 2099, 2114, 2123, 2136, 2151, 2160, 2181, 2202, 2226, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4274, 4306, 4319, 4361, 4586, 4605, 4614, 4644, 4665, 4688) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + 3 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + 3 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 138, 194, 395, 419, 436, 466, 500, 562, 1202, 1278, 1288, 1315, 1325, 1816, 2024, 2043, 2063, 2100, 2137, 3261, 3388, 3897, 3935, 3972, 3989, 4006, 4155, 4165, 4362, 4615, 4645] [2, 3, 9, 10, 11, 13, 14, 23, 38, 39, 40, 43, 47, 100, 101, 102, 105, 107, 108, 114, 115, 118, 124, 125, 152, 153, 154, 156, 157, 160, 167, 169, 170, 176, 177, 203, 255, 307, 331, 360, 361, 362, 365, 367, 368, 374, 377, 378, 384, 407, 412, 413, 414, 416, 417, 420, 426, 427, 430, 437, 439, 440, 463, 464, 467, 474, 476, 477, 501, 503, 504, 510, 511, 614, 817, 1021, 1022, 1023, 1026, 1028, 1029, 1036, 1038, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1082, 1083, 1086, 1109, 1110, 1113, 1119, 1120, 1224, 1225, 1226, 1229, 1231, 1232, 1239, 1241, 1242, 1249, 1251, 1252, 1275, 1276, 1279, 1285, 1286, 1289, 1312, 1313, 1316, 1322, 1323, 1426, 1630, 1631, 1632, 1635, 1637, 1638, 1644, 1645, 1648, 1654, 1655, 1658, 1682, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1848, 1850, 1851, 1857, 1858, 1861, 1885, 1887, 1888, 1894, 1895, 1898, 1922, 1924, 1925, 1931, 1932, 2036, 2037, 2038, 2040, 2041, 2044, 2051, 2053, 2054, 2060, 2061, 2064, 2088, 2090, 2091, 2097, 2098, 2101, 2125, 2127, 2128, 2134, 2135, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3352, 3355, 3456, 3543, 3659, 3863, 3864, 3865, 3868, 3870, 3871, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3927, 3928, 3951, 3954, 3955, 3961, 3964, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4081, 4083, 4084, 4091, 4093, 4120, 4121, 4127, 4130, 4131, 4154, 4157, 4158, 4164, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4588, 4590, 4591, 4598, 4599, 4605, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 2 * y² + 3 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation208.lean b/equational_theories/Generated/FinitePoly/Refutation208.lean new file mode 100644 index 00000000..e98c11ee --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation208.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 2 * x + 1 * y + 0 * x * y) % 3' (0, 22, 30, 46, 74, 202, 230, 1628, 1636, 1717, 1730, 1745, 2440, 2448, 2465, 2495, 2529, 2542, 2557, 2604, 2643, 2651, 2661, 2705, 2732, 2745, 2760, 2794, 3049, 3057, 3138, 3151, 3166, 3455, 3463, 3508, 3521, 3536, 3658, 3683, 3711, 3758, 3819, 4064, 4089, 4117, 4164, 4225, 4319, 4361, 4589, 4621) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * x + y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + 2 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * x + y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [31, 75, 231, 1637, 1718, 1731, 2466, 2496, 2558, 2652, 2662, 2706, 2733, 2746, 3058, 3139, 3152, 3464, 3509, 3659, 4090, 4590] [2, 3, 8, 24, 25, 26, 28, 29, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 99, 151, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2238, 2442, 2443, 2444, 2446, 2447, 2450, 2456, 2457, 2459, 2460, 2467, 2469, 2470, 2493, 2494, 2497, 2503, 2504, 2506, 2507, 2531, 2533, 2534, 2540, 2541, 2645, 2646, 2647, 2649, 2650, 2653, 2659, 2660, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2707, 2709, 2710, 2734, 2736, 2737, 2743, 2744, 2847, 3051, 3052, 3053, 3055, 3056, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3140, 3142, 3143, 3149, 3150, 3253, 3337, 3457, 3458, 3459, 3461, 3462, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3685, 3687, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3761, 3862, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + 2 * x + y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation212.lean b/equational_theories/Generated/FinitePoly/Refutation212.lean new file mode 100644 index 00000000..0ba890e7 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation212.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 3 * y**2 + 3 * x + 2 * y + 1 * x * y) % 4' (0, 2, 7, 22, 46, 98, 150, 202, 254, 306, 322, 325, 358, 374, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3305, 3308, 3318, 3455, 3508, 3521, 3658, 3711, 3714, 3721, 3861, 3914, 4064, 4117, 4283, 4379, 4395, 4469) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * y² + 3 * x + 2 * y + x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * y*y + 3 * x + 2 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * y² + 3 * x + 2 * y + x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [323, 3309, 3509, 3712, 4284, 4396] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * y² + 3 * x + 2 * y + x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation214.lean b/equational_theories/Generated/FinitePoly/Refutation214.lean new file mode 100644 index 00000000..59d1b912 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation214.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 2 * x + 2 * y + 2 * x * y) % 3' (0, 306, 3252, 3254, 3455, 3457, 4064, 4130) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + 2 * x + 2 * y + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + 2 * y*y + 2 * x + 2 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + 2 * x + 2 * y + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [307, 3255, 3458] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 308, 309, 310, 312, 313, 315, 316, 323, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3862, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + 2 * y² + 2 * x + 2 * y + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation216.lean b/equational_theories/Generated/FinitePoly/Refutation216.lean new file mode 100644 index 00000000..8c6652ad --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation216.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 1 * x + 0 * y + 0 * x * y) % 3' (0, 254, 263, 816, 845, 1019, 1048, 3252, 3318, 4597, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + x % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * y*y + x + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + x % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [264, 846, 1049, 3319] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 256, 257, 258, 260, 261, 263, 270, 271, 273, 274, 280, 281, 283, 307, 331, 359, 407, 411, 614, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * y² + x % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation218.lean b/equational_theories/Generated/FinitePoly/Refutation218.lean new file mode 100644 index 00000000..ddeef4e2 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation218.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 39, 3455, 3457, 3463, 3471, 3481, 3484, 3487, 3499, 3508, 3518, 3521, 3524, 3536, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3748, 4064, 4067, 4069, 4083, 4089, 4093, 4097, 4104, 4117, 4127, 4137, 4164, 4225, 4269, 4320, 4340, 4589, 4621, 4657) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + 2 * y*y + x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [3488, 3500, 3525, 3537, 3692, 4105, 4138, 4226, 4321, 4622, 4658] [2, 3, 8, 23, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3457, 3459, 3461, 3462, 3465, 3471, 3474, 3475, 3481, 3484, 3511, 3512, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4066, 4067, 4071, 4073, 4074, 4080, 4081, 4083, 4091, 4093, 4120, 4121, 4127, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4167, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + 2 * y² + x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation220.lean b/equational_theories/Generated/FinitePoly/Refutation220.lean new file mode 100644 index 00000000..f4fff904 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation220.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 1 * x + 1 * y + 3 * x * y) % 4' (0, 39, 1628, 1636, 1717, 1730, 1745, 3455, 3463, 3471, 3484, 3499, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 4064, 4067, 4089, 4093, 4097, 4130, 4269, 4340, 4589, 4621) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + x + y + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + 2 * y*y + x + y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + x + y + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1746, 3500, 3692, 4098, 4341, 4622] [8, 255, 411, 817, 1020, 1635, 1645, 1647, 1658, 1685, 1691, 1729, 1832, 2441, 3253, 3457, 3458, 3459, 3461, 3462, 3465, 3471, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3714, 3721, 3725, 3749, 3761, 3862, 4066, 4067, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4275, 4290, 4321, 4588, 4598, 4658] := + ⟨Fin 4, «FinitePoly x² + 2 * y² + x + y + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation226.lean b/equational_theories/Generated/FinitePoly/Refutation226.lean new file mode 100644 index 00000000..dba4dba4 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation226.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 4 * y**2 + 2 * x + 1 * y + 0 * x * y) % 5' (0, 816, 4607) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 4 * y² + 2 * x + y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => x*x + 4 * y*y + 2 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 4 * y² + 2 * x + y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [817, 4608] [3, 8, 23, 43, 47, 99, 151, 203, 255, 307, 359, 411, 614, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3456, 3659, 3862, 4065, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4380, 4598, 4599, 4605, 4606, 4629, 4635, 4636, 4658] := + ⟨Fin 5, «FinitePoly x² + 4 * y² + 2 * x + y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation232.lean b/equational_theories/Generated/FinitePoly/Refutation232.lean new file mode 100644 index 00000000..eeabcaaf --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation232.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 2 * x + 2 * y + 1 * x * y) % 3' (0, 358, 3252, 3305, 3861, 3866, 4064, 4069) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + 2 * x + 2 * y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + 2 * y*y + 2 * x + 2 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + 2 * x + 2 * y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [359, 3306, 3867, 4070] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 360, 361, 362, 364, 365, 367, 368, 374, 375, 377, 378, 384, 385, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3659, 3863, 3864, 3865, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + 2 * y² + 2 * x + 2 * y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation234.lean b/equational_theories/Generated/FinitePoly/Refutation234.lean new file mode 100644 index 00000000..4c2552d0 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation234.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 2 * x + 2 * y + 1 * x * y) % 3' (0, 2, 7, 22, 42, 46, 98, 150, 202, 254, 306, 322, 324, 325, 331, 332, 334, 358, 374, 376, 377, 383, 384, 386, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3305, 3307, 3308, 3314, 3315, 3317, 3318, 3341, 3342, 3344, 3345, 3351, 3352, 3354, 3455, 3508, 3510, 3511, 3517, 3518, 3520, 3521, 3544, 3545, 3547, 3548, 3554, 3555, 3557, 3658, 3711, 3713, 3714, 3720, 3721, 3723, 3724, 3747, 3748, 3750, 3751, 3757, 3758, 3760, 3861, 3914, 3916, 3917, 3923, 3924, 3926, 3927, 3950, 3951, 3953, 3954, 3960, 3961, 3963, 4064, 4117, 4119, 4120, 4126, 4127, 4129, 4130, 4153, 4154, 4156, 4157, 4163, 4164, 4166, 4282, 4283, 4289, 4290, 4292, 4313, 4319, 4320, 4342, 4357, 4379, 4395, 4397, 4398, 4404, 4405, 4407, 4432, 4434, 4435, 4441, 4442, 4444, 4469, 4471, 4472, 4478, 4479, 4481, 4530, 4543, 4597, 4598, 4604, 4605, 4607, 4628, 4634, 4635, 4657, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 2 * x + 2 * y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + 2 * x + 2 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 2 * x + 2 * y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3, 323, 325, 332, 333, 335, 377, 378, 384, 385, 387, 3308, 3309, 3315, 3318, 3345, 3346, 3352, 3355, 3509, 3511, 3512, 3519, 3521, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3712, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3964, 4120, 4121, 4154, 4155, 4157, 4158, 4164, 4165, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4358, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4472, 4473, 4479, 4480, 4544, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 331, 336, 360, 361, 362, 364, 365, 367, 368, 374, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3337, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3543, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4362, 4364, 4369, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4512, 4515, 4525, 4539, 4541, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4673, 4679, 4684, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + 2 * x + 2 * y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation236.lean b/equational_theories/Generated/FinitePoly/Refutation236.lean new file mode 100644 index 00000000..a0af9dc3 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation236.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 2 * x + 2 * y + 1 * x * y) % 3' (0, 3252, 3305, 4590) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + 2 * x + 2 * y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => y*y + 2 * x + 2 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + 2 * x + 2 * y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [4591] [8, 411, 1020, 1223, 1832, 3318, 3319, 3862, 4065] := + ⟨Fin 3, «FinitePoly y² + 2 * x + 2 * y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation238.lean b/equational_theories/Generated/FinitePoly/Refutation238.lean new file mode 100644 index 00000000..b1d72b63 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation238.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(4 * x**2 + 4 * y**2 + 3 * x + 2 * y + 3 * x * y) % 5' (0, 98, 103, 1019, 1037, 1222, 1227, 1237, 1247, 1257) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 4 * x² + 4 * y² + 3 * x + 2 * y + 3 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 4 * x*x + 4 * y*y + 3 * x + 2 * y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 4 * x² + 4 * y² + 3 * x + 2 * y + 3 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [104, 1038] [3253] := + ⟨Fin 5, «FinitePoly 4 * x² + 4 * y² + 3 * x + 2 * y + 3 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation24.lean b/equational_theories/Generated/FinitePoly/Refutation24.lean new file mode 100644 index 00000000..c40bc77b --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation24.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 0 * y + 0 * x * y) % 2' (0, 2, 3, 7, 8, 9, 10, 11, 22, 23, 24, 25, 26, 37, 41, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 358, 359, 360, 361, 362, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 1270, 1271, 1272, 1273, 1425, 1426, 1427, 1428, 1429, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 2034, 2035, 2036, 2037, 2038, 2039, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 2080, 2081, 2082, 2083, 2084, 2085, 2237, 2238, 2239, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 2490, 2491, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 2690, 2691, 2692, 2693, 2694, 2846, 2847, 2848, 2849, 2850, 2851, 2852, 2853, 2854, 2855, 2856, 2857, 2858, 2859, 2860, 2861, 2862, 2863, 2864, 2865, 2866, 2867, 2868, 2869, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887, 2888, 2889, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 3049, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 3100, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 3870, 3871, 3872, 3873, 3874, 3875, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4380, 4381, 4382, 4383, 4394, 4395, 4396, 4397, 4398, 4399, 4400, 4401, 4402, 4403, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 4440, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x % 2» : Magma (Fin 2) where + op := memoFinOp fun x y => x + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x % 2» : + ∃ (G : Type) (_ : Magma G), Facts G [4, 9, 10, 11, 24, 25, 26, 61, 113, 165, 217, 259, 262, 265, 266, 267, 268, 363, 376, 379, 380, 382, 449, 453, 457, 458, 459, 460, 461, 631, 634, 637, 641, 644, 647, 651, 655, 659, 826, 836, 843, 845, 861, 1044, 1054, 1058, 1062, 1066, 1069, 1070, 1227, 1233, 1235, 1243, 1245, 1253, 1255, 1264, 1267, 1464, 1468, 1472, 1473, 1474, 1475, 1476, 1646, 1649, 1652, 1656, 1659, 1666, 1670, 1674, 1835, 1842, 1844, 1852, 1854, 1862, 1864, 1876, 2086, 2255, 2258, 2261, 2265, 2268, 2271, 2275, 2279, 2283, 2444, 2451, 2453, 2461, 2463, 2471, 2473, 2482, 2695, 2898, 3101, 3747, 3950, 4075, 4078, 4125, 4140, 4144, 4149, 4150, 4151, 4359, 4674] [2, 5, 13, 14, 16, 28, 31, 39, 40, 43, 62, 63, 65, 66, 72, 73, 75, 114, 115, 117, 118, 124, 125, 127, 166, 167, 169, 170, 176, 177, 179, 218, 219, 221, 222, 228, 229, 231, 270, 271, 273, 274, 280, 281, 283, 312, 313, 315, 316, 332, 333, 335, 336, 364, 365, 367, 368, 384, 385, 407, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4385, 4386, 4388, 4405, 4406, 4408, 4442, 4443, 4445, 4479, 4480, 4482, 4539, 4547, 4571, 4587, 4588, 4590, 4591, 4605, 4606, 4608, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 2, «FinitePoly x % 2», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation246.lean b/equational_theories/Generated/FinitePoly/Refutation246.lean new file mode 100644 index 00000000..72cfccc1 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation246.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 2440, 2442, 2542, 2643, 2645, 2745, 3252, 3305, 4319, 4361) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [2443, 2543, 2646, 2746, 3306] [3, 8, 23, 40, 47, 99, 151, 203, 255, 307, 359, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2446, 2456, 2459, 2466, 2496, 2530, 2649, 2652, 2659, 2662, 2696, 2699, 2706, 2733, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3659, 3862, 4065, 4270, 4380, 4590] := + ⟨Fin 3, «FinitePoly y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation250.lean b/equational_theories/Generated/FinitePoly/Refutation250.lean new file mode 100644 index 00000000..ab12fe24 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation250.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 0 * y**2 + 1 * x + 1 * y + 1 * x * y) % 3' (0, 150, 1425, 1628, 1633, 1831, 1846, 2034, 2049, 2086, 3252, 3305, 3455, 3861, 3886, 4064, 4379) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + x + y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + x + y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + x + y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [151, 1426, 1634, 1847, 2050, 2087, 3306, 3887, 4065, 4380] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + x + y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation26.lean b/equational_theories/Generated/FinitePoly/Refutation26.lean new file mode 100644 index 00000000..cc1794bc --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation26.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(4 * x**2 + 4 * y**2 + 0 * x + 4 * y + 2 * x * y) % 5' (0, 150, 158) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 4 * x² + 4 * y² + 4 * y + 2 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 4 * x*x + 4 * y*y + 4 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 4 * x² + 4 * y² + 4 * y + 2 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 159] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 152, 153, 154, 156, 157, 160, 166, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 4 * x² + 4 * y² + 4 * y + 2 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation262.lean b/equational_theories/Generated/FinitePoly/Refutation262.lean new file mode 100644 index 00000000..37f8b92a --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation262.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 0 * x + 2 * y + 0 * x * y) % 3' (0, 7, 9, 12, 15, 18, 38, 44, 98, 100, 103, 106, 109, 113, 116, 119, 123, 126, 129, 133, 137, 141, 145, 150, 152, 155, 158, 161, 165, 168, 171, 175, 178, 181, 185, 189, 193, 197, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 462, 465, 468, 472, 475, 478, 482, 486, 490, 494, 499, 502, 505, 509, 512, 515, 519, 523, 527, 531, 536, 540, 544, 548, 553, 557, 561, 565, 570, 574, 578, 582, 587, 592, 597, 602, 607, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1071, 1074, 1077, 1081, 1084, 1087, 1091, 1095, 1099, 1103, 1108, 1111, 1114, 1118, 1121, 1124, 1128, 1132, 1136, 1140, 1145, 1149, 1153, 1157, 1162, 1166, 1170, 1174, 1179, 1183, 1187, 1191, 1196, 1201, 1206, 1211, 1216, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1274, 1277, 1280, 1284, 1287, 1290, 1294, 1298, 1302, 1306, 1311, 1314, 1317, 1321, 1324, 1327, 1331, 1335, 1339, 1343, 1348, 1352, 1356, 1360, 1365, 1369, 1373, 1377, 1382, 1386, 1390, 1394, 1399, 1404, 1409, 1414, 1419, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1680, 1683, 1686, 1690, 1693, 1696, 1700, 1704, 1708, 1712, 1717, 1720, 1723, 1727, 1730, 1733, 1737, 1741, 1745, 1749, 1754, 1758, 1762, 1766, 1771, 1775, 1779, 1783, 1788, 1792, 1796, 1800, 1805, 1810, 1815, 1820, 1825, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 1883, 1886, 1889, 1893, 1896, 1899, 1903, 1907, 1911, 1915, 1920, 1923, 1926, 1930, 1933, 1936, 1940, 1944, 1948, 1952, 1957, 1961, 1965, 1969, 1974, 1978, 1982, 1986, 1991, 1995, 1999, 2003, 2008, 2013, 2018, 2023, 2028, 2034, 2036, 2039, 2042, 2045, 2049, 2052, 2055, 2059, 2062, 2065, 2069, 2073, 2077, 2081, 2086, 2089, 2092, 2096, 2099, 2102, 2106, 2110, 2114, 2118, 2123, 2126, 2129, 2133, 2136, 2139, 2143, 2147, 2151, 2155, 2160, 2164, 2168, 2172, 2177, 2181, 2185, 2189, 2194, 2198, 2202, 2206, 2211, 2216, 2221, 2226, 2231, 3252, 3254, 3257, 3260, 3263, 3267, 3270, 3273, 3277, 3280, 3283, 3287, 3291, 3295, 3299, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3342, 3345, 3348, 3352, 3355, 3358, 3362, 3366, 3370, 3374, 3379, 3383, 3387, 3391, 3396, 3400, 3404, 3408, 3413, 3417, 3421, 3425, 3430, 3435, 3440, 3445, 3450, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4268, 4271, 4274, 4277, 4283, 4286, 4290, 4295, 4299, 4303, 4306, 4309, 4315, 4319, 4322, 4326, 4329, 4333, 4339, 4347, 4350, 4353, 4359, 4361, 4366, 4373, 4377, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [19, 120, 130, 134, 142, 153, 159, 169, 179, 458, 495, 532, 549, 566, 583, 588, 593, 598, 603, 1217, 1420, 1676, 1713, 1750, 1784, 1801, 1811, 1843, 1863, 1871, 1875, 1890, 1900, 1908, 1912, 1927, 1937, 1945, 1962, 1966, 1979, 1983, 1996, 2000, 2046, 2056, 2066, 2074, 2078, 2093, 2103, 2111, 2115, 2130, 2140, 2148, 2152, 2165, 2169, 2182, 2186, 2199, 2203, 3451, 4263, 4367, 4374, 4689] [2, 3, 9, 11, 14, 23, 38, 40, 43, 47, 100, 102, 105, 108, 115, 118, 125, 152, 154, 157, 160, 167, 170, 177, 203, 255, 307, 331, 360, 362, 365, 368, 374, 377, 384, 412, 414, 417, 420, 427, 430, 437, 440, 464, 467, 474, 477, 501, 504, 511, 614, 817, 1021, 1023, 1026, 1029, 1036, 1039, 1046, 1049, 1073, 1076, 1083, 1086, 1110, 1113, 1120, 1224, 1226, 1229, 1232, 1239, 1242, 1249, 1252, 1276, 1279, 1286, 1289, 1313, 1316, 1323, 1426, 1630, 1632, 1635, 1638, 1645, 1648, 1655, 1658, 1682, 1685, 1692, 1695, 1719, 1722, 1729, 1833, 1835, 1838, 1841, 1848, 1851, 1858, 1861, 1885, 1888, 1895, 1898, 1922, 1925, 1932, 2036, 2038, 2041, 2044, 2051, 2054, 2061, 2064, 2088, 2091, 2098, 2101, 2125, 2128, 2135, 2238, 2441, 2644, 2847, 3050, 3254, 3256, 3259, 3262, 3269, 3272, 3279, 3308, 3315, 3318, 3337, 3342, 3345, 3352, 3355, 3456, 3543, 3659, 3863, 3865, 3868, 3871, 3878, 3881, 3888, 3917, 3924, 3927, 3951, 3954, 3961, 3964, 4066, 4068, 4071, 4074, 4081, 4084, 4091, 4120, 4127, 4130, 4154, 4157, 4164, 4167, 4268, 4270, 4273, 4276, 4283, 4290, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4585, 4588, 4591, 4598, 4605, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation264.lean b/equational_theories/Generated/FinitePoly/Refutation264.lean new file mode 100644 index 00000000..8bddade9 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation264.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 0 * y + 2 * x * y) % 3' (0, 816, 831, 845, 1019, 1034, 1048, 4064, 4130, 4597, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [832, 846, 1035, 1049] [3, 8, 23, 47, 99, 151, 203, 255, 307, 359, 411, 614, 822, 1022, 1025, 1028, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3456, 3659, 3862, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4380] := + ⟨Fin 3, «FinitePoly x + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation268.lean b/equational_theories/Generated/FinitePoly/Refutation268.lean new file mode 100644 index 00000000..b41d924e --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation268.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 3 * y**2 + 1 * x + 3 * y + 2 * x * y) % 4' (0, 7, 22, 25, 410, 428, 613, 616, 816, 822, 832, 1019, 1022, 1037, 1222, 1225, 1228, 1230, 1425, 1441, 1454, 1628, 1631, 1644, 1646, 1653, 1657, 1661, 1831, 1837, 1849, 1860, 1872, 2034, 2040, 2050, 2059, 2237, 2240, 2266, 2440, 2443, 2446, 2448, 2456, 2469, 2484, 2643, 2646, 2659, 2661, 2846, 2849, 2852, 2854, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3305, 3318, 3455, 3458, 3508, 3510, 3517, 3521, 3525, 3658, 3664, 3711, 3720, 3861, 3864, 3914, 3916, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4379, 4382, 4395, 4397, 4584, 4597, 4655, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * y² + x + 3 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * y*y + x + 3 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * y² + x + 3 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [8, 26, 429, 617, 823, 833, 1023, 1038, 1226, 1229, 1231, 1442, 1455, 1632, 1645, 1647, 1654, 1658, 1838, 1850, 1861, 2041, 2051, 2060, 2241, 2267, 2444, 2447, 2449, 2457, 2470, 2647, 2660, 2662, 2850, 2853, 2855, 3053, 3058, 3066, 3075, 3091, 3306, 3459, 3509, 3511, 3518, 3665, 3712, 3721, 3865, 3917, 4073, 4143, 4383, 4396, 4398, 4585, 4673] [2, 3, 9, 10, 11, 13, 14, 16, 24, 25, 28, 31, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 825, 826, 832, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1025, 1026, 1028, 1029, 1035, 1036, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1228, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1444, 1445, 1451, 1452, 1454, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1634, 1635, 1637, 1638, 1644, 1648, 1655, 1657, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1840, 1841, 1847, 1848, 1851, 1857, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2043, 2044, 2050, 2053, 2054, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2446, 2450, 2456, 2459, 2460, 2466, 2467, 2469, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2649, 2650, 2652, 2653, 2659, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2852, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3055, 3059, 3065, 3069, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3512, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3714, 3715, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4070, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4385, 4386, 4388, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * y² + x + 3 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation270.lean b/equational_theories/Generated/FinitePoly/Refutation270.lean new file mode 100644 index 00000000..1ce55957 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation270.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 1 * x + 2 * y + 4 * x * y) % 5' (0, 202, 204, 2237, 2239, 2242, 2245, 2248, 2440, 2458) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x + 2 * y + 4 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x + 2 * y + 4 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x + 2 * y + 4 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [205, 2238, 2459] [4065] := + ⟨Fin 5, «FinitePoly 2 * x² + 2 * y² + x + 2 * y + 4 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation272.lean b/equational_theories/Generated/FinitePoly/Refutation272.lean new file mode 100644 index 00000000..ca9bd1f2 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation272.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 1 * y**2 + 1 * x + 1 * y + 3 * x * y) % 4' (0, 39, 1831, 1834, 1856, 1860, 1864, 3252, 3255, 3277, 3281, 3285, 3305, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3861, 3869, 3877, 3890, 3905, 4269, 4340, 4589, 4621) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + y² + x + y + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + y*y + x + y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + y² + x + y + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1865, 3286, 3692, 3906, 4341, 4622] [8, 23, 411, 817, 1020, 1426, 1629, 1838, 1840, 1848, 1850, 1887, 1921, 1925, 1934, 2238, 2441, 2644, 3050, 3259, 3261, 3269, 3308, 3315, 3319, 3353, 3456, 3714, 3721, 3725, 3761, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4065, 4275, 4283, 4290, 4585, 4588, 4598] := + ⟨Fin 4, «FinitePoly 2 * x² + y² + x + y + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation280.lean b/equational_theories/Generated/FinitePoly/Refutation280.lean new file mode 100644 index 00000000..d6f87825 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation280.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 2 * x + 3 * y + 2 * x * y) % 4' (0, 2, 7, 22, 24, 46, 98, 100, 150, 155, 202, 204, 207, 210, 213, 254, 256, 259, 262, 265, 306, 322, 325, 358, 360, 374, 377, 380, 410, 428, 613, 615, 816, 821, 1019, 1021, 1024, 1027, 1030, 1222, 1224, 1227, 1230, 1233, 1425, 1440, 1628, 1630, 1643, 1646, 1649, 1831, 1836, 1846, 1856, 1866, 2034, 2039, 2049, 2059, 2069, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2643, 2645, 2648, 2651, 2654, 2658, 2661, 2664, 2668, 2671, 2674, 2678, 2682, 2686, 2690, 2846, 2848, 2851, 2854, 2857, 2861, 2864, 2867, 2871, 2874, 2877, 2881, 2885, 2889, 2893, 3049, 3051, 3054, 3057, 3060, 3064, 3067, 3070, 3074, 3077, 3080, 3084, 3088, 3092, 3096, 3252, 3305, 3308, 3318, 3455, 3457, 3508, 3511, 3514, 3518, 3521, 3524, 3658, 3663, 3711, 3714, 3721, 3724, 3731, 3735, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4066, 4069, 4072, 4075, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4283, 4379, 4381, 4395, 4398, 4401, 4469, 4472, 4475, 4583, 4598, 4601, 4630, 4654, 4674) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 2 * x + 3 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + y*y + 2 * x + 3 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 2 * x + 3 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [25, 101, 156, 205, 208, 211, 266, 381, 429, 616, 822, 1234, 1441, 1631, 1644, 1647, 2070, 2285, 2488, 2659, 2662, 2669, 2672, 2849, 2855, 2865, 2875, 3097, 3515, 3519, 3732, 3736, 3918, 3925, 4076, 4124, 4134, 4142, 4146, 4402, 4476, 4602] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 26, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 206, 209, 212, 218, 219, 221, 222, 228, 229, 231, 256, 258, 261, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 325, 331, 332, 333, 335, 336, 360, 362, 364, 365, 367, 368, 374, 377, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1023, 1026, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1226, 1229, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1632, 1634, 1635, 1637, 1638, 1645, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1838, 1840, 1841, 1848, 1850, 1851, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2041, 2043, 2044, 2051, 2053, 2054, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2241, 2244, 2247, 2254, 2257, 2264, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2444, 2447, 2450, 2457, 2460, 2467, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2647, 2650, 2653, 2660, 2663, 2670, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2850, 2853, 2856, 2863, 2866, 2873, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3053, 3056, 3059, 3066, 3069, 3076, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3714, 3721, 3724, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3865, 3868, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4068, 4071, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4127, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4383, 4385, 4386, 4388, 4398, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4585, 4587, 4588, 4590, 4591, 4598, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + y² + 2 * x + 3 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation284.lean b/equational_theories/Generated/FinitePoly/Refutation284.lean new file mode 100644 index 00000000..e4d5e9f1 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation284.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 1 * y**2 + 1 * x + 1 * y + 0 * x * y) % 3' (0, 150, 4275, 4379, 4388, 4590) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + y² + x + y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + y*y + x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + y² + x + y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [151, 4389, 4591] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + y² + x + y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation286.lean b/equational_theories/Generated/FinitePoly/Refutation286.lean new file mode 100644 index 00000000..7facdde2 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation286.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 1 * y**2 + 2 * x + 1 * y + 2 * x * y) % 4' (0, 306, 311, 322, 332, 342, 3252, 3257, 3267, 3277, 3287, 3305, 3315, 3325, 3342, 3352, 3362, 3379, 3396, 3413, 3430, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4271, 4290, 4299, 4329, 4350, 4373, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + y² + 2 * x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + y*y + 2 * x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + y² + 2 * x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [343, 3326, 3363, 3380, 3397, 3414, 3712, 3722, 3749, 3759, 4300, 4330, 4682, 4689] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 308, 309, 310, 313, 315, 316, 325, 326, 331, 332, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3259, 3261, 3262, 3269, 3271, 3272, 3279, 3281, 3308, 3309, 3315, 3318, 3319, 3337, 3342, 3345, 3346, 3352, 3355, 3456, 3543, 3660, 3661, 3662, 3665, 3667, 3668, 3675, 3677, 3678, 3685, 3687, 3714, 3715, 3721, 3724, 3725, 3748, 3751, 3752, 3758, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4273, 4275, 4276, 4283, 4284, 4290, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4585, 4588, 4591, 4598, 4605, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + y² + 2 * x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation290.lean b/equational_theories/Generated/FinitePoly/Refutation290.lean new file mode 100644 index 00000000..cb49bff8 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation290.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 1 * x + 1 * y + 2 * x * y) % 3' (0, 150, 1425, 1426, 1427, 1628, 1630, 1831, 1836, 2034, 3252, 3455, 3458, 3861, 4064, 4130, 4379) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + x + y + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => y*y + x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + x + y + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [151, 1427, 1428, 1631, 1837, 2035, 3253, 3459] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly y² + x + y + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation302.lean b/equational_theories/Generated/FinitePoly/Refutation302.lean new file mode 100644 index 00000000..38e27f5e --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation302.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 3 * y**2 + 0 * x + 3 * y + 2 * x * y) % 4' (0, 7, 9, 98, 100, 103, 106, 109, 150, 152, 155, 158, 161, 358, 360, 374, 377, 380, 410, 412, 415, 425, 428, 431, 438, 449, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 2034, 2036, 2039, 2042, 2045, 2049, 2052, 2055, 2059, 2062, 2065, 2069, 2073, 2077, 2081, 3252, 3254, 3257, 3305, 3315, 3318, 3321, 3325, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4066, 4069, 4072, 4075, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4268, 4315, 4583, 4598, 4601, 4630, 4654, 4674) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 3 * y² + 3 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + 3 * y*y + 3 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 3 * y² + 3 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [10, 99, 162, 381, 413, 426, 450, 1031, 1041, 1051, 1055, 1059, 1063, 1225, 1228, 1231, 1238, 1241, 1248, 1251, 1644, 1647, 1654, 1657, 1834, 1840, 1850, 1860, 2082, 3255, 3326, 3918, 3925, 3928, 4076, 4124, 4134, 4138, 4142, 4146, 4269, 4602] [2, 3, 9, 11, 13, 14, 16, 23, 38, 39, 40, 43, 47, 100, 102, 105, 108, 114, 115, 117, 118, 124, 125, 127, 152, 154, 157, 160, 166, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 360, 362, 364, 365, 367, 368, 374, 377, 384, 385, 407, 412, 414, 417, 419, 420, 427, 430, 436, 437, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 614, 817, 1021, 1023, 1026, 1029, 1036, 1039, 1046, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1226, 1229, 1232, 1239, 1242, 1249, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1630, 1632, 1635, 1638, 1645, 1648, 1655, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1835, 1838, 1841, 1848, 1851, 1858, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2038, 2041, 2044, 2051, 2054, 2061, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2238, 2441, 2644, 2847, 3050, 3254, 3256, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3659, 3863, 3865, 3868, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4068, 4071, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4127, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4585, 4587, 4588, 4590, 4591, 4598, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + 3 * y² + 3 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation312.lean b/equational_theories/Generated/FinitePoly/Refutation312.lean new file mode 100644 index 00000000..21414094 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation312.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 3 * x + 2 * y + 3 * x * y) % 5' (0, 39, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3723, 4269, 4292, 4340, 4589, 4621, 4635) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 3 * x + 2 * y + 3 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => x*x + y*y + 3 * x + 2 * y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 3 * x + 2 * y + 3 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [3700, 4293, 4636] [307, 3253, 3664, 3668, 3674, 3678, 3721, 3725, 4065, 4272, 4276, 4343] := + ⟨Fin 5, «FinitePoly x² + y² + 3 * x + 2 * y + 3 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation314.lean b/equational_theories/Generated/FinitePoly/Refutation314.lean new file mode 100644 index 00000000..9a297be8 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation314.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 2 * x + 0 * y + 1 * x * y) % 3' (0, 22, 24, 202, 204, 207, 210, 213, 306, 322, 1628, 1630, 1643, 1646, 1649, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2299, 2302, 2305, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2643, 2658, 2698, 2735, 2773, 3049, 3051, 3064, 3067, 3070, 3252, 3305, 3455, 3457, 3518, 3521, 3524, 3658, 3748, 4064, 4069, 4117, 4127, 4137, 4583, 4630) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + 2 * x + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + 2 * x + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + 2 * x + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [25, 205, 208, 211, 323, 1631, 1644, 1647, 2285, 2306, 2488, 2774, 3052, 3065, 3068, 3458, 3519, 3749, 4070, 4128, 4584] [2, 3, 8, 24, 26, 28, 29, 31, 38, 39, 40, 43, 47, 99, 151, 204, 206, 209, 212, 218, 219, 221, 222, 228, 229, 231, 255, 308, 309, 310, 312, 313, 315, 316, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1632, 1634, 1635, 1637, 1638, 1645, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1832, 2035, 2239, 2241, 2244, 2247, 2254, 2257, 2264, 2267, 2290, 2291, 2293, 2294, 2301, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2444, 2447, 2450, 2457, 2460, 2467, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2737, 2743, 2744, 2746, 2847, 3051, 3053, 3055, 3056, 3058, 3059, 3066, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y² + 2 * x + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation316.lean b/equational_theories/Generated/FinitePoly/Refutation316.lean new file mode 100644 index 00000000..b805f368 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation316.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 0 * y**2 + 3 * x + 3 * y + 0 * x * y) % 4' (0, 7, 15, 22, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 638, 675, 702, 816, 834, 871, 905, 1019, 1027, 1037, 1044, 1074, 1081, 1108, 1121, 1136, 1170, 1183, 1222, 1230, 1311, 1324, 1339, 1425, 1433, 1480, 1487, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1849, 1856, 1886, 1893, 1920, 1933, 1948, 1982, 1995, 2034, 2059, 2089, 2136, 2198, 2237, 2262, 2299, 2326, 2440, 2458, 2495, 2529, 2643, 2651, 2698, 2705, 2846, 2871, 2908, 2935, 3049, 3057, 3067, 3074, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3480, 3521, 3548, 3658, 3676, 3724, 3758, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4117, 4130, 4145, 4274, 4306, 4319, 4361, 4379, 4408, 4441, 4472) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 3 * x + 3 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + 3 * x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 3 * x + 3 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1137, 1171, 1340, 1983, 1996, 2199, 2496, 2652, 2872, 2909, 3058, 3075, 3943, 3997, 4146] [2, 3, 9, 10, 11, 13, 14, 24, 25, 26, 28, 31, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 430, 437, 439, 440, 463, 464, 467, 474, 476, 477, 501, 503, 504, 510, 511, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 640, 642, 643, 666, 667, 669, 670, 677, 679, 680, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 836, 842, 843, 845, 846, 869, 870, 873, 879, 880, 882, 883, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1029, 1035, 1036, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1083, 1085, 1086, 1110, 1112, 1113, 1119, 1120, 1224, 1225, 1226, 1228, 1229, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1313, 1315, 1316, 1322, 1323, 1427, 1428, 1429, 1431, 1432, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1482, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1847, 1848, 1851, 1858, 1860, 1861, 1884, 1885, 1888, 1895, 1897, 1898, 1922, 1924, 1925, 1931, 1932, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2061, 2063, 2064, 2087, 2088, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2301, 2303, 2304, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2497, 2503, 2504, 2506, 2507, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2700, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2910, 2912, 2913, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3059, 3065, 3066, 3069, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3352, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3748, 3749, 3751, 3752, 3758, 3761, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3878, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3961, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4443, 4445, 4470, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + 3 * x + 3 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation318.lean b/equational_theories/Generated/FinitePoly/Refutation318.lean new file mode 100644 index 00000000..ab73cfa8 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation318.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 42, 3252, 3455, 3658, 3721, 3723, 3748, 3750, 3861, 4064, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [3722, 3724, 3749, 3751, 4635] [3, 8, 23, 47, 99, 151, 203, 255, 307, 359, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3258, 3268, 3278, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3664, 3674, 3684, 3712, 3714, 3715, 3721, 3725, 3748, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4272, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4584, 4587, 4590, 4598, 4599, 4605, 4606, 4608, 4629, 4636, 4658] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y² + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation32.lean b/equational_theories/Generated/FinitePoly/Refutation32.lean new file mode 100644 index 00000000..6a1c70e5 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation32.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 2, 7, 22, 46, 98, 150, 202, 254, 306, 325, 358, 374, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3318, 3455, 3521, 3658, 3714, 3721, 3861, 3914, 4064, 4117, 4130, 4379, 4469) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * y*y + y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3, 307, 359, 3456, 3862, 4131, 4380] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * y² + y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation320.lean b/equational_theories/Generated/FinitePoly/Refutation320.lean new file mode 100644 index 00000000..cce45e90 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation320.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 1 * x + 3 * y + 1 * x * y) % 4' (0, 7, 410, 816, 822, 845, 1019, 1222, 1831, 1860, 3252, 3305, 3314, 3318, 3861, 3914, 3927) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + x + 3 * y + x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => y*y + x + 3 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + x + 3 * y + x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [823, 846, 1223, 1861, 3306] [9, 10, 11, 13, 14, 16, 23, 99, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 614, 818, 819, 820, 822, 825, 826, 832, 833, 835, 836, 842, 843, 845, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1023, 1038, 1049, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3316, 3456, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4065, 4380, 4585, 4598] := + ⟨Fin 4, «FinitePoly y² + x + 3 * y + x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation326.lean b/equational_theories/Generated/FinitePoly/Refutation326.lean new file mode 100644 index 00000000..a1da1c0d --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation326.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 2 * x + 2 * y + 2 * x * y) % 4' (0, 306, 308, 322, 325, 328, 358, 363, 374, 384, 394, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3658, 3660, 3673, 3676, 3679, 3711, 3714, 3717, 3748, 3751, 3754, 3785, 3789, 3793, 3797, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4268, 4283, 4286, 4315, 4339, 4359, 4379, 4384, 4395, 4405, 4415, 4431, 4441, 4451, 4469, 4479, 4489, 4507, 4524, 4541, 4558, 4586, 4605, 4614, 4644, 4665, 4688) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + 2 * x + 2 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => y*y + 2 * x + 2 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + 2 * x + 2 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [329, 395, 3264, 3312, 3322, 3326, 3330, 3334, 3509, 3512, 3519, 3522, 3798, 3897, 3935, 3972, 3989, 4006, 4023, 4155, 4165, 4559, 4615, 4645] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 308, 310, 312, 313, 315, 316, 325, 331, 332, 333, 335, 336, 360, 361, 362, 365, 367, 368, 374, 377, 378, 384, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3256, 3259, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3315, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3459, 3462, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3662, 3664, 3665, 3667, 3668, 3675, 3678, 3684, 3685, 3687, 3714, 3721, 3722, 3724, 3725, 3748, 3751, 3758, 3759, 3761, 3863, 3864, 3865, 3868, 3870, 3871, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3927, 3928, 3951, 3954, 3955, 3961, 3964, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4081, 4083, 4084, 4091, 4093, 4120, 4121, 4127, 4130, 4131, 4154, 4157, 4158, 4164, 4167, 4258, 4268, 4270, 4272, 4273, 4275, 4276, 4283, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4386, 4388, 4398, 4399, 4405, 4408, 4433, 4435, 4436, 4443, 4445, 4472, 4473, 4479, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4588, 4590, 4591, 4598, 4599, 4605, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly y² + 2 * x + 2 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation328.lean b/equational_theories/Generated/FinitePoly/Refutation328.lean new file mode 100644 index 00000000..b6bfbffb --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation328.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 1 * y**2 + 1 * x + 1 * y + 0 * x * y) % 4' (0, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4274, 4306, 4319, 4361, 4584, 4597, 4655, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + y² + x + y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + y*y + x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + y² + x + y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [3334, 3388, 3414, 4135, 4146, 4307] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3352, 3355, 3456, 3543, 3659, 3862, 4055, 4066, 4067, 4070, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + y² + x + y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation330.lean b/equational_theories/Generated/FinitePoly/Refutation330.lean new file mode 100644 index 00000000..552ab8a7 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation330.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 2, 7, 8, 22, 46, 47, 48, 49, 50, 98, 99, 101, 150, 151, 202, 204, 254, 306, 307, 325, 358, 374, 377, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 428, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 816, 817, 818, 819, 820, 822, 824, 825, 828, 1019, 1020, 1021, 1022, 1023, 1025, 1028, 1031, 1038, 1222, 1223, 1225, 1231, 1425, 1426, 1427, 1428, 1429, 1480, 1628, 1629, 1631, 1831, 1832, 1836, 1837, 1838, 2034, 2035, 2050, 2097, 2237, 2239, 2242, 2245, 2248, 2440, 2442, 2448, 2643, 2645, 2846, 2851, 3049, 3252, 3253, 3254, 3255, 3256, 3317, 3318, 3319, 3455, 3456, 3458, 3510, 3518, 3521, 3658, 3659, 3714, 3721, 3724, 3861, 3863, 3914, 3917, 3920, 3927, 3954, 4064, 4117, 4120, 4130, 4267, 4281, 4379, 4394, 4469, 4472, 4598, 4635) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3, 9, 48, 49, 50, 100, 102, 152, 205, 308, 378, 425, 429, 628, 825, 829, 1021, 1023, 1032, 1039, 1224, 1226, 1232, 1427, 1428, 1429, 1481, 1630, 1632, 1833, 1837, 1838, 2036, 2051, 2098, 2443, 2449, 2646, 2852, 3318, 3457, 3459, 3511, 3519, 3660, 3725, 3864, 3918, 3928, 3955, 4121, 4395, 4473, 4599, 4636] [2, 4, 5, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 101, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 309, 310, 312, 313, 315, 316, 323, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 384, 385, 407, 426, 427, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 822, 827, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1025, 1028, 1035, 1036, 1038, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1225, 1228, 1229, 1231, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1631, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1834, 1835, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2241, 2244, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2444, 2446, 2447, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3458, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3512, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3724, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3925, 3927, 3951, 3952, 3954, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4605, 4606, 4608, 4629, 4635, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation34.lean b/equational_theories/Generated/FinitePoly/Refutation34.lean new file mode 100644 index 00000000..695b61fd --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation34.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 3 * x + 2 * y + 0 * x * y) % 4' (0, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4382, 4394, 4398, 4402, 4431, 4435, 4439, 4468, 4472, 4476, 4505, 4510, 4515, 4520, 4584, 4597, 4655, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 3 * x + 2 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + 3 * x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 3 * x + 2 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3730, 3947, 4135, 4143, 4146, 4521, 4585, 4673] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3865, 3868, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4070, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4385, 4386, 4388, 4396, 4398, 4405, 4406, 4408, 4433, 4435, 4442, 4443, 4445, 4470, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + 3 * x + 2 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation340.lean b/equational_theories/Generated/FinitePoly/Refutation340.lean new file mode 100644 index 00000000..4800a861 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation340.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 0 * x + 2 * y + 0 * x * y) % 4' (0, 37, 41, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + 2 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + 2 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [325, 326, 3544, 4359, 4360, 4683, 4688, 4689] [2, 3, 8, 23, 39, 40, 43, 47, 99, 151, 203, 255, 312, 313, 315, 316, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3862, 4055, 4065, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571] := + ⟨Fin 4, «FinitePoly 2 * x² + 2 * y² + 2 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation342.lean b/equational_theories/Generated/FinitePoly/Refutation342.lean new file mode 100644 index 00000000..7d2f8d1f --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation342.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 3 * y**2 + 1 * x + 3 * y + 0 * x * y) % 4' (0, 7, 22, 25, 410, 418, 428, 435, 613, 616, 619, 621, 816, 822, 832, 841, 1019, 1022, 1035, 1037, 1222, 1225, 1228, 1230, 1425, 1433, 1441, 1454, 1469, 1628, 1631, 1634, 1636, 1644, 1646, 1653, 1657, 1661, 1669, 1672, 1831, 1837, 1849, 1860, 1872, 2034, 2040, 2050, 2059, 2237, 2240, 2262, 2266, 2270, 2440, 2443, 2446, 2448, 2456, 2458, 2465, 2469, 2473, 2481, 2484, 2643, 2646, 2659, 2661, 2846, 2849, 2852, 2854, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3260, 3305, 3318, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3664, 3711, 3720, 3861, 3864, 3914, 3916, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4379, 4382, 4395, 4397, 4584, 4597, 4655, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 3 * y² + x + 3 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 3 * y*y + x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 3 * y² + x + 3 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [419, 436, 620, 622, 842, 1036, 1470, 1670, 1673, 2271, 2474, 2482, 3334, 3534, 3537] [2, 3, 9, 10, 11, 13, 14, 16, 24, 25, 28, 31, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 430, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 619, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 825, 826, 832, 835, 836, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1025, 1026, 1028, 1029, 1035, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1228, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1435, 1441, 1444, 1445, 1451, 1452, 1454, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1634, 1638, 1644, 1648, 1655, 1657, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1840, 1841, 1847, 1848, 1851, 1857, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2043, 2044, 2050, 2053, 2054, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2264, 2266, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2446, 2450, 2456, 2460, 2467, 2469, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2649, 2650, 2652, 2653, 2659, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2852, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3055, 3059, 3065, 3069, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3461, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3512, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3714, 3715, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4070, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4385, 4386, 4388, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 3 * y² + x + 3 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation344.lean b/equational_theories/Generated/FinitePoly/Refutation344.lean new file mode 100644 index 00000000..bdf7d19f --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation344.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 4 * x + 1 * y + 0 * x * y) % 5' (0, 22, 25, 30, 39, 1019, 1022, 1027, 1037, 1072, 1081, 1085, 1089, 1100, 1108, 1112, 1116, 1121, 1136, 1154, 1170, 1628, 1631, 1636, 1644, 1653, 1657, 1661, 1672, 1683, 1717, 1721, 1725, 1730, 1745, 1760, 1792, 1831, 1834, 1837, 1849, 1856, 1860, 1864, 1872, 1886, 1893, 1897, 1901, 1909, 1933, 1982, 1995, 2440, 2443, 2448, 2456, 2465, 2469, 2473, 2484, 2495, 2529, 2533, 2537, 2542, 2557, 2572, 2604, 2643, 2646, 2651, 2661, 2696, 2705, 2709, 2713, 2724, 2732, 2736, 2740, 2745, 2760, 2778, 2794, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3104, 3138, 3142, 3146, 3151, 3166, 3181, 3213, 3455, 3458, 3463, 3471, 3480, 3484, 3488, 3499, 3508, 3517, 3521, 3525, 3536, 3555, 3600, 3616, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3711, 3747, 3751, 3755, 3758, 3769, 3793, 3819, 4064, 4067, 4072, 4080, 4089, 4093, 4097, 4108, 4117, 4126, 4130, 4134, 4145, 4164, 4209, 4225, 4269, 4272, 4319, 4324, 4331, 4340, 4361, 4584, 4589, 4604, 4611, 4621, 4655, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 4 * x + y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 4 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 4 * x + y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [26, 31, 1090, 1101, 1117, 1137, 1155, 1171, 1673, 1726, 1761, 1793, 1865, 1902, 1910, 1983, 1996, 2474, 2538, 2558, 2573, 2714, 2725, 2741, 2746, 2779, 3079, 3147, 3182, 3214, 3489, 3500, 3601, 3617, 3692, 3756, 3770, 3794, 4098, 4109, 4210, 4325, 4332, 4341, 4612, 4684] [2, 3, 8, 24, 25, 28, 29, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1021, 1022, 1025, 1026, 1029, 1035, 1036, 1039, 1045, 1046, 1048, 1049, 1072, 1075, 1076, 1083, 1085, 1110, 1112, 1119, 1120, 1223, 1426, 1630, 1631, 1634, 1635, 1638, 1644, 1647, 1648, 1655, 1657, 1681, 1682, 1685, 1691, 1692, 1694, 1695, 1719, 1721, 1728, 1729, 1833, 1834, 1837, 1840, 1841, 1847, 1848, 1851, 1858, 1860, 1884, 1885, 1888, 1895, 1897, 1921, 1922, 1924, 1925, 1931, 1932, 2035, 2238, 2442, 2443, 2446, 2447, 2450, 2456, 2459, 2460, 2467, 2469, 2493, 2494, 2497, 2503, 2504, 2506, 2507, 2531, 2533, 2540, 2541, 2645, 2646, 2649, 2650, 2653, 2659, 2660, 2663, 2669, 2670, 2672, 2673, 2696, 2699, 2700, 2707, 2709, 2734, 2736, 2743, 2744, 2847, 3051, 3052, 3055, 3056, 3059, 3065, 3068, 3069, 3076, 3078, 3102, 3103, 3106, 3112, 3113, 3115, 3116, 3140, 3142, 3149, 3150, 3253, 3337, 3457, 3458, 3461, 3462, 3465, 3471, 3474, 3475, 3482, 3484, 3511, 3512, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3558, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3714, 3715, 3721, 3722, 3724, 3725, 3749, 3751, 3758, 3761, 3862, 4055, 4066, 4067, 4070, 4071, 4074, 4080, 4083, 4084, 4091, 4093, 4120, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4167, 4258, 4268, 4269, 4272, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4591, 4598, 4599, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 4 * x + y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation346.lean b/equational_theories/Generated/FinitePoly/Refutation346.lean new file mode 100644 index 00000000..79d242d1 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation346.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 0 * y**2 + 1 * x + 0 * y + 2 * x * y) % 4' (0, 358, 359, 376, 377, 378, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 4064, 4065, 4066, 4067, 4068, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4596, 4628, 4629, 4653, 4671) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + x + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + x + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [379, 3723, 3726, 3727, 3728, 3729, 4129, 4132, 4133, 4134, 4135, 4359, 4360, 4630, 4654] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 361, 362, 364, 365, 367, 368, 374, 375, 384, 385, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + x + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation352.lean b/equational_theories/Generated/FinitePoly/Refutation352.lean new file mode 100644 index 00000000..9e6e2692 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation352.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 3 * y**2 + 2 * x + 0 * y + 0 * x * y) % 4' (0, 42, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3341, 3345, 3349, 3352, 3354, 3363, 3369, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3544, 3548, 3552, 3555, 3557, 3566, 3572, 3861, 3869, 3879, 3886, 3914, 3916, 3923, 3927, 3942, 3950, 3954, 3961, 3963, 3978, 3996, 4012, 4022, 4025, 4064, 4072, 4082, 4089, 4117, 4119, 4126, 4130, 4145, 4153, 4157, 4164, 4166, 4181, 4199, 4215, 4225, 4228, 4269, 4282, 4340, 4357, 4379, 4387, 4397, 4404, 4434, 4441, 4468, 4481, 4496, 4530, 4543, 4589, 4621, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 3 * y² + 2 * x % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + 3 * y*y + 2 * x + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 3 * y² + 2 * x % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [3323, 3331, 3334, 3350, 3364, 3370, 3526, 3534, 3537, 3553, 3567, 3573, 3943, 3979, 3997, 4013, 4023, 4026, 4146, 4182, 4200, 4216, 4226, 4229, 4497, 4590, 4635] [8, 23, 40, 307, 359, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3258, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3309, 3316, 3318, 3343, 3345, 3352, 3457, 3458, 3461, 3472, 3474, 3481, 3482, 3512, 3519, 3521, 3659, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3878, 3881, 3888, 3890, 3918, 3925, 3927, 3952, 3954, 3961, 4067, 4068, 4070, 4071, 4080, 4081, 4084, 4121, 4128, 4155, 4268, 4269, 4273, 4275, 4284, 4290, 4314, 4320, 4321, 4381, 4382, 4383, 4385, 4386, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4584, 4585, 4587, 4588, 4598, 4599, 4605, 4606, 4658] := + ⟨Fin 4, «FinitePoly x² + 3 * y² + 2 * x % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation356.lean b/equational_theories/Generated/FinitePoly/Refutation356.lean new file mode 100644 index 00000000..b05427f1 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation356.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 0 * x + 2 * y + 2 * x * y) % 3' (0, 7, 9, 98, 100, 103, 106, 109, 358, 377, 410, 412, 425, 428, 431, 816, 818, 832, 835, 838, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1228, 1230, 1233, 1237, 1240, 1243, 1247, 1248, 1250, 1253, 1257, 1259, 1261, 1265, 1269, 1831, 1833, 1846, 1849, 1852, 3252, 3254, 3315, 3318, 3321, 3658, 3723, 3861, 3866, 3914, 3924, 3934, 4064, 4130, 4268, 4315) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 2 * y + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + 2 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 2 * y + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [10, 99, 378, 413, 426, 839, 1031, 1041, 1051, 1055, 1059, 1063, 1225, 1228, 1231, 1241, 1248, 1251, 1260, 1834, 1847, 1850, 3255, 3316, 3724, 3867, 3925, 4269] [2, 3, 9, 11, 13, 14, 16, 23, 38, 39, 40, 43, 47, 100, 102, 105, 108, 114, 115, 117, 118, 124, 125, 127, 151, 203, 255, 307, 331, 360, 361, 362, 364, 365, 367, 368, 374, 375, 377, 384, 385, 407, 412, 414, 416, 417, 419, 420, 427, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 614, 818, 820, 822, 823, 825, 826, 832, 835, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1023, 1026, 1029, 1036, 1039, 1046, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1226, 1232, 1239, 1242, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1833, 1835, 1837, 1838, 1840, 1841, 1848, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + 2 * y + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation364.lean b/equational_theories/Generated/FinitePoly/Refutation364.lean new file mode 100644 index 00000000..1032d4f3 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation364.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 3 * y**2 + 3 * x + 2 * y + 2 * x * y) % 4' (0, 2, 7, 9, 22, 46, 48, 51, 54, 57, 98, 100, 103, 106, 109, 150, 152, 202, 207, 254, 306, 308, 322, 325, 328, 358, 374, 377, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 613, 615, 618, 621, 624, 628, 631, 634, 638, 641, 644, 648, 652, 656, 660, 816, 818, 821, 824, 827, 831, 834, 837, 841, 844, 847, 851, 855, 859, 863, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1425, 1427, 1430, 1433, 1436, 1628, 1630, 1633, 1636, 1639, 1831, 1833, 1846, 1849, 1852, 2034, 2036, 2237, 2242, 2252, 2262, 2272, 2440, 2445, 2455, 2465, 2475, 2643, 2648, 2846, 2861, 3049, 3067, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3658, 3660, 3711, 3714, 3717, 3721, 3724, 3727, 3861, 3866, 3914, 3917, 3924, 3927, 3934, 3938, 4064, 4117, 4120, 4130, 4268, 4283, 4286, 4315, 4339, 4359, 4379, 4395, 4398, 4431, 4469, 4472, 4507, 4515, 4598) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 3 * y² + 3 * x + 2 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + 3 * y*y + 3 * x + 2 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 3 * y² + 3 * x + 2 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [10, 58, 153, 208, 329, 458, 629, 632, 639, 642, 819, 825, 835, 845, 1031, 1041, 1051, 1055, 1059, 1063, 1225, 1228, 1231, 1238, 1241, 1248, 1251, 1437, 1834, 1847, 1850, 2037, 2273, 2649, 2862, 3068, 3264, 3312, 3326, 3330, 3334, 3512, 3718, 3728, 3939, 4508, 4516] [2, 4, 5, 9, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 50, 53, 56, 62, 63, 65, 66, 72, 73, 75, 100, 102, 105, 108, 114, 115, 117, 118, 124, 125, 127, 152, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 205, 206, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 310, 312, 313, 315, 316, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 384, 385, 407, 412, 414, 417, 420, 427, 430, 437, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 617, 620, 623, 630, 633, 640, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 820, 823, 826, 833, 836, 843, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1023, 1026, 1029, 1036, 1039, 1046, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1226, 1229, 1232, 1239, 1242, 1249, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1429, 1432, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1632, 1635, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1835, 1837, 1838, 1840, 1841, 1848, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2244, 2246, 2247, 2254, 2256, 2257, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2447, 2449, 2450, 2457, 2459, 2460, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3256, 3259, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3315, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3459, 3462, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3714, 3721, 3724, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4270, 4272, 4273, 4275, 4276, 4283, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4398, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + 3 * y² + 3 * x + 2 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation366.lean b/equational_theories/Generated/FinitePoly/Refutation366.lean new file mode 100644 index 00000000..13e77120 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation366.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 1 * y**2 + 0 * x + 3 * y + 0 * x * y) % 4' (0, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4274, 4306, 4319, 4361, 4379, 4381, 4384, 4387, 4390, 4395, 4398, 4401, 4405, 4408, 4411, 4415, 4419, 4423, 4427, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + y² + 3 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + y*y + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + y² + 3 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [3388, 3414, 3541, 3837, 4428, 4682] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3352, 3355, 3457, 3459, 3462, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3665, 3667, 3668, 3675, 3677, 3678, 3685, 3687, 3714, 3715, 3721, 3724, 3725, 3748, 3751, 3752, 3758, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4383, 4386, 4398, 4405, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4585, 4588, 4591, 4598, 4605, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + y² + 3 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation370.lean b/equational_theories/Generated/FinitePoly/Refutation370.lean new file mode 100644 index 00000000..de45e988 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation370.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 0 * x + 3 * y + 0 * x * y) % 4' (0, 22, 30, 410, 512, 1628, 1636, 1717, 1730, 1745, 2237, 2245, 2255, 2262, 2292, 2299, 2326, 2339, 2354, 2388, 2401, 2440, 2448, 2458, 2465, 2495, 2502, 2529, 2542, 2557, 2591, 2604, 2643, 2651, 2661, 2668, 2698, 2705, 2732, 2745, 2760, 2794, 2807, 2846, 2854, 2864, 2871, 2901, 2908, 2935, 2948, 2963, 2997, 3010, 3049, 3057, 3067, 3074, 3104, 3111, 3138, 3151, 3166, 3200, 3213, 3455, 3463, 3508, 3521, 3536, 3658, 3683, 3711, 3758, 3819, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4082, 4089, 4117, 4130, 4145, 4157, 4164, 4199, 4225, 4319, 4361, 4589, 4621, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + 3 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + 2 * y*y + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + 3 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [31, 513, 1637, 1718, 1731, 2355, 2389, 2402, 2466, 2496, 2558, 2592, 2652, 2662, 2706, 2733, 2808, 2964, 2998, 3011, 3058, 3139, 3201, 3214, 3464, 3659, 3943, 3997, 4023, 4090, 4146, 4200, 4590, 4677] [8, 24, 25, 26, 28, 29, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 614, 817, 1020, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2239, 2240, 2241, 2243, 2244, 2247, 2253, 2254, 2257, 2264, 2266, 2267, 2290, 2291, 2294, 2301, 2303, 2304, 2328, 2330, 2331, 2337, 2338, 2442, 2443, 2444, 2446, 2447, 2450, 2456, 2457, 2460, 2467, 2469, 2470, 2493, 2494, 2497, 2504, 2506, 2507, 2531, 2533, 2534, 2540, 2541, 2645, 2646, 2647, 2649, 2650, 2653, 2659, 2660, 2663, 2670, 2672, 2673, 2696, 2697, 2700, 2707, 2709, 2710, 2734, 2736, 2737, 2743, 2744, 2848, 2849, 2850, 2852, 2853, 2856, 2862, 2863, 2866, 2873, 2875, 2876, 2899, 2900, 2903, 2910, 2912, 2913, 2937, 2939, 2940, 2946, 2947, 3051, 3052, 3053, 3055, 3056, 3059, 3065, 3066, 3069, 3076, 3078, 3079, 3102, 3103, 3106, 3113, 3115, 3116, 3140, 3142, 3143, 3149, 3150, 3253, 3459, 3462, 3472, 3474, 3481, 3511, 3518, 3545, 3549, 3556, 3661, 3667, 3674, 3677, 3715, 3725, 3749, 3752, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3878, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3961, 3964, 4275, 4380] := + ⟨Fin 4, «FinitePoly x² + 2 * y² + 3 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation374.lean b/equational_theories/Generated/FinitePoly/Refutation374.lean new file mode 100644 index 00000000..f9c6f3db --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation374.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 3 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 42, 3252, 3277, 3305, 3307, 3352, 3354, 3413, 3416, 3455, 3471, 3510, 3517, 3548, 3555, 3587, 3600, 3861, 3877, 3916, 3923, 3954, 3961, 3993, 4006, 4064, 4067, 4126, 4130, 4134, 4153, 4157, 4161, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 3 * y² + x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + 3 * y*y + x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 3 * y² + x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [3414, 3417, 3588, 3601, 3994, 4007, 4135, 4162] [2, 3, 8, 23, 38, 39, 40, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3279, 3281, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3474, 3475, 3481, 3482, 3484, 3509, 3512, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3555, 3558, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3880, 3881, 3887, 3888, 3890, 3915, 3918, 3925, 3927, 3928, 3951, 3952, 3954, 3961, 3964, 4055, 4066, 4067, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4128, 4130, 4155, 4157, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + 3 * y² + x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation380.lean b/equational_theories/Generated/FinitePoly/Refutation380.lean new file mode 100644 index 00000000..f0c545c2 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation380.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 1 * x + 1 * y + 1 * x * y) % 3' (0, 42, 150, 151, 152, 155, 165, 1425, 1426, 1427, 1428, 1429, 1628, 1630, 1633, 1636, 1639, 1831, 1836, 1846, 1856, 1866, 2034, 2049, 2086, 2123, 2160, 3252, 3257, 3455, 3456, 3861, 3876, 4064, 4066, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + x + y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + x + y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + x + y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [43, 152, 153, 156, 166, 1427, 1428, 1429, 1629, 1832, 2035, 3258, 3457, 3877, 4067] [2, 3, 8, 23, 38, 39, 40, 47, 99, 154, 157, 159, 160, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1632, 1635, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1838, 1840, 1841, 1848, 1850, 1851, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2125, 2127, 2128, 2134, 2135, 2137, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + x + y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation386.lean b/equational_theories/Generated/FinitePoly/Refutation386.lean new file mode 100644 index 00000000..c3191475 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation386.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 1 * x + 2 * y + 2 * x * y) % 4' (0, 306, 307, 308, 309, 310, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 4064, 4067, 4126, 4130, 4134, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + x + 2 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + x + 2 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + x + 2 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [311, 3258, 3259, 3261, 3262, 3457, 3459, 3462, 3465, 3730, 4135, 4359, 4360] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 312, 313, 315, 316, 323, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4066, 4067, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + x + 2 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation388.lean b/equational_theories/Generated/FinitePoly/Refutation388.lean new file mode 100644 index 00000000..b5b0b619 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation388.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 1 * y + 0 * x * y) % 4' (0, 42, 410, 439, 476, 503, 510, 512, 613, 642, 679, 706, 713, 715, 816, 845, 882, 909, 916, 918, 1019, 1048, 1085, 1112, 1119, 1121, 1222, 1251, 1288, 1315, 1322, 1324, 1425, 1454, 1491, 1518, 1525, 1527, 1628, 1657, 1694, 1721, 1728, 1730, 1831, 1860, 1897, 1924, 1931, 1933, 2034, 2063, 2100, 2127, 2134, 2136, 2237, 2266, 2303, 2330, 2337, 2339, 2440, 2469, 2506, 2533, 2540, 2542, 2643, 2672, 2709, 2736, 2743, 2745, 2846, 2875, 2912, 2939, 2946, 2948, 3049, 3078, 3115, 3142, 3149, 3151, 4282, 4289, 4319, 4357, 4361, 4363, 4368, 4379, 4395, 4397, 4404, 4432, 4434, 4441, 4472, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4597, 4604, 4634, 4672, 4676, 4678, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x + y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x + y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [43, 440, 477, 504, 511, 513, 643, 680, 707, 714, 716, 846, 883, 910, 917, 919, 1049, 1086, 1113, 1120, 1122, 1252, 1289, 1316, 1323, 1325, 1455, 1492, 1519, 1526, 1528, 1658, 1695, 1722, 1729, 1731, 1861, 1898, 1925, 1932, 1934, 2064, 2101, 2128, 2135, 2137, 2267, 2304, 2331, 2338, 2340, 2470, 2507, 2534, 2541, 2543, 2673, 2710, 2737, 2744, 2746, 2876, 2913, 2940, 2947, 2949, 3079, 3116, 3143, 3150, 3152, 4364, 4369, 4512, 4515, 4525, 4541, 4679, 4684] [2, 3, 8, 23, 38, 39, 40, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 463, 464, 466, 467, 473, 474, 476, 500, 501, 503, 510, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 666, 667, 669, 670, 676, 677, 679, 703, 704, 706, 713, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 869, 870, 872, 873, 879, 880, 882, 906, 907, 909, 916, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1109, 1110, 1112, 1119, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1312, 1313, 1315, 1322, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1515, 1516, 1518, 1525, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1718, 1719, 1721, 1728, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1921, 1922, 1924, 1931, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2124, 2125, 2127, 2134, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2327, 2328, 2330, 2337, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2530, 2531, 2533, 2540, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2733, 2734, 2736, 2743, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2936, 2937, 2939, 2946, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3139, 3140, 3142, 3149, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4284, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4399, 4406, 4408, 4436, 4443, 4445, 4470, 4472, 4479, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4599, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x + y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation390.lean b/equational_theories/Generated/FinitePoly/Refutation390.lean new file mode 100644 index 00000000..061e94c6 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation390.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 0 * y**2 + 1 * x + 0 * y + 2 * x * y) % 4' (0, 2, 7, 8, 22, 25, 46, 47, 48, 49, 50, 98, 99, 100, 101, 102, 150, 151, 158, 159, 160, 202, 204, 208, 211, 214, 254, 257, 260, 262, 306, 307, 324, 325, 326, 358, 361, 374, 376, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1425, 1426, 1427, 1428, 1429, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1628, 1629, 1630, 1631, 1632, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1831, 1832, 1836, 1837, 1838, 1849, 1850, 1851, 1859, 1860, 1861, 1870, 1871, 1872, 1873, 2034, 2035, 2042, 2043, 2044, 2052, 2053, 2054, 2059, 2060, 2061, 2237, 2239, 2242, 2245, 2248, 2253, 2256, 2259, 2263, 2266, 2269, 2273, 2277, 2281, 2285, 2440, 2442, 2445, 2448, 2451, 2456, 2459, 2462, 2466, 2469, 2472, 2476, 2480, 2484, 2488, 2643, 2645, 2649, 2652, 2655, 2659, 2662, 2665, 2668, 2671, 2674, 2846, 2849, 2851, 2855, 2859, 2862, 2864, 2872, 2874, 2882, 2885, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3658, 3659, 3666, 3667, 3668, 3713, 3714, 3715, 3720, 3721, 3722, 3861, 3863, 3867, 3870, 3873, 3914, 3917, 3920, 3923, 3926, 3929, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4267, 4281, 4313, 4314, 4338, 4356, 4379, 4382, 4394, 4398, 4402, 4432, 4434, 4469, 4471, 4506, 4509, 4584, 4597, 4655, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + x + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + x + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [9, 26, 48, 49, 50, 103, 161, 215, 258, 261, 263, 327, 362, 377, 425, 628, 822, 823, 825, 826, 1021, 1023, 1026, 1029, 1237, 1453, 1456, 1457, 1458, 1459, 1663, 1874, 2045, 2055, 2062, 2254, 2257, 2264, 2267, 2489, 2656, 2666, 2675, 2860, 2883, 2886, 3053, 3058, 3066, 3075, 3091, 3315, 3318, 3460, 3520, 3523, 3524, 3525, 3669, 3716, 3723, 3874, 3918, 3930, 4143, 4403, 4507, 4510, 4585, 4673] [2, 4, 5, 10, 11, 13, 14, 16, 24, 25, 28, 31, 38, 39, 40, 43, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 153, 154, 156, 157, 166, 167, 169, 170, 176, 177, 179, 204, 206, 208, 211, 218, 219, 221, 222, 228, 229, 231, 256, 257, 260, 264, 270, 271, 273, 274, 280, 281, 283, 309, 310, 312, 313, 315, 316, 323, 331, 332, 333, 335, 336, 360, 361, 364, 365, 367, 368, 374, 378, 384, 385, 407, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1834, 1835, 1840, 1841, 1847, 1848, 1857, 1858, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2037, 2038, 2040, 2041, 2050, 2051, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2241, 2244, 2247, 2253, 2256, 2263, 2266, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2444, 2447, 2450, 2456, 2459, 2466, 2469, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2647, 2649, 2652, 2659, 2662, 2670, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2853, 2855, 2862, 2866, 2872, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3055, 3059, 3065, 3069, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3661, 3662, 3664, 3665, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3865, 3867, 3870, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3925, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4070, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4385, 4386, 4388, 4396, 4398, 4405, 4406, 4408, 4436, 4442, 4443, 4445, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + x + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation394.lean b/equational_theories/Generated/FinitePoly/Refutation394.lean new file mode 100644 index 00000000..91d15d32 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation394.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 0 * x + 2 * y + 2 * x * y) % 4' (0, 42, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4379, 4380, 4381, 4382, 4383, 4384, 4385, 4386, 4387, 4388, 4389, 4390, 4391, 4392, 4393, 4394, 4395, 4396, 4397, 4398, 4399, 4400, 4401, 4402, 4403, 4404, 4405, 4406, 4407, 4408, 4409, 4410, 4411, 4412, 4413, 4414, 4415, 4416, 4417, 4418, 4419, 4420, 4421, 4422, 4423, 4424, 4425, 4426, 4427, 4428, 4429, 4430, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 4440, 4441, 4442, 4443, 4444, 4445, 4446, 4447, 4448, 4449, 4450, 4451, 4452, 4453, 4454, 4455, 4456, 4457, 4458, 4459, 4460, 4461, 4462, 4463, 4464, 4465, 4466, 4467, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4478, 4479, 4480, 4481, 4482, 4483, 4484, 4485, 4486, 4487, 4488, 4489, 4490, 4491, 4492, 4493, 4494, 4495, 4496, 4497, 4498, 4499, 4500, 4501, 4502, 4503, 4504, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4522, 4523, 4524, 4525, 4526, 4527, 4528, 4529, 4530, 4531, 4532, 4533, 4534, 4535, 4536, 4537, 4538, 4539, 4540, 4541, 4542, 4543, 4544, 4545, 4546, 4547, 4548, 4549, 4550, 4551, 4552, 4553, 4554, 4555, 4556, 4557, 4558, 4559, 4560, 4561, 4562, 4563, 4564, 4565, 4566, 4567, 4568, 4569, 4570, 4571, 4572, 4573, 4574, 4575, 4576, 4577, 4578, 4579, 4580, 4581, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + 2 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * y*y + 2 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + 2 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [4368, 4373, 4582, 4683, 4688] [2, 3, 8, 23, 38, 39, 40, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258] := + ⟨Fin 4, «FinitePoly 2 * y² + 2 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation40.lean b/equational_theories/Generated/FinitePoly/Refutation40.lean new file mode 100644 index 00000000..39bfaa5c --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation40.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 0 * y**2 + 3 * x + 0 * y + 0 * x * y) % 4' (0, 37, 41, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 358, 359, 360, 361, 362, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 3870, 3871, 3872, 3873, 3874, 3875, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4380, 4381, 4382, 4383, 4394, 4395, 4396, 4397, 4398, 4399, 4400, 4401, 4402, 4403, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 4440, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 3 * x % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + 3 * x + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 3 * x % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [383, 3734, 3738, 3742, 3743, 3744, 3745, 3746, 3915, 3919, 3922, 3926, 3929, 3932, 3936, 3940, 3944, 4153, 4359, 4384, 4400, 4402, 4437, 4439, 4474, 4476, 4512, 4515, 4674] [2, 3, 8, 23, 39, 40, 43, 47, 99, 151, 203, 255, 312, 313, 315, 316, 332, 333, 335, 336, 364, 365, 367, 368, 384, 385, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4385, 4386, 4388, 4405, 4406, 4408, 4442, 4443, 4445, 4479, 4480, 4482, 4539, 4547, 4571, 4587, 4588, 4590, 4591, 4605, 4606, 4608, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + 3 * x % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation400.lean b/equational_theories/Generated/FinitePoly/Refutation400.lean new file mode 100644 index 00000000..eeb9823d --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation400.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 0 * x + 0 * y + 2 * x * y) % 4' (0, 42, 306, 307, 308, 309, 310, 358, 360, 363, 366, 369, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4381, 4384, 4387, 4390, 4394, 4397, 4400, 4404, 4407, 4410, 4414, 4418, 4422, 4426, 4431, 4434, 4437, 4441, 4444, 4447, 4451, 4455, 4459, 4463, 4468, 4471, 4474, 4478, 4481, 4484, 4488, 4492, 4496, 4500, 4505, 4509, 4513, 4517, 4522, 4526, 4530, 4534, 4539, 4543, 4547, 4551, 4556, 4561, 4566, 4571, 4576, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 43, 311, 370, 3258, 3259, 3261, 3262, 3457, 3459, 3462, 3465, 3877, 3880, 3887, 3890, 4067, 4073, 4083, 4093, 4577, 4682] [2, 3, 8, 23, 38, 39, 40, 47, 99, 151, 203, 255, 312, 313, 315, 316, 323, 325, 326, 331, 332, 333, 335, 336, 360, 362, 365, 368, 374, 375, 377, 378, 384, 385, 387, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3863, 3865, 3868, 3871, 3878, 3881, 3888, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4068, 4071, 4074, 4081, 4084, 4091, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4381, 4383, 4386, 4396, 4399, 4406, 4433, 4436, 4443, 4470, 4473, 4480, 4539, 4547, 4571, 4583, 4585, 4588, 4591, 4598, 4605, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 2 * y² + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation402.lean b/equational_theories/Generated/FinitePoly/Refutation402.lean new file mode 100644 index 00000000..2c5d9bac --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation402.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 3 * y + 0 * x * y) % 4' (0, 7, 10, 15, 39, 410, 413, 418, 426, 435, 439, 443, 454, 465, 499, 503, 507, 512, 527, 542, 574, 816, 819, 822, 834, 841, 845, 849, 857, 869, 905, 909, 913, 916, 927, 951, 977, 1019, 1022, 1027, 1035, 1044, 1048, 1052, 1063, 1074, 1108, 1112, 1116, 1121, 1136, 1151, 1183, 1628, 1634, 1636, 1644, 1646, 1657, 1669, 1672, 1690, 1717, 1728, 1730, 1739, 1745, 1773, 1779, 1831, 1834, 1839, 1847, 1856, 1860, 1864, 1875, 1886, 1920, 1924, 1928, 1933, 1948, 1963, 1995, 2440, 2443, 2446, 2458, 2465, 2469, 2473, 2481, 2493, 2529, 2533, 2537, 2540, 2551, 2575, 2601, 3049, 3078, 3102, 3104, 3111, 3138, 3252, 3255, 3260, 3268, 3277, 3281, 3285, 3296, 3305, 3314, 3318, 3322, 3333, 3352, 3397, 3413, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3713, 3720, 3724, 3728, 3736, 3760, 3809, 3822, 3861, 3864, 3869, 3877, 3886, 3890, 3894, 3905, 3914, 3923, 3927, 3931, 3942, 3961, 4006, 4022, 4269, 4274, 4289, 4296, 4306, 4340, 4368, 4587, 4589, 4597, 4619, 4621, 4646, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x + 3 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x + 3 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [11, 436, 455, 508, 543, 914, 928, 952, 978, 1053, 1117, 1137, 1152, 1670, 1673, 1740, 1746, 1774, 1876, 1929, 1964, 1996, 2474, 2482, 2538, 2552, 2576, 2602, 3079, 3103, 3105, 3112, 3139, 3286, 3297, 3398, 3692, 3737, 3810, 3823, 3895, 3906, 3932, 4007, 4297, 4620, 4622, 4647] [2, 3, 9, 10, 13, 14, 23, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 416, 417, 420, 426, 429, 430, 437, 439, 463, 464, 467, 473, 474, 476, 477, 501, 503, 510, 511, 614, 818, 819, 822, 825, 826, 832, 833, 836, 843, 845, 869, 872, 873, 879, 880, 882, 883, 907, 909, 916, 919, 1021, 1022, 1025, 1026, 1029, 1035, 1038, 1039, 1046, 1048, 1072, 1073, 1076, 1082, 1083, 1085, 1086, 1110, 1112, 1119, 1120, 1223, 1426, 1630, 1631, 1632, 1634, 1638, 1644, 1648, 1654, 1655, 1657, 1681, 1682, 1684, 1685, 1692, 1694, 1695, 1719, 1721, 1722, 1728, 1833, 1834, 1837, 1838, 1841, 1847, 1850, 1851, 1858, 1860, 1884, 1885, 1888, 1894, 1895, 1897, 1898, 1922, 1924, 1931, 1932, 2035, 2238, 2442, 2443, 2446, 2449, 2450, 2456, 2457, 2460, 2467, 2469, 2493, 2496, 2497, 2503, 2504, 2506, 2507, 2531, 2533, 2540, 2543, 2644, 2847, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3102, 3106, 3113, 3115, 3116, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3258, 3259, 3262, 3268, 3271, 3272, 3279, 3281, 3308, 3309, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3355, 3456, 3543, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3712, 3715, 3722, 3724, 3748, 3749, 3751, 3752, 3758, 3759, 3863, 3864, 3867, 3868, 3871, 3877, 3880, 3881, 3888, 3890, 3917, 3918, 3925, 3927, 3951, 3952, 3954, 3955, 3961, 3964, 4055, 4065, 4258, 4268, 4269, 4272, 4273, 4276, 4283, 4284, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x + 3 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation404.lean b/equational_theories/Generated/FinitePoly/Refutation404.lean new file mode 100644 index 00000000..a2f1677c --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation404.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 0 * x + 1 * y + 2 * x * y) % 4' (0, 2, 7, 15, 22, 27, 46, 54, 64, 71, 98, 103, 116, 126, 137, 150, 158, 165, 178, 193, 202, 207, 217, 227, 237, 254, 259, 269, 279, 289, 306, 314, 325, 332, 358, 363, 374, 384, 394, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 618, 631, 641, 652, 668, 678, 689, 702, 712, 722, 816, 824, 831, 844, 859, 871, 878, 908, 915, 946, 959, 1019, 1024, 1034, 1044, 1054, 1074, 1084, 1095, 1111, 1121, 1132, 1149, 1166, 1183, 1201, 1222, 1227, 1237, 1247, 1257, 1277, 1287, 1298, 1314, 1324, 1335, 1352, 1369, 1386, 1404, 1425, 1433, 1443, 1450, 1477, 1490, 1505, 1517, 1524, 1559, 1585, 1628, 1633, 1646, 1656, 1667, 1680, 1690, 1700, 1720, 1730, 1741, 1762, 1779, 1796, 1815, 1831, 1839, 1846, 1859, 1874, 1883, 1896, 1911, 1920, 1933, 1948, 1957, 1978, 1999, 2023, 2034, 2042, 2049, 2062, 2077, 2086, 2099, 2114, 2123, 2136, 2151, 2160, 2181, 2202, 2226, 2237, 2242, 2252, 2262, 2272, 2289, 2299, 2309, 2326, 2336, 2346, 2363, 2380, 2397, 2414, 2440, 2445, 2455, 2465, 2475, 2492, 2502, 2512, 2529, 2539, 2549, 2566, 2583, 2600, 2617, 2643, 2648, 2658, 2668, 2678, 2695, 2705, 2715, 2732, 2742, 2752, 2769, 2786, 2803, 2820, 2846, 2851, 2861, 2871, 2881, 2898, 2908, 2918, 2935, 2945, 2955, 2972, 2989, 3006, 3023, 3049, 3054, 3064, 3074, 3084, 3101, 3111, 3121, 3138, 3148, 3158, 3175, 3192, 3209, 3226, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3460, 3473, 3483, 3494, 3511, 3521, 3532, 3545, 3555, 3565, 3658, 3666, 3673, 3686, 3701, 3714, 3721, 3751, 3758, 3789, 3802, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4274, 4306, 4319, 4361, 4379, 4384, 4398, 4408, 4419, 4434, 4444, 4455, 4469, 4479, 4489, 4586, 4605, 4614, 4644, 4665, 4688) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * y*y + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 28, 55, 65, 72, 138, 194, 238, 315, 333, 395, 419, 436, 466, 500, 562, 653, 690, 723, 860, 947, 960, 1202, 1278, 1288, 1315, 1325, 1506, 1560, 1586, 1816, 2024, 2043, 2063, 2100, 2137, 2415, 2493, 2503, 2530, 2540, 2649, 2669, 2706, 2743, 2852, 2862, 2872, 2899, 2909, 2936, 2946, 3055, 3065, 3075, 3102, 3112, 3139, 3149, 3388, 3495, 3512, 3566, 3702, 3790, 3803, 3897, 3935, 3972, 3989, 4006, 4155, 4165, 4420, 4456, 4490, 4615, 4645] [2, 4, 5, 9, 10, 11, 13, 14, 24, 25, 26, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 56, 62, 63, 66, 73, 75, 100, 101, 102, 105, 107, 108, 114, 115, 118, 124, 125, 152, 153, 154, 156, 157, 160, 167, 169, 170, 176, 177, 204, 205, 206, 209, 211, 212, 219, 221, 222, 229, 231, 256, 257, 258, 261, 263, 264, 271, 273, 274, 281, 283, 308, 309, 310, 312, 313, 316, 323, 325, 331, 332, 335, 336, 360, 361, 362, 365, 367, 368, 374, 377, 378, 384, 407, 412, 413, 414, 416, 417, 420, 426, 427, 430, 437, 439, 440, 463, 464, 467, 474, 476, 477, 501, 503, 504, 510, 511, 615, 616, 617, 620, 622, 623, 629, 630, 633, 639, 640, 643, 666, 667, 670, 676, 677, 680, 704, 706, 707, 714, 716, 818, 819, 820, 822, 823, 826, 833, 835, 836, 842, 843, 846, 869, 870, 873, 880, 882, 883, 906, 907, 910, 917, 919, 1021, 1022, 1023, 1026, 1028, 1029, 1036, 1038, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1082, 1083, 1086, 1109, 1110, 1113, 1119, 1120, 1224, 1225, 1226, 1229, 1231, 1232, 1239, 1241, 1242, 1249, 1251, 1252, 1275, 1276, 1279, 1285, 1286, 1289, 1312, 1313, 1316, 1322, 1323, 1427, 1428, 1429, 1431, 1432, 1435, 1441, 1442, 1445, 1452, 1454, 1455, 1479, 1481, 1482, 1488, 1489, 1492, 1515, 1516, 1519, 1526, 1528, 1630, 1631, 1632, 1635, 1637, 1638, 1644, 1645, 1648, 1654, 1655, 1658, 1682, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1848, 1850, 1851, 1857, 1858, 1861, 1885, 1887, 1888, 1894, 1895, 1898, 1922, 1924, 1925, 1931, 1932, 2036, 2037, 2038, 2040, 2041, 2044, 2051, 2053, 2054, 2060, 2061, 2064, 2088, 2090, 2091, 2097, 2098, 2101, 2125, 2127, 2128, 2134, 2135, 2239, 2240, 2241, 2244, 2246, 2247, 2254, 2256, 2257, 2264, 2266, 2267, 2291, 2293, 2294, 2301, 2303, 2304, 2328, 2330, 2331, 2338, 2340, 2442, 2443, 2444, 2447, 2449, 2450, 2457, 2459, 2460, 2467, 2469, 2470, 2494, 2496, 2497, 2504, 2506, 2507, 2531, 2533, 2534, 2541, 2543, 2645, 2646, 2647, 2650, 2652, 2653, 2660, 2662, 2663, 2670, 2672, 2673, 2697, 2699, 2700, 2707, 2709, 2710, 2734, 2736, 2737, 2744, 2746, 2848, 2849, 2850, 2853, 2855, 2856, 2863, 2865, 2866, 2873, 2875, 2876, 2900, 2902, 2903, 2910, 2912, 2913, 2937, 2939, 2940, 2947, 2949, 3051, 3052, 3053, 3056, 3058, 3059, 3066, 3068, 3069, 3076, 3078, 3079, 3103, 3105, 3106, 3113, 3115, 3116, 3140, 3142, 3143, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3352, 3355, 3457, 3458, 3459, 3462, 3464, 3465, 3471, 3472, 3475, 3481, 3482, 3509, 3511, 3518, 3519, 3521, 3543, 3545, 3548, 3549, 3555, 3558, 3660, 3661, 3662, 3664, 3665, 3668, 3675, 3677, 3678, 3684, 3685, 3712, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3758, 3761, 3863, 3864, 3865, 3868, 3870, 3871, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3927, 3928, 3951, 3954, 3955, 3961, 3964, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4081, 4083, 4084, 4091, 4093, 4120, 4121, 4127, 4130, 4131, 4154, 4157, 4158, 4164, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4386, 4388, 4396, 4398, 4405, 4406, 4408, 4433, 4436, 4442, 4443, 4472, 4473, 4479, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4588, 4590, 4591, 4598, 4599, 4605, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * y² + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation406.lean b/equational_theories/Generated/FinitePoly/Refutation406.lean new file mode 100644 index 00000000..7884a4e6 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation406.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 2 * x + 1 * y + 2 * x * y) % 4' (0, 410, 428, 472, 512, 561, 613, 621, 668, 675, 1425, 1443, 1480, 1514, 1628, 1636, 1717, 1730, 1745, 3658, 3683, 3724, 3751, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4082, 4089, 4117, 4130, 4145, 4157, 4164, 4199, 4225, 4379, 4387, 4472, 4479, 4589, 4621, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + 2 * x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + 2 * y*y + 2 * x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + 2 * x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [562, 622, 669, 676, 1444, 1481, 1515, 1746, 3684, 3725, 3752, 3943, 3997, 4023, 4200, 4226, 4388, 4473, 4480, 4590, 4677] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 430, 436, 437, 439, 440, 463, 464, 466, 467, 474, 476, 477, 500, 501, 503, 504, 510, 511, 615, 616, 617, 619, 620, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 670, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 817, 1020, 1223, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1482, 1488, 1489, 1491, 1492, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3748, 3749, 3751, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3878, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3961, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4074, 4080, 4081, 4084, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4164, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4479, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + 2 * y² + 2 * x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation408.lean b/equational_theories/Generated/FinitePoly/Refutation408.lean new file mode 100644 index 00000000..fd8e9a58 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation408.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 2 * x + 1 * y + 0 * x * y) % 5' (0, 3049, 3055, 3067, 3078, 3090) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + 2 * x + y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 2 * y*y + 2 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + 2 * x + y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [3091] [23, 1426, 1629, 1832, 2238, 2441, 3053, 3058, 3066, 3075, 3253, 3456, 4065, 4585, 4598] := + ⟨Fin 5, «FinitePoly 2 * y² + 2 * x + y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation410.lean b/equational_theories/Generated/FinitePoly/Refutation410.lean new file mode 100644 index 00000000..c5a69d82 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation410.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 1 * x + 0 * y + 2 * x * y) % 3' (0, 2, 7, 22, 27, 46, 98, 103, 150, 165, 202, 217, 227, 254, 259, 269, 279, 289, 306, 322, 325, 358, 363, 374, 410, 613, 618, 816, 831, 1019, 1034, 1044, 1222, 1227, 1237, 1247, 1257, 1425, 1477, 1480, 1488, 1628, 1633, 1680, 1690, 1700, 1831, 1883, 1920, 2034, 2049, 2050, 2086, 2123, 2160, 2237, 2289, 2326, 2336, 2440, 2455, 2492, 2502, 2529, 2532, 2539, 2566, 2583, 2643, 2658, 2668, 2695, 2705, 2732, 2742, 2769, 2786, 2846, 2851, 2861, 2871, 2881, 2898, 2908, 2918, 2935, 2945, 2955, 2972, 2989, 3006, 3023, 3049, 3054, 3064, 3067, 3074, 3084, 3101, 3111, 3121, 3138, 3148, 3158, 3175, 3192, 3209, 3226, 3252, 3305, 3308, 3318, 3455, 3460, 3508, 3510, 3511, 3521, 3532, 3658, 3673, 3711, 3714, 3721, 3861, 3876, 3886, 3914, 3924, 3954, 4064, 4069, 4079, 4089, 4099, 4117, 4154, 4191, 4283, 4320, 4379, 4384, 4395, 4469, 4586, 4665) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3, 28, 104, 166, 218, 228, 323, 364, 619, 832, 1035, 1045, 1478, 1481, 1489, 1634, 1681, 1691, 1884, 1921, 2051, 2290, 2327, 2337, 2493, 2530, 2533, 2584, 2669, 2787, 2852, 2862, 2872, 2899, 2909, 2936, 2946, 3055, 3065, 3068, 3075, 3102, 3112, 3139, 3149, 3309, 3461, 3509, 3511, 3512, 3674, 3712, 3877, 3887, 3925, 3955, 4155, 4284, 4321, 4385, 4396, 4587] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 167, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 219, 221, 222, 229, 231, 256, 257, 258, 261, 263, 264, 271, 273, 274, 281, 283, 308, 309, 310, 312, 313, 315, 316, 325, 331, 332, 333, 335, 336, 360, 361, 362, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 617, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1036, 1038, 1039, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1229, 1231, 1232, 1239, 1241, 1242, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1479, 1482, 1488, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1682, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2053, 2054, 2060, 2061, 2063, 2064, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2328, 2330, 2331, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2494, 2496, 2497, 2504, 2506, 2507, 2531, 2534, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2660, 2662, 2663, 2670, 2672, 2673, 2697, 2699, 2700, 2707, 2709, 2710, 2734, 2736, 2737, 2744, 2746, 2804, 2848, 2849, 2850, 2853, 2855, 2856, 2863, 2865, 2866, 2873, 2875, 2876, 2900, 2902, 2903, 2910, 2912, 2913, 2937, 2939, 2940, 2947, 2949, 3051, 3052, 3053, 3056, 3058, 3059, 3066, 3069, 3076, 3078, 3079, 3103, 3105, 3106, 3113, 3115, 3116, 3140, 3142, 3143, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3675, 3677, 3678, 3684, 3685, 3687, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3927, 3928, 3951, 3952, 3954, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4081, 4083, 4084, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4290, 4291, 4293, 4314, 4320, 4343, 4368, 4373, 4381, 4382, 4383, 4386, 4388, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y² + x + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation418.lean b/equational_theories/Generated/FinitePoly/Refutation418.lean new file mode 100644 index 00000000..c22ef9b2 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation418.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 3 * y**2 + 1 * x + 0 * y + 0 * x * y) % 4' (0, 7, 10, 410, 413, 416, 418, 426, 428, 435, 439, 443, 451, 454, 613, 616, 619, 621, 629, 631, 638, 642, 646, 654, 657, 816, 819, 822, 824, 832, 834, 841, 845, 849, 857, 860, 1019, 1022, 1025, 1027, 1035, 1037, 1044, 1048, 1052, 1060, 1063, 1222, 1225, 1228, 1230, 1238, 1240, 1247, 1251, 1255, 1263, 1266, 1831, 1834, 1856, 1860, 1864, 3049, 3078, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3661, 3720, 3724, 3728, 3861, 3869, 3914, 3927, 3942, 4269, 4282, 4340, 4357, 4597, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * y² + x % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * y*y + x + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * y² + x % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [414, 452, 455, 647, 655, 658, 820, 842, 861, 1028, 1036, 1053, 1061, 1256, 1264, 1267, 1835, 1857, 3079, 3256, 3315, 3331, 3526, 3534, 3537, 3659, 3870, 4270] [9, 10, 13, 14, 16, 23, 40, 43, 99, 255, 412, 413, 416, 420, 426, 430, 437, 439, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 619, 623, 629, 633, 640, 642, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 822, 826, 832, 836, 843, 845, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1025, 1029, 1035, 1039, 1046, 1048, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1228, 1232, 1238, 1242, 1249, 1251, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1833, 1834, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3269, 3271, 3278, 3342, 3346, 3353, 3355, 3457, 3458, 3461, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3512, 3519, 3521, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3664, 3665, 3667, 3675, 3677, 3684, 3712, 3714, 3715, 3724, 3748, 3752, 3759, 3761, 3865, 3868, 3878, 3880, 3887, 3917, 3924, 3951, 3955, 3962, 3964, 4065, 4273, 4275, 4290, 4320, 4380, 4585, 4588, 4590, 4605, 4635] := + ⟨Fin 4, «FinitePoly 3 * y² + x % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation420.lean b/equational_theories/Generated/FinitePoly/Refutation420.lean new file mode 100644 index 00000000..7df94d3c --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation420.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 4 * y + 0 * x * y) % 5' (0, 2, 7, 15, 22, 46, 54, 71, 98, 117, 126, 150, 166, 178, 202, 208, 221, 227, 254, 260, 273, 306, 314, 325, 358, 374, 383, 410, 418, 435, 465, 473, 499, 512, 527, 574, 613, 632, 641, 668, 676, 702, 816, 832, 844, 882, 908, 915, 1019, 1025, 1038, 1044, 1074, 1085, 1097, 1121, 1183, 1222, 1228, 1241, 1278, 1312, 1324, 1425, 1433, 1443, 1451, 1481, 1524, 1628, 1646, 1654, 1681, 1690, 1721, 1730, 1763, 1779, 1831, 1839, 1850, 1884, 1897, 1912, 1920, 1933, 1948, 2034, 2053, 2060, 2100, 2124, 2136, 2237, 2253, 2262, 2303, 2326, 2440, 2449, 2466, 2496, 2505, 2530, 2539, 2643, 2649, 2659, 2698, 2709, 2721, 2736, 2742, 2775, 2846, 2864, 2872, 2902, 2911, 2935, 3049, 3055, 3067, 3078, 3090, 3102, 3114, 3142, 3184, 3252, 3260, 3277, 3305, 3318, 3333, 3344, 3352, 3413, 3455, 3474, 3483, 3521, 3547, 3555, 3658, 3674, 3686, 3714, 3721, 3747, 3861, 3867, 3880, 3886, 3914, 3950, 3961, 3972, 4022, 4064, 4070, 4083, 4117, 4129, 4163, 4274, 4306, 4320, 4379, 4408, 4434, 4442, 4469, 4478, 4604, 4635, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + 4 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 2 * x + 4 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + 4 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 55, 72, 118, 127, 167, 179, 209, 222, 228, 261, 274, 315, 384, 419, 436, 466, 474, 500, 513, 633, 642, 669, 677, 703, 833, 845, 883, 909, 916, 1039, 1045, 1098, 1122, 1229, 1242, 1279, 1313, 1325, 1434, 1444, 1452, 1482, 1525, 1655, 1764, 1851, 1913, 1921, 1934, 2054, 2061, 2101, 2125, 2137, 2254, 2263, 2304, 2327, 2450, 2467, 2497, 2506, 2531, 2540, 2722, 2743, 2776, 2865, 2873, 2903, 2912, 2936, 3091, 3115, 3185, 3345, 3475, 3484, 3548, 3556, 3675, 3687, 3748, 3881, 3887, 3973, 4071, 4084, 4164, 4321, 4409, 4435, 4443, 4479, 4636, 4684] [2, 4, 5, 9, 10, 11, 13, 14, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 56, 62, 63, 65, 66, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 124, 125, 152, 153, 154, 156, 157, 159, 160, 166, 169, 170, 176, 177, 204, 205, 206, 208, 211, 212, 218, 219, 221, 229, 231, 256, 257, 258, 260, 263, 264, 270, 271, 273, 280, 281, 283, 308, 309, 310, 312, 313, 316, 323, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 385, 407, 412, 413, 414, 416, 417, 420, 426, 427, 429, 430, 437, 439, 440, 463, 464, 467, 473, 476, 477, 501, 503, 504, 510, 511, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 639, 640, 643, 666, 667, 670, 676, 679, 680, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 835, 836, 842, 843, 846, 869, 870, 872, 873, 879, 880, 882, 906, 907, 910, 917, 919, 1021, 1022, 1023, 1025, 1028, 1029, 1035, 1036, 1038, 1046, 1048, 1049, 1072, 1073, 1076, 1082, 1083, 1085, 1109, 1110, 1112, 1113, 1119, 1120, 1224, 1225, 1226, 1228, 1231, 1232, 1238, 1239, 1241, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1285, 1286, 1288, 1289, 1312, 1315, 1316, 1322, 1323, 1427, 1428, 1429, 1431, 1432, 1435, 1441, 1442, 1445, 1451, 1454, 1455, 1478, 1479, 1481, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1648, 1654, 1657, 1658, 1681, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1721, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1847, 1848, 1850, 1857, 1858, 1860, 1861, 1884, 1887, 1888, 1894, 1895, 1897, 1922, 1924, 1925, 1931, 1932, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2060, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2124, 2127, 2128, 2134, 2135, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2256, 2257, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2456, 2457, 2459, 2460, 2466, 2469, 2470, 2493, 2494, 2496, 2503, 2504, 2507, 2530, 2533, 2534, 2541, 2543, 2645, 2646, 2647, 2649, 2652, 2653, 2659, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2700, 2706, 2707, 2709, 2733, 2734, 2736, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2866, 2872, 2875, 2876, 2899, 2900, 2902, 2909, 2910, 2913, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3105, 3106, 3112, 3113, 3116, 3139, 3140, 3142, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3271, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3346, 3352, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3481, 3482, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3549, 3555, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3677, 3678, 3684, 3685, 3712, 3714, 3721, 3724, 3725, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3870, 3871, 3877, 3878, 3880, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3952, 3954, 3955, 3961, 3964, 4055, 4066, 4067, 4068, 4070, 4073, 4074, 4080, 4081, 4083, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4131, 4154, 4155, 4157, 4158, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4436, 4442, 4445, 4472, 4473, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4606, 4608, 4629, 4635, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 2 * x + 4 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation422.lean b/equational_theories/Generated/FinitePoly/Refutation422.lean new file mode 100644 index 00000000..90dfcf76 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation422.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 22, 25, 410, 416, 428, 439, 451, 463, 472, 503, 512, 545, 561, 816, 824, 832, 845, 860, 871, 878, 909, 916, 948, 961, 1019, 1025, 1037, 1048, 1060, 1072, 1081, 1112, 1121, 1154, 1170, 1628, 1631, 1653, 1657, 1661, 1681, 1683, 1728, 1730, 1789, 1792, 1831, 1837, 1849, 1860, 1872, 1884, 1893, 1924, 1933, 1966, 1982, 2440, 2448, 2456, 2469, 2484, 2495, 2502, 2533, 2540, 2572, 2585, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3455, 3458, 3471, 3473, 3517, 3521, 3525, 3555, 3557, 3600, 3606, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4272, 4289, 4331, 4368, 4584, 4597, 4655, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * y*y + x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [26, 452, 546, 562, 861, 949, 962, 1061, 1155, 1171, 1632, 1658, 1790, 1793, 1838, 1861, 1967, 1983, 2449, 2470, 2573, 2586, 3053, 3066, 3075, 3459, 3601, 3607, 4073, 4143, 4332, 4369, 4585] [8, 29, 31, 40, 43, 412, 413, 414, 416, 419, 420, 426, 427, 430, 436, 437, 439, 463, 466, 467, 474, 476, 477, 500, 501, 503, 510, 511, 614, 818, 819, 820, 822, 823, 826, 832, 835, 836, 842, 843, 845, 869, 870, 873, 880, 882, 883, 906, 907, 909, 916, 919, 1023, 1028, 1036, 1045, 1075, 1086, 1109, 1120, 1223, 1426, 1635, 1637, 1645, 1647, 1691, 1695, 1718, 1722, 1835, 1840, 1848, 1857, 1887, 1898, 1921, 1932, 2035, 2238, 2444, 2447, 2459, 2466, 2494, 2507, 2530, 2543, 2644, 2847, 3103, 3105, 3112, 3116, 3139, 3143, 3150, 3152, 3253, 3462, 3464, 3481, 3509, 3511, 3545, 3549, 3659, 3862, 4081, 4083, 4090, 4154, 4158, 4165, 4167, 4270, 4275, 4283, 4320, 4380, 4588, 4590, 4605, 4635] := + ⟨Fin 4, «FinitePoly 2 * y² + x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation424.lean b/equational_theories/Generated/FinitePoly/Refutation424.lean new file mode 100644 index 00000000..862c2d8e --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation424.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 0 * x + 0 * y + 0 * x * y) % 3' (0, 42, 306, 325, 331, 358, 374, 386, 3252, 3318, 3341, 3455, 3521, 3544, 3658, 3714, 3757, 3861, 3914, 3963, 4064, 4117, 4166, 4282, 4342, 4357, 4379, 4397, 4404, 4434, 4441, 4469, 4481, 4530, 4543, 4607, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [326, 332, 375, 387, 3522, 3545, 3758, 3915, 3964, 4343, 4358, 4470, 4544, 4608, 4635] [2, 3, 8, 23, 38, 39, 40, 47, 99, 151, 203, 255, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4472, 4473, 4479, 4480, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y² % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation426.lean b/equational_theories/Generated/FinitePoly/Refutation426.lean new file mode 100644 index 00000000..ae88afe8 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation426.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 1 * y + 0 * x * y) % 3' (0, 22, 25, 30, 39, 46, 49, 52, 62, 74, 1019, 1022, 1027, 1037, 1045, 1072, 1081, 1085, 1089, 1100, 1108, 1112, 1116, 1121, 1136, 1154, 1170, 1628, 1631, 1636, 1644, 1653, 1657, 1661, 1672, 1683, 1691, 1717, 1721, 1725, 1730, 1745, 1760, 1792, 1831, 1834, 1837, 1849, 1856, 1860, 1864, 1872, 1886, 1893, 1897, 1901, 1909, 1921, 1933, 1982, 1995, 2440, 2443, 2448, 2456, 2465, 2469, 2473, 2484, 2495, 2503, 2529, 2533, 2537, 2542, 2557, 2572, 2604, 2643, 2646, 2651, 2661, 2669, 2696, 2705, 2709, 2713, 2724, 2732, 2736, 2740, 2745, 2760, 2778, 2794, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3104, 3112, 3138, 3142, 3146, 3151, 3166, 3181, 3213, 3455, 3458, 3463, 3471, 3480, 3484, 3488, 3499, 3508, 3517, 3521, 3525, 3536, 3547, 3555, 3600, 3616, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3711, 3723, 3747, 3751, 3755, 3758, 3769, 3793, 3819, 4064, 4067, 4072, 4080, 4089, 4093, 4097, 4108, 4117, 4126, 4130, 4134, 4145, 4156, 4164, 4209, 4225, 4269, 4272, 4292, 4319, 4324, 4331, 4340, 4361, 4584, 4589, 4604, 4611, 4621, 4635, 4655, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [26, 50, 53, 63, 75, 1046, 1090, 1101, 1117, 1137, 1155, 1171, 1673, 1692, 1726, 1761, 1793, 1865, 1902, 1910, 1922, 1983, 1996, 2474, 2504, 2538, 2573, 2670, 2714, 2725, 2741, 2779, 3079, 3113, 3147, 3182, 3214, 3489, 3500, 3548, 3601, 3617, 3692, 3724, 3756, 3770, 3794, 4098, 4109, 4157, 4210, 4293, 4325, 4332, 4341, 4612, 4636] [2, 3, 8, 24, 25, 28, 29, 38, 39, 43, 48, 49, 52, 55, 56, 62, 65, 66, 72, 73, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1021, 1022, 1025, 1026, 1029, 1035, 1036, 1039, 1045, 1048, 1049, 1072, 1075, 1076, 1083, 1085, 1110, 1112, 1119, 1120, 1223, 1426, 1630, 1631, 1634, 1635, 1638, 1644, 1647, 1648, 1655, 1657, 1681, 1682, 1685, 1691, 1694, 1695, 1719, 1721, 1728, 1729, 1833, 1834, 1837, 1840, 1841, 1847, 1848, 1851, 1858, 1860, 1884, 1885, 1888, 1895, 1897, 1921, 1924, 1925, 1931, 1932, 2035, 2238, 2442, 2443, 2446, 2447, 2450, 2456, 2459, 2460, 2467, 2469, 2493, 2494, 2497, 2503, 2506, 2507, 2531, 2533, 2540, 2541, 2645, 2646, 2649, 2650, 2653, 2659, 2660, 2663, 2669, 2672, 2673, 2696, 2699, 2700, 2707, 2709, 2734, 2736, 2743, 2744, 2847, 3051, 3052, 3055, 3056, 3059, 3065, 3068, 3069, 3076, 3078, 3102, 3103, 3106, 3112, 3115, 3116, 3140, 3142, 3149, 3150, 3253, 3337, 3457, 3458, 3461, 3462, 3465, 3471, 3474, 3475, 3482, 3484, 3511, 3512, 3519, 3521, 3543, 3545, 3546, 3549, 3555, 3558, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3714, 3715, 3721, 3722, 3725, 3749, 3751, 3758, 3761, 3862, 4055, 4066, 4067, 4070, 4071, 4074, 4080, 4083, 4084, 4091, 4093, 4120, 4121, 4128, 4130, 4154, 4155, 4158, 4164, 4167, 4258, 4268, 4269, 4272, 4275, 4276, 4283, 4284, 4290, 4291, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4591, 4598, 4599, 4606, 4608, 4629, 4635, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x + y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation432.lean b/equational_theories/Generated/FinitePoly/Refutation432.lean new file mode 100644 index 00000000..636bf21f --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation432.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 1 * y**2 + 2 * x + 1 * y + 0 * x * y) % 3' (0, 39, 3252, 3254, 3255, 3277, 3278, 3281, 3284, 3285, 3314, 3315, 3318, 3321, 3322, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3723, 3861, 3866, 3869, 3877, 3880, 3890, 3901, 3905, 3914, 3924, 3927, 3934, 3942, 4269, 4292, 4340, 4589, 4621, 4635) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + y² + 2 * x + y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + y*y + 2 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + y² + 2 * x + y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [3285, 3322, 3323, 3692, 3902, 3906, 3935, 3943] [2, 3, 8, 23, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3281, 3306, 3308, 3309, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3868, 3871, 3877, 3880, 3887, 3888, 3890, 3917, 3918, 3924, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4065, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + y² + 2 * x + y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation444.lean b/equational_theories/Generated/FinitePoly/Refutation444.lean new file mode 100644 index 00000000..4e7c4729 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation444.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 2 * x + 0 * y + 2 * x * y) % 3' (0, 150, 155, 158, 1831, 1836, 1846, 1856, 1866, 4064, 4066) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + 2 * x + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + 2 * x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + 2 * x + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [156, 159, 1832, 4067] [43, 152, 153, 166, 1426, 1629, 1834, 1840, 1850, 1860, 1884, 1887, 1894, 1897, 1921, 1924, 1931, 1934, 2035, 3253, 3456, 3862, 4070, 4073, 4080, 4083, 4090, 4093, 4118, 4121, 4128, 4131, 4155, 4158, 4165, 4283, 4380, 4635] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y² + 2 * x + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation454.lean b/equational_theories/Generated/FinitePoly/Refutation454.lean new file mode 100644 index 00000000..1757ea5f --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation454.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 3 * x + 1 * y + 2 * x * y) % 4' (0, 7, 15, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 1019, 1025, 1035, 1044, 1074, 1085, 1097, 1112, 1121, 1151, 1183, 1628, 1634, 1646, 1657, 1669, 1681, 1690, 1721, 1730, 1763, 1779, 1831, 1839, 1847, 1860, 1875, 1884, 1897, 1912, 1920, 1933, 1948, 2440, 2446, 2458, 2469, 2481, 2493, 2502, 2533, 2542, 2575, 2591, 2643, 2649, 2659, 2668, 2698, 2709, 2721, 2736, 2745, 2775, 2807, 3049, 3055, 3067, 3078, 3090, 3102, 3111, 3142, 3151, 3184, 3200, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3861, 3867, 3877, 3886, 3914, 3923, 3950, 3961, 3972, 4006, 4022, 4274, 4306, 4319, 4361, 4587, 4604, 4646, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [562, 1098, 1152, 1764, 1876, 1913, 2576, 2592, 2722, 2776, 2808, 3185, 3201, 3261, 3388, 3973, 4007, 4647] [11, 23, 40, 414, 427, 440, 504, 614, 817, 1023, 1028, 1038, 1049, 1082, 1109, 1223, 1426, 1637, 1645, 1718, 1729, 1835, 1850, 1857, 1887, 1894, 1925, 2035, 2238, 2444, 2449, 2466, 2496, 2530, 2541, 2645, 2646, 2647, 2649, 2652, 2653, 2659, 2662, 2663, 2670, 2672, 2673, 2696, 2697, 2700, 2706, 2707, 2709, 2733, 2734, 2736, 2743, 2744, 2847, 3058, 3075, 3105, 3139, 3256, 3269, 3315, 3456, 3659, 3865, 3870, 3880, 3928, 3955, 4065, 4270, 4290, 4380, 4590, 4598, 4635] := + ⟨Fin 4, «FinitePoly 3 * x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation46.lean b/equational_theories/Generated/FinitePoly/Refutation46.lean new file mode 100644 index 00000000..09d74a9a --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation46.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 39, 42, 3658, 3661, 3664, 3666, 3674, 3676, 3683, 3687, 3691, 3699, 3702, 3711, 3713, 3720, 3724, 3728, 3747, 3751, 3755, 3758, 3760, 3819, 3822, 4269, 4282, 4340, 4357, 4379, 4387, 4397, 4404, 4434, 4441, 4468, 4481, 4496, 4530, 4543, 4589, 4621, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + y*y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 43, 3692, 3703, 3729, 3756, 3820, 3823, 4358, 4497, 4544, 4590, 4635] [2, 3, 8, 23, 38, 39, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3660, 3661, 3664, 3668, 3674, 3678, 3685, 3687, 3715, 3722, 3724, 3737, 3740, 3749, 3751, 3758, 3770, 3776, 3791, 3794, 3804, 3810, 3862, 4055, 4065, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + y² + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation470.lean b/equational_theories/Generated/FinitePoly/Refutation470.lean new file mode 100644 index 00000000..5eda680b --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation470.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 0 * y**2 + 2 * x + 2 * y + 2 * x * y) % 4' (0, 39, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * x + 2 * y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 2 * x + 2 * y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * x + 2 * y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [321, 3262, 3278, 3289, 3290, 3292, 3293, 3294, 3296, 3297, 3473, 3476, 3479, 3483, 3486, 3489, 3493, 3497, 3501, 3663, 3669, 3671, 3679, 3681, 3689, 3691, 3703, 4368, 4373, 4374, 4682, 4689] [2, 3, 8, 23, 38, 39, 43, 47, 99, 151, 203, 255, 323, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4380, 4539, 4547, 4571, 4583, 4585, 4588, 4591, 4598, 4605, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 2 * x + 2 * y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation472.lean b/equational_theories/Generated/FinitePoly/Refutation472.lean new file mode 100644 index 00000000..baa92be8 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation472.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 0 * y**2 + 0 * x + 0 * y + 2 * x * y) % 5' (0, 39, 358, 359, 366, 367, 368, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 4064, 4065, 4066, 4067, 4068, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4269, 4340, 4582, 4589, 4590, 4591, 4596, 4607, 4608, 4621, 4622) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 2 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 3 * x*x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 2 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [369, 3684, 3685, 4099, 4341, 4609] [378, 4131] := + ⟨Fin 5, «FinitePoly 3 * x² + 2 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation474.lean b/equational_theories/Generated/FinitePoly/Refutation474.lean new file mode 100644 index 00000000..881549eb --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation474.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 3 * y**2 + 2 * x + 1 * y + 2 * x * y) % 4' (0, 358, 360, 363, 366, 369, 3252, 3277, 3305, 3352, 3413, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * y² + 2 * x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * y*y + 2 * x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * y² + 2 * x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [370, 3414, 3837, 3877, 3880, 3890, 4067, 4073, 4083, 4093, 4689] [43, 307, 360, 362, 365, 368, 374, 375, 377, 378, 384, 385, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3271, 3319, 3346, 3456, 3660, 3661, 3662, 3665, 3667, 3668, 3675, 3677, 3678, 3685, 3687, 3714, 3715, 3721, 3724, 3725, 3748, 3751, 3752, 3758, 3761, 3863, 3865, 3868, 3871, 3878, 3881, 3888, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4066, 4068, 4071, 4074, 4081, 4084, 4091, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4268, 4269, 4270, 4275, 4283, 4284, 4314, 4320, 4380] := + ⟨Fin 4, «FinitePoly 3 * y² + 2 * x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation476.lean b/equational_theories/Generated/FinitePoly/Refutation476.lean new file mode 100644 index 00000000..3fac364e --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation476.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 2 * y + 0 * x * y) % 3' (0, 2, 7, 13, 15, 22, 25, 28, 42, 46, 52, 54, 65, 71, 98, 101, 104, 114, 126, 150, 159, 169, 176, 178, 202, 211, 218, 220, 227, 254, 257, 262, 272, 280, 306, 312, 314, 325, 331, 358, 361, 364, 374, 386, 410, 416, 418, 429, 435, 463, 465, 476, 488, 491, 499, 510, 512, 521, 527, 571, 574, 613, 616, 619, 629, 641, 668, 675, 679, 683, 691, 702, 706, 710, 713, 724, 745, 758, 816, 825, 835, 842, 844, 872, 879, 881, 906, 908, 915, 1019, 1028, 1035, 1037, 1044, 1072, 1074, 1081, 1112, 1119, 1121, 1151, 1154, 1164, 1170, 1180, 1183, 1222, 1225, 1230, 1240, 1248, 1275, 1284, 1288, 1292, 1303, 1311, 1315, 1319, 1324, 1339, 1357, 1373, 1425, 1431, 1433, 1441, 1443, 1454, 1466, 1469, 1478, 1480, 1491, 1503, 1506, 1518, 1524, 1557, 1560, 1628, 1631, 1634, 1646, 1653, 1657, 1661, 1669, 1683, 1690, 1694, 1698, 1706, 1718, 1730, 1779, 1792, 1831, 1837, 1839, 1847, 1849, 1860, 1872, 1875, 1887, 1893, 1920, 1931, 1933, 1942, 1948, 1976, 1982, 2034, 2043, 2050, 2052, 2059, 2087, 2089, 2096, 2127, 2134, 2136, 2166, 2169, 2179, 2185, 2195, 2198, 2237, 2240, 2243, 2255, 2262, 2266, 2270, 2278, 2290, 2302, 2326, 2330, 2334, 2337, 2348, 2372, 2398, 2440, 2446, 2448, 2456, 2458, 2469, 2481, 2484, 2493, 2495, 2506, 2518, 2521, 2533, 2539, 2572, 2575, 2643, 2652, 2662, 2669, 2671, 2699, 2706, 2708, 2733, 2735, 2742, 2846, 2849, 2852, 2862, 2874, 2901, 2908, 2912, 2916, 2924, 2935, 2939, 2943, 2946, 2957, 2978, 2991, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3102, 3111, 3115, 3119, 3130, 3141, 3149, 3194, 3210, 3252, 3258, 3260, 3271, 3277, 3305, 3307, 3318, 3330, 3333, 3341, 3352, 3354, 3363, 3369, 3413, 3416, 3455, 3458, 3461, 3471, 3483, 3510, 3517, 3521, 3525, 3533, 3544, 3548, 3552, 3555, 3566, 3587, 3600, 3658, 3667, 3677, 3684, 3686, 3714, 3721, 3723, 3748, 3750, 3757, 3861, 3870, 3877, 3879, 3886, 3914, 3916, 3923, 3954, 3961, 3963, 3993, 3996, 4006, 4012, 4022, 4025, 4064, 4067, 4072, 4082, 4090, 4117, 4126, 4130, 4134, 4145, 4153, 4157, 4161, 4166, 4181, 4199, 4215, 4272, 4274, 4282, 4304, 4306, 4331, 4342, 4357, 4379, 4382, 4385, 4397, 4404, 4408, 4412, 4420, 4434, 4441, 4445, 4449, 4457, 4469, 4481, 4530, 4543, 4584, 4587, 4607, 4634, 4639, 4646, 4655, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [26, 29, 53, 66, 102, 105, 115, 127, 160, 170, 177, 179, 212, 219, 221, 228, 258, 263, 273, 281, 313, 362, 365, 430, 492, 513, 522, 572, 642, 684, 692, 711, 725, 759, 826, 836, 843, 845, 873, 880, 882, 907, 909, 916, 1029, 1152, 1165, 1171, 1181, 1249, 1293, 1304, 1320, 1340, 1358, 1374, 1467, 1470, 1504, 1507, 1525, 1561, 1670, 1699, 1719, 1793, 1876, 1888, 1943, 1983, 2044, 2170, 2180, 2186, 2196, 2199, 2271, 2279, 2303, 2335, 2349, 2373, 2399, 2482, 2519, 2522, 2573, 2653, 2663, 2670, 2672, 2700, 2707, 2709, 2734, 2736, 2875, 2917, 2925, 2944, 2958, 2992, 3066, 3079, 3120, 3131, 3142, 3211, 3272, 3364, 3370, 3417, 3484, 3553, 3567, 3601, 3668, 3678, 3685, 3687, 3724, 3749, 3751, 3871, 4007, 4013, 4026, 4091, 4162, 4182, 4216, 4305, 4413, 4421, 4450, 4458, 4640] [2, 4, 5, 9, 10, 11, 13, 24, 25, 28, 31, 38, 39, 40, 48, 49, 50, 52, 56, 62, 63, 65, 73, 75, 100, 101, 104, 107, 108, 114, 117, 118, 124, 125, 152, 153, 154, 156, 157, 159, 166, 167, 169, 176, 204, 205, 206, 208, 209, 211, 218, 222, 229, 231, 256, 257, 260, 261, 264, 270, 271, 274, 280, 283, 308, 309, 310, 312, 316, 323, 325, 331, 333, 335, 336, 360, 361, 364, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 420, 426, 427, 429, 437, 439, 440, 463, 467, 473, 474, 476, 501, 503, 504, 510, 615, 616, 619, 622, 623, 629, 632, 633, 639, 640, 643, 666, 667, 670, 677, 679, 704, 706, 713, 716, 818, 819, 820, 822, 823, 825, 832, 833, 835, 842, 846, 869, 870, 872, 879, 883, 906, 910, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1035, 1039, 1046, 1048, 1049, 1072, 1076, 1083, 1085, 1086, 1109, 1110, 1112, 1119, 1224, 1225, 1228, 1229, 1232, 1238, 1239, 1242, 1248, 1251, 1252, 1275, 1278, 1279, 1286, 1288, 1313, 1315, 1322, 1323, 1427, 1428, 1429, 1431, 1435, 1441, 1445, 1451, 1452, 1454, 1478, 1482, 1488, 1489, 1491, 1515, 1516, 1518, 1526, 1528, 1630, 1631, 1634, 1637, 1638, 1644, 1645, 1648, 1655, 1657, 1681, 1682, 1685, 1692, 1694, 1718, 1721, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1841, 1847, 1851, 1857, 1858, 1860, 1884, 1885, 1887, 1895, 1897, 1898, 1922, 1924, 1925, 1931, 2036, 2037, 2038, 2040, 2041, 2043, 2050, 2054, 2061, 2063, 2064, 2087, 2091, 2098, 2100, 2101, 2124, 2125, 2127, 2134, 2239, 2240, 2243, 2246, 2247, 2253, 2254, 2257, 2264, 2266, 2290, 2293, 2294, 2300, 2301, 2304, 2328, 2330, 2337, 2340, 2442, 2443, 2444, 2446, 2450, 2456, 2460, 2466, 2467, 2469, 2493, 2497, 2503, 2504, 2506, 2530, 2531, 2533, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2659, 2660, 2662, 2669, 2673, 2696, 2697, 2699, 2706, 2710, 2733, 2737, 2744, 2746, 2848, 2849, 2852, 2855, 2856, 2862, 2865, 2866, 2872, 2873, 2876, 2899, 2900, 2903, 2910, 2912, 2937, 2939, 2946, 2949, 3051, 3052, 3055, 3056, 3059, 3065, 3068, 3069, 3076, 3078, 3102, 3105, 3106, 3113, 3115, 3139, 3140, 3143, 3149, 3152, 3254, 3255, 3256, 3258, 3262, 3268, 3269, 3271, 3279, 3281, 3309, 3315, 3316, 3318, 3337, 3343, 3345, 3346, 3352, 3457, 3458, 3461, 3464, 3465, 3471, 3474, 3475, 3481, 3482, 3509, 3512, 3519, 3521, 3543, 3546, 3548, 3555, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3674, 3675, 3677, 3684, 3712, 3714, 3721, 3725, 3748, 3752, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3877, 3881, 3888, 3890, 3918, 3925, 3927, 3928, 3951, 3952, 3954, 3961, 4055, 4066, 4067, 4070, 4071, 4074, 4080, 4081, 4084, 4090, 4093, 4120, 4121, 4128, 4130, 4155, 4157, 4164, 4165, 4258, 4268, 4269, 4270, 4272, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4368, 4373, 4381, 4382, 4385, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4472, 4473, 4479, 4480, 4539, 4547, 4571, 4583, 4584, 4587, 4590, 4591, 4598, 4599, 4605, 4606, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation482.lean b/equational_theories/Generated/FinitePoly/Refutation482.lean new file mode 100644 index 00000000..20ee7f67 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation482.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 1 * y + 0 * x * y) % 5' (0, 202, 208, 218, 230, 613, 619, 632, 669, 703, 715, 816, 825, 832, 872, 879, 918, 1425, 1434, 1444, 1451, 1478, 1527, 3049, 3055, 3067, 3078, 3090, 3111, 3139, 3151, 3200, 4275, 4319, 4361, 4587, 4607, 4646) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 2 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [209, 219, 231, 620, 633, 670, 704, 716, 826, 833, 873, 880, 919, 1435, 1445, 1452, 1479, 1528, 3140, 3201, 4276, 4647] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 204, 205, 206, 208, 211, 212, 218, 221, 222, 228, 229, 255, 307, 331, 359, 407, 411, 615, 616, 617, 619, 622, 623, 629, 630, 632, 639, 640, 642, 643, 666, 667, 669, 676, 677, 679, 680, 703, 706, 707, 713, 714, 818, 819, 820, 822, 823, 825, 832, 835, 836, 842, 843, 845, 846, 869, 870, 872, 879, 882, 883, 906, 907, 909, 910, 916, 917, 1020, 1223, 1427, 1428, 1429, 1431, 1432, 1434, 1441, 1442, 1444, 1451, 1454, 1455, 1478, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3103, 3105, 3106, 3113, 3115, 3116, 3139, 3142, 3143, 3149, 3150, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4590, 4591, 4598, 4599, 4605, 4606, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 2 * x + y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation488.lean b/equational_theories/Generated/FinitePoly/Refutation488.lean new file mode 100644 index 00000000..e1a561e3 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation488.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 3 * y**2 + 4 * x + 2 * y + 4 * x * y) % 5' (0, 2, 7, 22, 46, 48, 98, 150, 166, 202, 254, 306, 325, 358, 374, 410, 412, 415, 428, 613, 615, 618, 621, 624, 816, 818, 832, 1019, 1222, 1425, 1427, 1481, 1628, 1681, 1831, 1884, 2034, 2087, 2124, 2237, 2242, 2440, 2643, 2698, 2846, 2861, 3049, 3252, 3254, 3318, 3455, 3521, 3658, 3674, 3714, 3721, 3861, 3914, 3917, 4064, 4117, 4379, 4469) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + 3 * y² + 4 * x + 2 * y + 4 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 3 * x*x + 3 * y*y + 4 * x + 2 * y + 4 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + 3 * y² + 4 * x + 2 * y + 4 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [49, 167, 413, 416, 429, 819, 833, 1428, 1482, 1682, 1885, 2088, 2125, 2243, 2699, 2862, 3255, 3675, 3918] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 414, 417, 419, 420, 426, 427, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 617, 620, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 820, 822, 823, 825, 826, 832, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 3 * x² + 3 * y² + 4 * x + 2 * y + 4 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation492.lean b/equational_theories/Generated/FinitePoly/Refutation492.lean new file mode 100644 index 00000000..20846c49 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation492.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 0 * y + 2 * x * y) % 4' (0, 39, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 3910, 3911, 3912, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 4110, 4111, 4112, 4113, 4114, 4115, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [373, 3697, 3701, 3705, 3706, 3707, 3708, 3709, 3879, 3882, 3885, 3889, 3892, 3895, 3899, 3903, 3907, 4068, 4075, 4077, 4085, 4087, 4093, 4097, 4106, 4109, 4359, 4360, 4683, 4688] [2, 3, 8, 23, 38, 39, 43, 47, 99, 151, 203, 255, 307, 331, 374, 375, 377, 378, 384, 385, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4272, 4273, 4275, 4276, 4290, 4291, 4293, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571] := + ⟨Fin 4, «FinitePoly 2 * x + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation50.lean b/equational_theories/Generated/FinitePoly/Refutation50.lean new file mode 100644 index 00000000..bf038c3b --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation50.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 0 * y**2 + 2 * x + 2 * y + 0 * x * y) % 3' (0, 7, 15, 410, 418, 435, 465, 499, 512, 527, 574, 1019, 1044, 1074, 1121, 1183, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1920, 1933, 1948, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3861, 3886, 3914, 3961, 4022, 4274, 4306) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 419, 436, 466, 500, 513, 1045, 1075, 1122, 1629, 1840, 1921, 1934, 3261, 3887, 3962, 4275] [2, 3, 9, 10, 11, 13, 14, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 429, 430, 437, 439, 440, 463, 464, 467, 473, 474, 476, 477, 501, 503, 504, 510, 511, 614, 817, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1922, 1924, 1925, 1931, 1932, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3271, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3355, 3456, 3543, 3659, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3964, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation502.lean b/equational_theories/Generated/FinitePoly/Refutation502.lean new file mode 100644 index 00000000..0812c0b9 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation502.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 2 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 39, 42, 410, 413, 426, 428, 472, 476, 480, 510, 512, 555, 561, 613, 621, 631, 638, 666, 679, 694, 706, 713, 748, 774, 1019, 1022, 1025, 1027, 1108, 1112, 1116, 1119, 1121, 1130, 1136, 1222, 1228, 1238, 1247, 1277, 1288, 1300, 1315, 1324, 1354, 1386, 1425, 1428, 1450, 1454, 1458, 1487, 1491, 1495, 1514, 1518, 1522, 1628, 1636, 1644, 1657, 1672, 1681, 1694, 1709, 1717, 1730, 1745, 1831, 1834, 1856, 1860, 1864, 1884, 1886, 1931, 1933, 1992, 1995, 2034, 2037, 2040, 2042, 2123, 2127, 2131, 2134, 2136, 2145, 2151, 2237, 2245, 2253, 2266, 2281, 2292, 2299, 2330, 2337, 2369, 2382, 2440, 2443, 2465, 2469, 2473, 2502, 2506, 2510, 2529, 2533, 2537, 2846, 2854, 2864, 2871, 2899, 2912, 2927, 2939, 2946, 2981, 3007, 3049, 3055, 3067, 3078, 3090, 3104, 3115, 3127, 3138, 3149, 3160, 3658, 3661, 3664, 3666, 3674, 3676, 3683, 3687, 3691, 3699, 3702, 4269, 4282, 4340, 4357, 4379, 4387, 4397, 4404, 4434, 4441, 4468, 4481, 4496, 4530, 4543, 4589, 4621, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y² + x + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 2 * y*y + x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y² + x + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [481, 556, 562, 695, 749, 775, 1117, 1131, 1137, 1301, 1355, 1387, 1459, 1496, 1523, 1673, 1710, 1746, 1865, 1993, 1996, 2132, 2146, 2152, 2282, 2370, 2383, 2474, 2511, 2538, 2928, 2982, 3008, 3128, 3161, 3692, 3703, 4497, 4590] [8, 23, 412, 413, 416, 417, 419, 420, 426, 430, 436, 437, 439, 440, 463, 464, 466, 467, 474, 476, 500, 501, 503, 504, 510, 615, 616, 617, 619, 620, 623, 629, 630, 633, 640, 642, 643, 666, 669, 670, 676, 677, 679, 703, 704, 706, 713, 716, 817, 1036, 1038, 1045, 1049, 1073, 1075, 1082, 1086, 1224, 1225, 1226, 1228, 1231, 1232, 1238, 1241, 1242, 1249, 1251, 1252, 1275, 1276, 1279, 1285, 1286, 1288, 1312, 1313, 1315, 1322, 1323, 1432, 1434, 1442, 1444, 1479, 1481, 1526, 1528, 1632, 1635, 1647, 1654, 1684, 1691, 1722, 1729, 1838, 1840, 1848, 1850, 1894, 1898, 1921, 1925, 2036, 2037, 2040, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2125, 2127, 2134, 2239, 2240, 2241, 2243, 2244, 2247, 2253, 2256, 2257, 2263, 2264, 2266, 2290, 2291, 2294, 2301, 2303, 2304, 2327, 2328, 2330, 2337, 2340, 2447, 2449, 2457, 2459, 2494, 2496, 2541, 2543, 2644, 2848, 2849, 2850, 2852, 2853, 2856, 2862, 2863, 2866, 2873, 2875, 2876, 2899, 2902, 2903, 2909, 2910, 2912, 2936, 2937, 2939, 2946, 2949, 3053, 3058, 3066, 3075, 3103, 3112, 3143, 3152, 3253, 3456, 3712, 3714, 3721, 3725, 3748, 3752, 3759, 3761, 3862, 4065, 4273, 4275, 4290, 4320, 4381, 4382, 4383, 4385, 4386, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4585, 4588, 4598, 4605] := + ⟨Fin 4, «FinitePoly 2 * x² + 2 * y² + x + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation532.lean b/equational_theories/Generated/FinitePoly/Refutation532.lean new file mode 100644 index 00000000..43687eb4 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation532.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 3 * x + 0 * y + 2 * x * y) % 4' (0, 1831, 1834, 1856, 1860, 1864, 2034, 2037, 2050, 2052, 2846, 2852, 2862, 2871, 3049, 3055, 3067, 3078, 3090, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3661, 3711, 3713, 4269, 4282, 4340, 4357, 4379, 4395, 4432, 4468) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + 3 * x + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => y*y + 3 * x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + 3 * x + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1865, 2038, 2051, 2053, 2853, 2863, 2872, 3323, 3331, 3526, 3534, 3537, 3662, 3714, 4358, 4396, 4433, 4469] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1833, 1834, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2040, 2041, 2043, 2044, 2050, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2238, 2441, 2644, 2848, 2849, 2850, 2852, 2855, 2856, 2862, 2865, 2866, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3258, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3309, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3461, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3512, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4398, 4399, 4405, 4406, 4408, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly y² + 3 * x + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation550.lean b/equational_theories/Generated/FinitePoly/Refutation550.lean new file mode 100644 index 00000000..7a036dae --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation550.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 3 * x + 0 * y + 2 * x * y) % 4' (0, 22, 24, 150, 152, 155, 158, 161, 202, 204, 207, 210, 213, 306, 308, 322, 325, 328, 1425, 1427, 1430, 1433, 1436, 1440, 1443, 1446, 1450, 1453, 1456, 1460, 1464, 1468, 1472, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 3049, 3051, 3054, 3064, 3067, 3070, 3077, 3088, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 4064, 4066, 4069, 4117, 4127, 4130, 4133, 4137, 4268, 4283, 4286, 4315, 4339, 4359, 4583, 4630) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 3 * x + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + y*y + 3 * x + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 3 * x + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [25, 162, 208, 211, 329, 1473, 1654, 1657, 1834, 1840, 1860, 2285, 2488, 3052, 3065, 3089, 3264, 3312, 3322, 3326, 3330, 3512, 3519, 4070, 4134, 4287, 4340, 4584] [2, 3, 8, 24, 26, 28, 29, 31, 38, 39, 40, 43, 47, 99, 152, 154, 157, 160, 166, 167, 169, 170, 176, 177, 179, 204, 206, 209, 212, 218, 219, 221, 222, 228, 229, 231, 255, 308, 310, 312, 313, 315, 316, 325, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1427, 1429, 1432, 1435, 1442, 1445, 1452, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1632, 1635, 1638, 1645, 1648, 1655, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1835, 1838, 1841, 1848, 1851, 1858, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2239, 2241, 2244, 2247, 2254, 2257, 2264, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2444, 2447, 2450, 2457, 2460, 2467, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2644, 2847, 3051, 3053, 3056, 3058, 3059, 3066, 3069, 3075, 3076, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3256, 3259, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3315, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3459, 3462, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3511, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3862, 4055, 4066, 4068, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4270, 4272, 4273, 4275, 4276, 4283, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + y² + 3 * x + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation56.lean b/equational_theories/Generated/FinitePoly/Refutation56.lean new file mode 100644 index 00000000..b8d32f88 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation56.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 0 * y**2 + 0 * x + 2 * y + 1 * x * y) % 3' (0, 150, 1425, 1831, 3455, 4064, 4130) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 2 * y + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + 2 * y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 2 * y + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 151, 1426, 1832, 3456, 4131] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1629, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3659, 3862, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + 2 * y + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation568.lean b/equational_theories/Generated/FinitePoly/Refutation568.lean new file mode 100644 index 00000000..10306aa3 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation568.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 1 * y + 0 * x * y) % 3' (0, 42, 46, 55, 65, 72, 74, 98, 107, 117, 124, 126, 150, 159, 169, 176, 178, 202, 211, 221, 228, 230, 254, 263, 273, 280, 282, 4275, 4282, 4289, 4319, 4357, 4361, 4363, 4368, 4379, 4388, 4395, 4397, 4404, 4432, 4434, 4441, 4472, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4590, 4597, 4604, 4634, 4672, 4676, 4678, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x + y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x + y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [43, 56, 66, 73, 75, 108, 118, 125, 127, 160, 170, 177, 179, 212, 222, 229, 231, 264, 274, 281, 283, 4389, 4591] [2, 3, 8, 23, 38, 39, 40, 48, 49, 50, 52, 53, 55, 62, 63, 65, 72, 100, 101, 102, 104, 105, 107, 114, 115, 117, 124, 152, 153, 154, 156, 157, 159, 166, 167, 169, 176, 204, 205, 206, 208, 209, 211, 218, 219, 221, 228, 256, 257, 258, 260, 261, 263, 270, 271, 273, 280, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4284, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4399, 4406, 4408, 4436, 4443, 4445, 4470, 4472, 4479, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4599, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x + y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation6.lean b/equational_theories/Generated/FinitePoly/Refutation6.lean new file mode 100644 index 00000000..369a8436 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation6.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 0 * y**2 + 1 * x + 1 * y + 2 * x * y) % 3' (0, 22, 202, 306, 1628, 1730, 2237, 2242, 2326, 2440, 2455, 2458, 2465, 2529, 2643, 2658, 2695, 2698, 2705, 3049, 3064, 3067, 3252, 3305, 3455, 3460, 3521, 3658, 3673, 4064, 4069, 4117, 4154) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + x + y + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * x*x + x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + x + y + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 23, 203, 307, 1731, 2243, 2327, 2456, 2459, 2466, 2530, 2659, 2696, 2699, 2706, 3065, 3068, 3306, 3461, 3674, 4070, 4155] [2, 3, 8, 24, 25, 26, 28, 29, 31, 38, 39, 40, 43, 47, 99, 151, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 255, 308, 309, 310, 312, 313, 315, 316, 323, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1832, 2035, 2239, 2240, 2241, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2457, 2460, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2697, 2700, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2847, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3066, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly 2 * x² + x + y + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation60.lean b/equational_theories/Generated/FinitePoly/Refutation60.lean new file mode 100644 index 00000000..000db778 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation60.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 3 * x + 1 * y + 1 * x * y) % 4' (0, 3252, 3305, 3455, 3510, 3658, 3861, 3954, 4064, 4130, 4379) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 3 * x + y + x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => x*x + y*y + 3 * x + y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 3 * x + y + x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 3306, 3511, 3659, 3955, 4131, 4380] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly x² + y² + 3 * x + y + x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation620.lean b/equational_theories/Generated/FinitePoly/Refutation620.lean new file mode 100644 index 00000000..fddae880 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation620.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 3 * x + 1 * y + 0 * x * y) % 5' (0, 98, 104, 126, 150, 166, 178, 2237, 2243, 2253, 2290, 2339, 3049, 3055, 3067, 3078, 3090, 3105, 3111, 3151, 3200, 4292, 4319, 4361, 4587, 4646, 4657) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x + y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 3 * x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x + y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [105, 127, 167, 179, 2244, 2254, 2291, 2340, 3106, 3201, 4293, 4647, 4658] [2, 3, 8, 23, 38, 39, 40, 43, 47, 100, 101, 102, 104, 107, 108, 114, 115, 117, 118, 124, 125, 152, 153, 154, 156, 157, 159, 160, 166, 169, 170, 176, 177, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2239, 2240, 2241, 2243, 2246, 2247, 2253, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2441, 2644, 2847, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3103, 3105, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4314, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4683, 4688] := + ⟨Fin 5, «FinitePoly 3 * x + y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation622.lean b/equational_theories/Generated/FinitePoly/Refutation622.lean new file mode 100644 index 00000000..c731b1f0 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation622.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 2 * x + 4 * y + 3 * x * y) % 5' (0, 2, 7, 22, 46, 98, 150, 166, 202, 254, 259, 306, 325, 358, 374, 410, 613, 615, 816, 832, 1019, 1222, 1227, 1425, 1478, 1481, 1628, 1681, 1831, 1884, 2034, 2049, 2124, 2237, 2440, 2643, 2658, 2698, 2846, 2851, 2861, 2871, 2881, 3049, 3054, 3064, 3067, 3252, 3318, 3455, 3511, 3521, 3658, 3674, 3714, 3721, 3861, 3914, 4064, 4069, 4117, 4379, 4469) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + 2 * x + 4 * y + 3 * x * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => x*x + y*y + 2 * x + 4 * y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + 2 * x + 4 * y + 3 * x * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [260, 616, 1228, 1479, 1682, 1885, 2050, 2659, 2699, 3055, 3065, 3068, 3512, 4070] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1481, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2853, 2855, 2856, 2863, 2865, 2866, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3056, 3058, 3059, 3066, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly x² + y² + 2 * x + 4 * y + 3 * x * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation636.lean b/equational_theories/Generated/FinitePoly/Refutation636.lean new file mode 100644 index 00000000..982607f7 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation636.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 3 * y + 0 * x * y) % 5' (0, 39, 98, 106, 116, 410, 413, 428, 436, 472, 476, 480, 512, 561, 1425, 1428, 1453, 1487, 1491, 1495, 1514, 1518, 1522, 2034, 2037, 2040, 2099, 2123, 2127, 2131, 2134, 2145, 3049, 3055, 3067, 3078, 3090, 3105, 3138, 3149, 3160, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3748, 4269, 4320, 4340, 4589, 4621, 4657) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + 3 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 2 * x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + 3 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [107, 117, 437, 481, 562, 1454, 1496, 1523, 2100, 2132, 2146, 3106, 3161, 3692, 3700, 4341, 4622] [2, 3, 8, 23, 38, 39, 43, 47, 100, 101, 102, 104, 105, 108, 114, 115, 118, 124, 125, 127, 151, 203, 255, 307, 331, 359, 407, 412, 413, 416, 417, 419, 420, 426, 427, 430, 436, 439, 440, 463, 464, 466, 467, 474, 476, 500, 501, 503, 504, 510, 511, 614, 817, 1020, 1223, 1427, 1428, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1455, 1478, 1479, 1481, 1482, 1489, 1491, 1516, 1518, 1525, 1526, 1528, 1629, 1832, 2036, 2037, 2040, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2101, 2125, 2127, 2134, 2137, 2238, 2441, 2644, 2847, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3103, 3105, 3112, 3113, 3115, 3116, 3140, 3142, 3143, 3149, 3152, 3253, 3337, 3456, 3543, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4683, 4688] := + ⟨Fin 5, «FinitePoly 2 * x + 3 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation656.lean b/equational_theories/Generated/FinitePoly/Refutation656.lean new file mode 100644 index 00000000..67b8de7d --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation656.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 1 * x + 3 * y + 0 * x * y) % 5' (0, 150, 159, 166, 202, 211, 220, 410, 416, 428, 439, 451, 472, 500, 512, 561, 1222, 1251, 1275, 1277, 1284, 4272, 4292, 4331, 4597, 4657, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x + 3 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x + 3 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [160, 167, 212, 221, 452, 501, 562, 1252, 1276, 1278, 1285, 4332] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 152, 153, 154, 156, 157, 159, 166, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 218, 219, 222, 228, 229, 231, 255, 307, 331, 359, 407, 412, 413, 414, 416, 419, 420, 426, 427, 430, 436, 437, 439, 463, 464, 466, 467, 474, 476, 477, 500, 503, 504, 510, 511, 614, 817, 1020, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1275, 1279, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4275, 4276, 4283, 4284, 4290, 4291, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4683, 4688] := + ⟨Fin 5, «FinitePoly x + 3 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation66.lean b/equational_theories/Generated/FinitePoly/Refutation66.lean new file mode 100644 index 00000000..67b85ef8 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation66.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 1 * y**2 + 1 * x + 1 * y + 0 * x * y) % 2' (0, 37, 38, 39, 40, 41, 42, 43, 44, 45, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347, 3348, 3349, 3350, 3351, 3352, 3353, 3354, 3355, 3356, 3357, 3358, 3359, 3360, 3361, 3362, 3363, 3364, 3365, 3366, 3367, 3368, 3369, 3370, 3371, 3372, 3373, 3374, 3375, 3376, 3377, 3378, 3379, 3380, 3381, 3382, 3383, 3384, 3385, 3386, 3387, 3388, 3389, 3390, 3391, 3392, 3393, 3394, 3395, 3396, 3397, 3398, 3399, 3400, 3401, 3402, 3403, 3404, 3405, 3406, 3407, 3408, 3409, 3410, 3411, 3412, 3413, 3414, 3415, 3416, 3417, 3418, 3419, 3420, 3421, 3422, 3423, 3424, 3425, 3426, 3427, 3428, 3429, 3430, 3431, 3432, 3433, 3434, 3435, 3436, 3437, 3438, 3439, 3440, 3441, 3442, 3443, 3444, 3445, 3446, 3447, 3448, 3449, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 3544, 3545, 3546, 3547, 3548, 3549, 3550, 3551, 3552, 3553, 3554, 3555, 3556, 3557, 3558, 3559, 3560, 3561, 3562, 3563, 3564, 3565, 3566, 3567, 3568, 3569, 3570, 3571, 3572, 3573, 3574, 3575, 3576, 3577, 3578, 3579, 3580, 3581, 3582, 3583, 3584, 3585, 3586, 3587, 3588, 3589, 3590, 3591, 3592, 3593, 3594, 3595, 3596, 3597, 3598, 3599, 3600, 3601, 3602, 3603, 3604, 3605, 3606, 3607, 3608, 3609, 3610, 3611, 3612, 3613, 3614, 3615, 3616, 3617, 3618, 3619, 3620, 3621, 3622, 3623, 3624, 3625, 3626, 3627, 3628, 3629, 3630, 3631, 3632, 3633, 3634, 3635, 3636, 3637, 3638, 3639, 3640, 3641, 3642, 3643, 3644, 3645, 3646, 3647, 3648, 3649, 3650, 3651, 3652, 3653, 3654, 3655, 3656, 3657, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3747, 3748, 3749, 3750, 3751, 3752, 3753, 3754, 3755, 3756, 3757, 3758, 3759, 3760, 3761, 3762, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 3770, 3771, 3772, 3773, 3774, 3775, 3776, 3777, 3778, 3779, 3780, 3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3789, 3790, 3791, 3792, 3793, 3794, 3795, 3796, 3797, 3798, 3799, 3800, 3801, 3802, 3803, 3804, 3805, 3806, 3807, 3808, 3809, 3810, 3811, 3812, 3813, 3814, 3815, 3816, 3817, 3818, 3819, 3820, 3821, 3822, 3823, 3824, 3825, 3826, 3827, 3828, 3829, 3830, 3831, 3832, 3833, 3834, 3835, 3836, 3837, 3838, 3839, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 3850, 3851, 3852, 3853, 3854, 3855, 3856, 3857, 3858, 3859, 3860, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 3910, 3911, 3912, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 3950, 3951, 3952, 3953, 3954, 3955, 3956, 3957, 3958, 3959, 3960, 3961, 3962, 3963, 3964, 3965, 3966, 3967, 3968, 3969, 3970, 3971, 3972, 3973, 3974, 3975, 3976, 3977, 3978, 3979, 3980, 3981, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 3990, 3991, 3992, 3993, 3994, 3995, 3996, 3997, 3998, 3999, 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 4010, 4011, 4012, 4013, 4014, 4015, 4016, 4017, 4018, 4019, 4020, 4021, 4022, 4023, 4024, 4025, 4026, 4027, 4028, 4029, 4030, 4031, 4032, 4033, 4034, 4035, 4036, 4037, 4038, 4039, 4040, 4041, 4042, 4043, 4044, 4045, 4046, 4047, 4048, 4049, 4050, 4051, 4052, 4053, 4054, 4055, 4056, 4057, 4058, 4059, 4060, 4061, 4062, 4063, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 4110, 4111, 4112, 4113, 4114, 4115, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4153, 4154, 4155, 4156, 4157, 4158, 4159, 4160, 4161, 4162, 4163, 4164, 4165, 4166, 4167, 4168, 4169, 4170, 4171, 4172, 4173, 4174, 4175, 4176, 4177, 4178, 4179, 4180, 4181, 4182, 4183, 4184, 4185, 4186, 4187, 4188, 4189, 4190, 4191, 4192, 4193, 4194, 4195, 4196, 4197, 4198, 4199, 4200, 4201, 4202, 4203, 4204, 4205, 4206, 4207, 4208, 4209, 4210, 4211, 4212, 4213, 4214, 4215, 4216, 4217, 4218, 4219, 4220, 4221, 4222, 4223, 4224, 4225, 4226, 4227, 4228, 4229, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 4240, 4241, 4242, 4243, 4244, 4245, 4246, 4247, 4248, 4249, 4250, 4251, 4252, 4253, 4254, 4255, 4256, 4257, 4258, 4259, 4260, 4261, 4262, 4263, 4264, 4265, 4266, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4379, 4380, 4381, 4382, 4383, 4384, 4385, 4386, 4387, 4388, 4389, 4390, 4391, 4392, 4393, 4394, 4395, 4396, 4397, 4398, 4399, 4400, 4401, 4402, 4403, 4404, 4405, 4406, 4407, 4408, 4409, 4410, 4411, 4412, 4413, 4414, 4415, 4416, 4417, 4418, 4419, 4420, 4421, 4422, 4423, 4424, 4425, 4426, 4427, 4428, 4429, 4430, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 4440, 4441, 4442, 4443, 4444, 4445, 4446, 4447, 4448, 4449, 4450, 4451, 4452, 4453, 4454, 4455, 4456, 4457, 4458, 4459, 4460, 4461, 4462, 4463, 4464, 4465, 4466, 4467, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4478, 4479, 4480, 4481, 4482, 4483, 4484, 4485, 4486, 4487, 4488, 4489, 4490, 4491, 4492, 4493, 4494, 4495, 4496, 4497, 4498, 4499, 4500, 4501, 4502, 4503, 4504, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4522, 4523, 4524, 4525, 4526, 4527, 4528, 4529, 4530, 4531, 4532, 4533, 4534, 4535, 4536, 4537, 4538, 4539, 4540, 4541, 4542, 4543, 4544, 4545, 4546, 4547, 4548, 4549, 4550, 4551, 4552, 4553, 4554, 4555, 4556, 4557, 4558, 4559, 4560, 4561, 4562, 4563, 4564, 4565, 4566, 4567, 4568, 4569, 4570, 4571, 4572, 4573, 4574, 4575, 4576, 4577, 4578, 4579, 4580, 4581, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + y² + x + y % 2» : Magma (Fin 2) where + op := memoFinOp fun x y => x*x + y*y + x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + y² + x + y % 2» : + ∃ (G : Type) (_ : Magma G), Facts G [321, 341, 345, 349, 354, 355, 373, 393, 397, 401, 404, 406, 3294, 3455, 3626, 3658, 3850, 3855, 3858, 3859, 4032, 4064, 4235, 4267, 4370, 4371, 4377, 4537, 4556, 4566, 4568, 4576, 4580, 4581, 4681, 4682, 4685] [2, 3, 8, 23, 47, 99, 151, 203, 255, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050] := + ⟨Fin 2, «FinitePoly x² + y² + x + y % 2», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation664.lean b/equational_theories/Generated/FinitePoly/Refutation664.lean new file mode 100644 index 00000000..de29574e --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation664.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 3 * x + 4 * y + 0 * x * y) % 5' (0, 7, 15, 410, 418, 429, 435, 465, 499, 512, 527, 574, 1019, 1025, 1044, 1074, 1085, 1097, 1109, 1121, 1183, 1628, 1637, 1646, 1681, 1690, 1721, 1730, 1763, 1779, 1831, 1839, 1857, 1884, 1897, 1912, 1920, 1933, 1948, 2643, 2649, 2659, 2671, 2698, 2709, 2721, 2736, 2775, 3049, 3055, 3067, 3078, 3090, 3102, 3142, 3148, 3184, 3252, 3260, 3271, 3277, 3305, 3318, 3333, 3352, 3413, 3861, 3867, 3886, 3914, 3926, 3950, 3961, 3972, 4022, 4274, 4306, 4342, 4590, 4604, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x + 4 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 3 * x + 4 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x + 4 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [430, 1098, 1110, 1638, 1764, 1858, 1913, 2672, 2722, 2776, 3149, 3185, 3272, 3927, 3973, 4275, 4343, 4591] [2, 3, 9, 10, 11, 13, 14, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 429, 437, 439, 440, 463, 464, 467, 473, 474, 476, 477, 501, 503, 504, 510, 511, 614, 817, 1021, 1022, 1023, 1025, 1028, 1029, 1035, 1036, 1038, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1082, 1083, 1085, 1109, 1112, 1113, 1119, 1120, 1223, 1426, 1630, 1631, 1632, 1634, 1635, 1637, 1644, 1645, 1648, 1654, 1655, 1657, 1658, 1681, 1684, 1685, 1692, 1694, 1695, 1718, 1719, 1721, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1847, 1848, 1850, 1851, 1857, 1860, 1861, 1884, 1887, 1888, 1894, 1895, 1897, 1922, 1924, 1925, 1931, 1932, 2035, 2238, 2441, 2645, 2646, 2647, 2649, 2652, 2653, 2659, 2662, 2663, 2669, 2670, 2673, 2696, 2697, 2700, 2706, 2707, 2709, 2733, 2734, 2736, 2743, 2744, 2746, 2847, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3271, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3355, 3456, 3543, 3659, 3863, 3864, 3865, 3867, 3870, 3871, 3877, 3878, 3880, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3928, 3952, 3954, 3955, 3961, 3964, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4598, 4599, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 3 * x + 4 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation672.lean b/equational_theories/Generated/FinitePoly/Refutation672.lean new file mode 100644 index 00000000..7d3476f0 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation672.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 3 * x + 2 * y + 0 * x * y) % 5' (0, 39, 202, 208, 210, 410, 413, 428, 472, 476, 480, 500, 512, 561, 1425, 1428, 1451, 1487, 1491, 1495, 1514, 1518, 1522, 2034, 2037, 2040, 2062, 2123, 2127, 2131, 2134, 2145, 3049, 3055, 3067, 3078, 3090, 3114, 3138, 3149, 3160, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3723, 4269, 4292, 4340, 4589, 4621, 4635) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x + 2 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 3 * x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x + 2 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [209, 211, 481, 501, 1452, 1496, 1523, 2063, 2132, 2146, 3115, 3161, 3692, 3700, 4341, 4622] [3, 8, 23, 47, 99, 151, 204, 205, 206, 208, 212, 218, 219, 221, 222, 228, 229, 231, 255, 307, 359, 417, 419, 436, 437, 440, 466, 474, 500, 614, 817, 1020, 1223, 1427, 1428, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1454, 1455, 1478, 1479, 1481, 1482, 1489, 1491, 1516, 1518, 1525, 1526, 1528, 1629, 1832, 2036, 2037, 2040, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2125, 2127, 2134, 2137, 2238, 2441, 2644, 2847, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3116, 3140, 3142, 3143, 3149, 3152, 3253, 3456, 3660, 3661, 3664, 3667, 3668, 3674, 3675, 3678, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4065, 4273, 4275, 4320, 4321, 4380, 4587, 4598, 4605, 4606, 4658] := + ⟨Fin 5, «FinitePoly 3 * x + 2 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation674.lean b/equational_theories/Generated/FinitePoly/Refutation674.lean new file mode 100644 index 00000000..e2b16a0c --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation674.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 3 * x + 3 * y + 0 * x * y) % 5' (0, 2, 7, 22, 42, 46, 62, 64, 98, 116, 123, 150, 202, 205, 208, 254, 260, 270, 306, 325, 331, 358, 374, 386, 410, 426, 428, 466, 472, 510, 512, 555, 561, 613, 631, 638, 666, 678, 706, 713, 748, 774, 816, 869, 871, 878, 905, 1019, 1022, 1025, 1084, 1108, 1112, 1116, 1119, 1130, 1222, 1228, 1238, 1277, 1288, 1300, 1315, 1321, 1354, 1425, 1451, 1453, 1488, 1490, 1515, 1517, 1628, 1647, 1654, 1684, 1691, 1720, 1727, 1831, 1840, 1850, 1894, 1896, 1921, 1923, 2034, 2053, 2060, 2062, 2090, 2097, 2099, 2237, 2246, 2253, 2292, 2299, 2330, 2337, 2369, 2382, 2440, 2443, 2466, 2502, 2506, 2510, 2529, 2533, 2537, 2643, 2646, 2649, 2659, 2696, 2846, 2854, 2864, 2872, 2899, 2912, 2927, 2939, 2981, 3049, 3055, 3067, 3078, 3090, 3104, 3115, 3127, 3139, 3252, 3268, 3270, 3318, 3341, 3455, 3473, 3480, 3521, 3544, 3658, 3714, 3721, 3723, 3748, 3750, 3757, 3861, 3864, 3867, 3914, 3963, 4064, 4070, 4080, 4117, 4166, 4282, 4342, 4357, 4379, 4397, 4404, 4434, 4441, 4469, 4481, 4530, 4543, 4607, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x + 3 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 3 * x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x + 3 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [63, 65, 117, 124, 206, 209, 261, 271, 467, 556, 562, 679, 749, 775, 870, 872, 879, 906, 1085, 1117, 1131, 1301, 1322, 1355, 1452, 1454, 1489, 1491, 1516, 1518, 1648, 1655, 1685, 1692, 1721, 1728, 1841, 1851, 1895, 1897, 1922, 1924, 2054, 2061, 2063, 2091, 2098, 2100, 2247, 2370, 2383, 2467, 2511, 2538, 2647, 2650, 2660, 2697, 2873, 2928, 2982, 3128, 3140, 3269, 3271, 3474, 3481, 3865, 3868, 4071, 4081] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 48, 49, 50, 52, 53, 55, 56, 62, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 118, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 205, 208, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 263, 264, 270, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 430, 436, 437, 439, 440, 463, 464, 466, 474, 476, 477, 500, 501, 503, 504, 510, 615, 616, 617, 619, 620, 622, 623, 629, 630, 633, 640, 642, 643, 666, 669, 670, 676, 677, 680, 703, 704, 706, 713, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 873, 880, 882, 883, 907, 909, 910, 916, 917, 919, 1021, 1022, 1025, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1086, 1110, 1112, 1119, 1122, 1224, 1225, 1226, 1228, 1231, 1232, 1238, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1279, 1285, 1286, 1288, 1312, 1313, 1315, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1455, 1478, 1479, 1481, 1482, 1488, 1492, 1515, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1654, 1657, 1658, 1681, 1682, 1684, 1691, 1694, 1695, 1718, 1719, 1722, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1847, 1848, 1850, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1898, 1921, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2060, 2064, 2087, 2088, 2090, 2097, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2253, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2294, 2301, 2303, 2304, 2327, 2328, 2330, 2337, 2340, 2442, 2443, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2469, 2470, 2493, 2494, 2496, 2497, 2504, 2506, 2531, 2533, 2540, 2541, 2543, 2645, 2646, 2649, 2652, 2653, 2659, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2856, 2862, 2863, 2866, 2872, 2875, 2876, 2899, 2902, 2903, 2909, 2910, 2912, 2936, 2937, 2939, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3103, 3106, 3112, 3113, 3115, 3139, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3475, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3543, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3725, 3748, 3752, 3759, 3761, 3863, 3864, 3867, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 4055, 4066, 4067, 4068, 4070, 4073, 4074, 4080, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4472, 4473, 4479, 4480, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 3 * x + 3 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation676.lean b/equational_theories/Generated/FinitePoly/Refutation676.lean new file mode 100644 index 00000000..11ba829d --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation676.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 4 * x + 2 * y + 0 * x * y) % 5' (0, 2, 7, 22, 25, 46, 64, 72, 98, 101, 116, 124, 150, 159, 166, 202, 211, 228, 254, 257, 262, 306, 325, 334, 358, 361, 374, 410, 428, 436, 463, 472, 503, 512, 545, 561, 613, 616, 631, 639, 678, 703, 816, 825, 832, 871, 878, 909, 916, 948, 961, 1019, 1028, 1045, 1075, 1084, 1109, 1118, 1222, 1225, 1230, 1277, 1322, 1425, 1454, 1481, 1490, 1517, 1525, 1628, 1631, 1653, 1657, 1661, 1681, 1720, 1728, 1789, 1831, 1837, 1849, 1860, 1872, 1884, 1896, 1924, 1966, 2034, 2043, 2052, 2059, 2099, 2124, 2237, 2266, 2293, 2299, 2327, 2329, 2440, 2448, 2456, 2469, 2484, 2502, 2532, 2540, 2585, 2643, 2652, 2662, 2671, 2698, 2743, 2846, 2849, 2862, 2874, 2909, 2938, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3112, 3252, 3270, 3278, 3318, 3342, 3351, 3455, 3458, 3473, 3481, 3517, 3521, 3525, 3557, 3606, 3658, 3667, 3674, 3714, 3721, 3760, 3861, 3870, 3887, 3914, 3923, 3953, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4156, 4289, 4320, 4368, 4379, 4382, 4407, 4434, 4442, 4469, 4584, 4635, 4655) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 4 * x + 2 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 4 * x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 4 * x + 2 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [65, 73, 102, 117, 125, 160, 212, 229, 258, 263, 335, 362, 437, 546, 617, 632, 640, 679, 704, 826, 949, 962, 1029, 1046, 1076, 1085, 1110, 1119, 1226, 1231, 1278, 1323, 1455, 1491, 1518, 1526, 1632, 1658, 1721, 1790, 1838, 1861, 1897, 1967, 2044, 2053, 2060, 2100, 2267, 2294, 2300, 2328, 2330, 2449, 2470, 2533, 2586, 2653, 2663, 2672, 2744, 2850, 2863, 2875, 2910, 2939, 3053, 3058, 3079, 3113, 3271, 3279, 3352, 3459, 3482, 3607, 3668, 3761, 3871, 3888, 3924, 3954, 4157, 4369, 4383, 4408, 4435, 4443, 4585] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 66, 72, 75, 100, 101, 104, 105, 107, 108, 114, 115, 118, 124, 127, 152, 153, 154, 156, 157, 159, 166, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 218, 219, 221, 222, 228, 231, 256, 257, 260, 261, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 332, 333, 336, 360, 361, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 430, 436, 439, 440, 463, 466, 467, 474, 476, 477, 500, 501, 503, 510, 511, 615, 616, 619, 620, 622, 623, 629, 630, 633, 639, 642, 643, 666, 667, 669, 670, 676, 677, 680, 703, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 832, 835, 836, 842, 843, 845, 846, 869, 870, 873, 880, 882, 883, 906, 907, 909, 916, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1035, 1036, 1038, 1039, 1045, 1048, 1049, 1072, 1073, 1075, 1082, 1083, 1086, 1109, 1112, 1113, 1120, 1122, 1224, 1225, 1228, 1229, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1478, 1479, 1481, 1488, 1489, 1492, 1515, 1516, 1519, 1525, 1528, 1630, 1631, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1655, 1657, 1681, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1722, 1728, 1731, 1833, 1834, 1835, 1837, 1840, 1841, 1847, 1848, 1851, 1857, 1858, 1860, 1884, 1887, 1888, 1894, 1895, 1898, 1921, 1922, 1924, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2050, 2051, 2054, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2101, 2124, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2290, 2291, 2293, 2301, 2303, 2304, 2327, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2450, 2456, 2459, 2460, 2466, 2467, 2469, 2493, 2494, 2496, 2497, 2504, 2506, 2507, 2530, 2531, 2534, 2540, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2659, 2660, 2662, 2669, 2670, 2673, 2696, 2697, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2746, 2848, 2849, 2852, 2853, 2855, 2856, 2862, 2865, 2866, 2872, 2873, 2876, 2899, 2900, 2902, 2903, 2909, 2912, 2913, 2936, 2937, 2940, 2946, 2947, 2949, 3051, 3052, 3055, 3056, 3059, 3065, 3068, 3069, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3272, 3278, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3345, 3346, 3353, 3355, 3457, 3458, 3461, 3462, 3464, 3465, 3471, 3472, 3475, 3481, 3484, 3509, 3511, 3512, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3660, 3661, 3662, 3664, 3665, 3667, 3674, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3863, 3864, 3865, 3867, 3868, 3870, 3877, 3878, 3880, 3881, 3887, 3890, 3917, 3918, 3925, 3927, 3928, 3951, 3952, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4070, 4071, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4128, 4130, 4154, 4155, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4291, 4293, 4314, 4320, 4343, 4368, 4373, 4381, 4382, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4433, 4436, 4442, 4445, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 4 * x + 2 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation68.lean b/equational_theories/Generated/FinitePoly/Refutation68.lean new file mode 100644 index 00000000..f12c8a16 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation68.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 1 * x + 1 * y + 2 * x * y) % 3' (0, 306, 2034, 2049, 3252, 3658, 3659) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + x + y + 2 * x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + 2 * y*y + x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + x + y + 2 * x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [307, 2050, 3660] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 308, 309, 310, 312, 313, 315, 316, 323, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + 2 * y² + x + y + 2 * x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation682.lean b/equational_theories/Generated/FinitePoly/Refutation682.lean new file mode 100644 index 00000000..9611f634 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation682.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 4 * x + 3 * y + 0 * x * y) % 5' (0, 22, 25, 410, 419, 428, 463, 472, 503, 512, 545, 561, 816, 832, 844, 871, 878, 909, 916, 948, 961, 1628, 1631, 1653, 1657, 1661, 1681, 1693, 1728, 1789, 1831, 1837, 1849, 1860, 1872, 1884, 1924, 1930, 1966, 2440, 2448, 2456, 2469, 2484, 2496, 2502, 2540, 2585, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3141, 3455, 3458, 3473, 3517, 3521, 3525, 3545, 3557, 3606, 4064, 4067, 4072, 4090, 4117, 4126, 4130, 4134, 4145, 4275, 4289, 4368, 4584, 4607, 4655) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 4 * x + 3 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 4 * x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 4 * x + 3 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [420, 546, 845, 949, 962, 1658, 1694, 1790, 1931, 1967, 2470, 2497, 2586, 3142, 3546, 3607, 4091, 4276, 4608] [2, 3, 8, 24, 25, 28, 29, 31, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 419, 426, 427, 430, 436, 437, 439, 440, 463, 466, 467, 474, 476, 477, 500, 501, 503, 510, 511, 614, 818, 819, 820, 822, 823, 825, 826, 832, 835, 836, 842, 843, 846, 869, 870, 873, 880, 882, 883, 906, 907, 909, 916, 919, 1020, 1223, 1426, 1630, 1631, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1655, 1657, 1681, 1684, 1685, 1691, 1692, 1695, 1718, 1719, 1721, 1722, 1728, 1731, 1833, 1834, 1835, 1837, 1840, 1841, 1847, 1848, 1851, 1857, 1858, 1860, 1884, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1932, 1934, 2035, 2238, 2442, 2443, 2444, 2446, 2447, 2450, 2456, 2459, 2460, 2466, 2467, 2469, 2493, 2494, 2496, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2543, 2644, 2847, 3051, 3052, 3055, 3056, 3059, 3065, 3068, 3069, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3143, 3149, 3150, 3152, 3253, 3337, 3457, 3458, 3461, 3462, 3464, 3465, 3471, 3472, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3519, 3521, 3543, 3545, 3548, 3549, 3555, 3556, 3659, 3862, 4055, 4066, 4067, 4070, 4071, 4074, 4080, 4081, 4083, 4084, 4090, 4093, 4120, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4283, 4284, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 4 * x + 3 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation690.lean b/equational_theories/Generated/FinitePoly/Refutation690.lean new file mode 100644 index 00000000..03159dc4 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation690.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 2 * x + 2 * y + 0 * x * y) % 5' (0, 42, 150, 410, 419, 426, 428, 472, 510, 512, 555, 561, 613, 622, 631, 638, 666, 706, 713, 748, 774, 1019, 1022, 1025, 1047, 1108, 1112, 1116, 1119, 1130, 1222, 1228, 1238, 1250, 1277, 1288, 1300, 1315, 1354, 2237, 2253, 2265, 2292, 2299, 2330, 2337, 2369, 2382, 2440, 2443, 2468, 2502, 2506, 2510, 2529, 2533, 2537, 2846, 2854, 2864, 2899, 2912, 2927, 2939, 2945, 2981, 3049, 3055, 3067, 3078, 3090, 3104, 3115, 3127, 3148, 4275, 4282, 4357, 4379, 4388, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4590, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x + 2 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 2 * x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x + 2 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [43, 151, 420, 556, 623, 749, 775, 1048, 1117, 1131, 1251, 1301, 1355, 2266, 2370, 2383, 2469, 2511, 2538, 2928, 2946, 2982, 3128, 3149, 4389, 4591] [2, 3, 8, 23, 38, 39, 40, 47, 99, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 419, 426, 430, 436, 437, 439, 440, 463, 464, 466, 467, 474, 476, 477, 500, 501, 503, 504, 510, 615, 616, 617, 619, 620, 622, 629, 630, 633, 640, 642, 643, 666, 669, 670, 676, 677, 679, 680, 703, 704, 706, 713, 716, 817, 1021, 1022, 1025, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1110, 1112, 1119, 1122, 1224, 1225, 1226, 1228, 1231, 1232, 1238, 1241, 1242, 1248, 1249, 1252, 1275, 1276, 1279, 1285, 1286, 1288, 1312, 1313, 1315, 1322, 1323, 1325, 1426, 1629, 1832, 2035, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2256, 2257, 2263, 2264, 2267, 2290, 2291, 2294, 2301, 2303, 2304, 2327, 2328, 2330, 2337, 2340, 2442, 2443, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2470, 2493, 2494, 2496, 2497, 2504, 2506, 2531, 2533, 2540, 2541, 2543, 2644, 2848, 2849, 2850, 2852, 2853, 2856, 2862, 2863, 2866, 2872, 2873, 2875, 2876, 2899, 2902, 2903, 2909, 2910, 2912, 2936, 2937, 2939, 2947, 2949, 3051, 3052, 3053, 3055, 3058, 3059, 3065, 3066, 3069, 3075, 3076, 3078, 3102, 3103, 3106, 3112, 3113, 3115, 3139, 3140, 3142, 3143, 3150, 3152, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4399, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4473, 4479, 4480, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4598, 4599, 4605, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 2 * x + 2 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation72.lean b/equational_theories/Generated/FinitePoly/Refutation72.lean new file mode 100644 index 00000000..12b7323e --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation72.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 0 * x + 1 * y + 0 * x * y) % 3' (0, 38, 44, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => y*y + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [4263, 4368, 4373, 4374, 4682, 4689] [2, 3, 8, 23, 38, 40, 43, 47, 99, 151, 203, 255, 307, 331, 360, 362, 365, 368, 374, 377, 384, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3863, 3865, 3868, 3871, 3878, 3881, 3888, 3917, 3924, 3927, 3951, 3954, 3961, 3964, 4066, 4068, 4071, 4074, 4081, 4084, 4091, 4120, 4127, 4130, 4154, 4157, 4164, 4167, 4380, 4539, 4547, 4571, 4583, 4585, 4588, 4591, 4598, 4605, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly y² + y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation74.lean b/equational_theories/Generated/FinitePoly/Refutation74.lean new file mode 100644 index 00000000..69338d85 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation74.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 2 * y**2 + 2 * x + 2 * y + 0 * x * y) % 3' (0, 2, 7, 22, 46, 98, 100, 103, 150, 202, 204, 207, 254, 306, 325, 358, 374, 410, 613, 615, 618, 816, 821, 831, 1019, 1021, 1024, 1027, 1030, 1034, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1257, 1425, 1628, 1630, 1633, 1831, 1836, 1846, 2034, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2272, 2440, 2442, 2445, 2455, 2465, 2475, 2643, 2645, 2648, 2846, 2851, 2861, 3049, 3252, 3318, 3455, 3457, 3460, 3511, 3518, 3521, 3524, 3532, 3658, 3714, 3721, 3861, 3863, 3866, 3914, 3917, 3920, 3924, 3934, 4064, 4117, 4379, 4469) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + 2 * y² + 2 * x + 2 * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => x*x + 2 * y*y + 2 * x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + 2 * y² + 2 * x + 2 * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [3, 101, 104, 205, 208, 359, 616, 619, 822, 832, 1035, 1234, 1244, 1631, 1634, 1837, 1847, 2259, 2273, 2443, 2646, 2649, 2852, 2862, 3525, 3533, 3921, 3935, 4380] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 43, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 102, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 206, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 323, 325, 331, 332, 333, 335, 336, 360, 361, 362, 364, 365, 367, 368, 374, 377, 378, 384, 385, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 617, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 823, 825, 826, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1023, 1026, 1029, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1226, 1229, 1232, 1239, 1242, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1632, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1838, 1840, 1841, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2241, 2244, 2247, 2254, 2257, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2444, 2447, 2449, 2450, 2457, 2459, 2460, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2647, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2853, 2855, 2856, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3459, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3721, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3865, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3917, 3924, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4396, 4398, 4399, 4405, 4406, 4408, 4433, 4435, 4436, 4442, 4443, 4445, 4472, 4473, 4479, 4480, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 3, «FinitePoly x² + 2 * y² + 2 * x + 2 * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation78.lean b/equational_theories/Generated/FinitePoly/Refutation78.lean new file mode 100644 index 00000000..01e6dbf4 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation78.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 1 * y**2 + 0 * x + 0 * y + 1 * x * y) % 2' (0, 22, 24, 30, 39, 202, 204, 207, 210, 213, 217, 220, 223, 230, 241, 245, 306, 308, 309, 311, 312, 315, 318, 319, 322, 1628, 1630, 1636, 1643, 1646, 1649, 1656, 1671, 1717, 1720, 1723, 1730, 1745, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2289, 2292, 2295, 2299, 2302, 2305, 2309, 2313, 2317, 2321, 2326, 2329, 2332, 2339, 2350, 2354, 2363, 2367, 2371, 2375, 2384, 2388, 2401, 2405, 2419, 2424, 2429, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2495, 2505, 2516, 2529, 2532, 2535, 2542, 2553, 2557, 2570, 2587, 2604, 2622, 2643, 2645, 2651, 2658, 2661, 2664, 2671, 2686, 2695, 2698, 2701, 2705, 2708, 2711, 2723, 2732, 2735, 2738, 2745, 2760, 2769, 2773, 2777, 2781, 2790, 2794, 2811, 2835, 3049, 3051, 3057, 3064, 3067, 3070, 3077, 3092, 3104, 3114, 3138, 3141, 3144, 3151, 3166, 3179, 3196, 3252, 3254, 3255, 3257, 3258, 3260, 3261, 3263, 3264, 3265, 3267, 3268, 3270, 3271, 3273, 3274, 3275, 3277, 3278, 3281, 3284, 3285, 3287, 3288, 3289, 3292, 3293, 3296, 3297, 3300, 3301, 3302, 3305, 3455, 3457, 3458, 3460, 3463, 3466, 3471, 3474, 3477, 3480, 3481, 3484, 3487, 3488, 3491, 3495, 3499, 3503, 3508, 3518, 3521, 3524, 3528, 3536, 3658, 3661, 3663, 3664, 3667, 3671, 3673, 3676, 3677, 3681, 3683, 3687, 3691, 3693, 3698, 3699, 3703, 3708, 3711, 3748, 3758, 3768, 3785, 3819, 4064, 4067, 4069, 4083, 4089, 4093, 4097, 4104, 4117, 4127, 4130, 4137, 4154, 4164, 4174, 4225, 4268, 4269, 4271, 4272, 4275, 4278, 4279, 4313, 4315, 4317, 4319, 4320, 4323, 4324, 4326, 4330, 4331, 4335, 4336, 4340, 4342, 4345, 4350, 4354, 4361, 4583, 4589, 4605, 4610, 4621, 4630, 4657) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly y² + x * y % 2» : Magma (Fin 2) where + op := memoFinOp fun x y => y*y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly y² + x * y % 2» : + ∃ (G : Type) (_ : Magma G), Facts G [25, 31, 224, 242, 246, 319, 320, 323, 1647, 1672, 1724, 2285, 2376, 2420, 2425, 2430, 2488, 2496, 2506, 2536, 2558, 2652, 2662, 2672, 2712, 2736, 2746, 3093, 3145, 3180, 3197, 3265, 3274, 3290, 3294, 3301, 3303, 3472, 3475, 3482, 3489, 3529, 3662, 3668, 3678, 3769, 3786, 4098, 4105, 4128, 4131, 4175, 4324, 4337, 4346, 4362, 4611, 4658] [2, 3, 8, 24, 26, 28, 29, 38, 39, 43, 47, 99, 151, 204, 206, 209, 212, 219, 222, 228, 229, 255, 308, 315, 325, 326, 331, 332, 333, 335, 336, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1630, 1632, 1634, 1635, 1638, 1645, 1648, 1654, 1655, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1719, 1722, 1728, 1729, 1832, 2035, 2239, 2241, 2244, 2247, 2254, 2257, 2264, 2267, 2291, 2294, 2301, 2304, 2328, 2331, 2337, 2338, 2442, 2444, 2447, 2450, 2457, 2460, 2467, 2470, 2493, 2494, 2497, 2503, 2504, 2507, 2531, 2534, 2540, 2541, 2645, 2647, 2649, 2650, 2653, 2660, 2663, 2669, 2670, 2673, 2697, 2700, 2707, 2710, 2734, 2737, 2743, 2744, 2847, 3051, 3053, 3055, 3056, 3059, 3066, 3069, 3075, 3076, 3079, 3102, 3103, 3106, 3112, 3113, 3116, 3140, 3143, 3149, 3150, 3254, 3281, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3462, 3465, 3471, 3474, 3484, 3511, 3512, 3518, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3667, 3675, 3685, 3687, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3751, 3752, 3758, 3761, 3862, 4055, 4066, 4067, 4071, 4073, 4074, 4080, 4081, 4083, 4091, 4093, 4120, 4121, 4127, 4130, 4154, 4157, 4158, 4164, 4167, 4258, 4268, 4275, 4283, 4284, 4290, 4291, 4293, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4608, 4629, 4635, 4636, 4683, 4688] := + ⟨Fin 2, «FinitePoly y² + x * y % 2», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation8.lean b/equational_theories/Generated/FinitePoly/Refutation8.lean new file mode 100644 index 00000000..b299542f --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation8.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 1 * x + 1 * y + 0 * x * y) % 2' (0, 2, 4, 7, 9, 12, 15, 18, 22, 24, 27, 30, 33, 38, 44, 46, 48, 51, 54, 57, 61, 64, 67, 71, 74, 77, 81, 85, 89, 93, 98, 100, 103, 106, 109, 113, 116, 119, 123, 126, 129, 133, 137, 141, 145, 150, 152, 155, 158, 161, 165, 168, 171, 175, 178, 181, 185, 189, 193, 197, 202, 204, 207, 210, 213, 217, 220, 223, 227, 230, 233, 237, 241, 245, 249, 254, 256, 259, 262, 265, 269, 272, 275, 279, 282, 285, 289, 293, 297, 301, 306, 308, 311, 314, 317, 322, 325, 328, 332, 335, 338, 342, 346, 350, 354, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 462, 465, 468, 472, 475, 478, 482, 486, 490, 494, 499, 502, 505, 509, 512, 515, 519, 523, 527, 531, 536, 540, 544, 548, 553, 557, 561, 565, 570, 574, 578, 582, 587, 592, 597, 602, 607, 613, 615, 618, 621, 624, 628, 631, 634, 638, 641, 644, 648, 652, 656, 660, 665, 668, 671, 675, 678, 681, 685, 689, 693, 697, 702, 705, 708, 712, 715, 718, 722, 726, 730, 734, 739, 743, 747, 751, 756, 760, 764, 768, 773, 777, 781, 785, 790, 795, 800, 805, 810, 816, 818, 821, 824, 827, 831, 834, 837, 841, 844, 847, 851, 855, 859, 863, 868, 871, 874, 878, 881, 884, 888, 892, 896, 900, 905, 908, 911, 915, 918, 921, 925, 929, 933, 937, 942, 946, 950, 954, 959, 963, 967, 971, 976, 980, 984, 988, 993, 998, 1003, 1008, 1013, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1071, 1074, 1077, 1081, 1084, 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2384, 2388, 2392, 2397, 2401, 2405, 2409, 2414, 2419, 2424, 2429, 2434, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2492, 2495, 2498, 2502, 2505, 2508, 2512, 2516, 2520, 2524, 2529, 2532, 2535, 2539, 2542, 2545, 2549, 2553, 2557, 2561, 2566, 2570, 2574, 2578, 2583, 2587, 2591, 2595, 2600, 2604, 2608, 2612, 2617, 2622, 2627, 2632, 2637, 2643, 2645, 2648, 2651, 2654, 2658, 2661, 2664, 2668, 2671, 2674, 2678, 2682, 2686, 2690, 2695, 2698, 2701, 2705, 2708, 2711, 2715, 2719, 2723, 2727, 2732, 2735, 2738, 2742, 2745, 2748, 2752, 2756, 2760, 2764, 2769, 2773, 2777, 2781, 2786, 2790, 2794, 2798, 2803, 2807, 2811, 2815, 2820, 2825, 2830, 2835, 2840, 2846, 2848, 2851, 2854, 2857, 2861, 2864, 2867, 2871, 2874, 2877, 2881, 2885, 2889, 2893, 2898, 2901, 2904, 2908, 2911, 2914, 2918, 2922, 2926, 2930, 2935, 2938, 2941, 2945, 2948, 2951, 2955, 2959, 2963, 2967, 2972, 2976, 2980, 2984, 2989, 2993, 2997, 3001, 3006, 3010, 3014, 3018, 3023, 3028, 3033, 3038, 3043, 3049, 3051, 3054, 3057, 3060, 3064, 3067, 3070, 3074, 3077, 3080, 3084, 3088, 3092, 3096, 3101, 3104, 3107, 3111, 3114, 3117, 3121, 3125, 3129, 3133, 3138, 3141, 3144, 3148, 3151, 3154, 3158, 3162, 3166, 3170, 3175, 3179, 3183, 3187, 3192, 3196, 3200, 3204, 3209, 3213, 3217, 3221, 3226, 3231, 3236, 3241, 3246, 3252, 3254, 3257, 3260, 3263, 3267, 3270, 3273, 3277, 3280, 3283, 3287, 3291, 3295, 3299, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3342, 3345, 3348, 3352, 3355, 3358, 3362, 3366, 3370, 3374, 3379, 3383, 3387, 3391, 3396, 3400, 3404, 3408, 3413, 3417, 3421, 3425, 3430, 3435, 3440, 3445, 3450, 3455, 3457, 3460, 3463, 3466, 3470, 3473, 3476, 3480, 3483, 3486, 3490, 3494, 3498, 3502, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3545, 3548, 3551, 3555, 3558, 3561, 3565, 3569, 3573, 3577, 3582, 3586, 3590, 3594, 3599, 3603, 3607, 3611, 3616, 3620, 3624, 3628, 3633, 3638, 3643, 3648, 3653, 3658, 3660, 3663, 3666, 3669, 3673, 3676, 3679, 3683, 3686, 3689, 3693, 3697, 3701, 3705, 3711, 3714, 3717, 3721, 3724, 3727, 3731, 3735, 3739, 3743, 3748, 3751, 3754, 3758, 3761, 3764, 3768, 3772, 3776, 3780, 3785, 3789, 3793, 3797, 3802, 3806, 3810, 3814, 3819, 3823, 3827, 3831, 3836, 3841, 3846, 3851, 3856, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4268, 4271, 4274, 4277, 4283, 4286, 4290, 4295, 4299, 4303, 4306, 4309, 4315, 4319, 4322, 4326, 4329, 4333, 4339, 4347, 4350, 4353, 4359, 4361, 4366, 4373, 4377, 4379, 4381, 4384, 4387, 4390, 4395, 4398, 4401, 4405, 4408, 4411, 4415, 4419, 4423, 4427, 4431, 4434, 4437, 4441, 4444, 4447, 4451, 4455, 4459, 4463, 4469, 4472, 4475, 4479, 4482, 4485, 4489, 4493, 4497, 4501, 4507, 4511, 4515, 4519, 4524, 4528, 4532, 4536, 4541, 4545, 4549, 4553, 4558, 4563, 4568, 4573, 4578, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + x + y % 2» : Magma (Fin 2) where + op := memoFinOp fun x y => x*x + x + y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + x + y % 2» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 5, 10, 13, 16, 25, 28, 31, 58, 68, 78, 82, 86, 90, 146, 198, 250, 302, 318, 329, 339, 343, 347, 351, 608, 811, 1014, 1158, 1175, 1192, 1197, 1202, 1207, 1212, 1307, 1344, 1361, 1378, 1395, 1410, 1415, 1623, 1657, 1697, 1705, 1734, 1742, 1793, 1890, 1900, 1912, 1927, 1937, 1966, 1983, 2000, 2046, 2066, 2074, 2103, 2111, 2140, 2148, 2186, 2199, 2376, 2393, 2410, 2415, 2420, 2425, 2430, 2499, 2509, 2521, 2536, 2546, 2558, 2575, 2592, 2609, 2662, 2672, 2712, 2720, 2749, 2757, 2808, 2905, 2915, 2927, 2942, 2952, 2964, 2981, 2998, 3015, 3061, 3081, 3089, 3118, 3126, 3155, 3163, 3201, 3214, 3284, 3296, 3375, 3392, 3409, 3418, 3441, 3654, 3857, 4112, 4187, 4221, 4238, 4243, 4248, 4253, 4258, 4579, 4682] [2, 4, 9, 11, 14, 24, 26, 38, 40, 43, 48, 50, 53, 56, 63, 66, 73, 100, 102, 105, 108, 115, 118, 125, 152, 154, 157, 160, 167, 170, 177, 204, 206, 209, 212, 219, 222, 229, 256, 258, 261, 264, 271, 274, 281, 308, 310, 313, 316, 325, 331, 332, 335, 360, 362, 365, 368, 374, 377, 384, 412, 414, 417, 420, 427, 430, 437, 440, 464, 467, 474, 477, 501, 504, 511, 615, 617, 620, 623, 630, 633, 640, 643, 667, 670, 677, 680, 704, 707, 714, 818, 820, 823, 826, 833, 836, 843, 846, 870, 873, 880, 883, 907, 910, 917, 1021, 1023, 1026, 1029, 1036, 1039, 1046, 1049, 1073, 1076, 1083, 1086, 1110, 1113, 1120, 1224, 1226, 1229, 1232, 1239, 1242, 1249, 1252, 1276, 1279, 1286, 1289, 1313, 1316, 1323, 1427, 1429, 1432, 1435, 1442, 1445, 1452, 1455, 1479, 1482, 1489, 1492, 1516, 1519, 1526, 1630, 1632, 1635, 1638, 1645, 1648, 1655, 1658, 1682, 1685, 1692, 1695, 1719, 1722, 1729, 1833, 1835, 1838, 1841, 1848, 1851, 1858, 1861, 1885, 1888, 1895, 1898, 1922, 1925, 1932, 2036, 2038, 2041, 2044, 2051, 2054, 2061, 2064, 2088, 2091, 2098, 2101, 2125, 2128, 2135, 2239, 2241, 2244, 2247, 2254, 2257, 2264, 2267, 2291, 2294, 2301, 2304, 2328, 2331, 2338, 2442, 2444, 2447, 2450, 2457, 2460, 2467, 2470, 2494, 2497, 2504, 2507, 2531, 2534, 2541, 2645, 2647, 2650, 2653, 2660, 2663, 2670, 2673, 2697, 2700, 2707, 2710, 2734, 2737, 2744, 2848, 2850, 2853, 2856, 2863, 2866, 2873, 2876, 2900, 2903, 2910, 2913, 2937, 2940, 2947, 3051, 3053, 3056, 3059, 3066, 3069, 3076, 3079, 3103, 3106, 3113, 3116, 3140, 3143, 3150, 3254, 3256, 3259, 3262, 3269, 3272, 3279, 3308, 3315, 3318, 3337, 3342, 3345, 3352, 3355, 3457, 3459, 3462, 3465, 3472, 3475, 3482, 3511, 3518, 3521, 3543, 3545, 3548, 3555, 3558, 3660, 3662, 3665, 3668, 3675, 3678, 3685, 3714, 3721, 3724, 3748, 3751, 3758, 3761, 3863, 3865, 3868, 3871, 3878, 3881, 3888, 3917, 3924, 3927, 3951, 3954, 3961, 3964, 4066, 4068, 4071, 4074, 4081, 4084, 4091, 4120, 4127, 4130, 4154, 4157, 4164, 4167, 4268, 4270, 4273, 4276, 4283, 4290, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4383, 4386, 4398, 4405, 4408, 4433, 4436, 4443, 4472, 4479, 4482, 4539, 4547, 4571, 4583, 4585, 4588, 4591, 4598, 4605, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 2, «FinitePoly x² + x + y % 2», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation82.lean b/equational_theories/Generated/FinitePoly/Refutation82.lean new file mode 100644 index 00000000..09b6df57 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation82.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(1 * x**2 + 0 * y**2 + 0 * x + 0 * y + 1 * x * y) % 2' (0, 7, 9, 10, 39, 98, 99, 100, 103, 104, 105, 106, 107, 108, 109, 110, 358, 359, 360, 364, 366, 367, 368, 370, 377, 410, 412, 413, 425, 426, 428, 429, 431, 432, 433, 435, 436, 438, 439, 441, 442, 443, 816, 817, 818, 819, 820, 822, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 853, 857, 1019, 1021, 1022, 1024, 1027, 1030, 1034, 1035, 1037, 1038, 1040, 1041, 1042, 1044, 1045, 1047, 1048, 1050, 1051, 1052, 1054, 1055, 1058, 1059, 1062, 1063, 1066, 1067, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1233, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1269, 1270, 1831, 1833, 1834, 1846, 1849, 1850, 1852, 1854, 1856, 1859, 1860, 1862, 1864, 3252, 3254, 3255, 3277, 3278, 3281, 3284, 3285, 3305, 3314, 3315, 3317, 3318, 3320, 3321, 3322, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 3720, 3723, 3724, 3725, 3726, 3728, 3861, 3863, 3864, 3866, 3869, 3872, 3877, 3880, 3883, 3886, 3887, 3890, 3893, 3894, 3897, 3901, 3905, 3909, 3914, 3924, 3927, 3930, 3934, 3942, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4075, 4080, 4082, 4083, 4084, 4086, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4100, 4103, 4104, 4105, 4106, 4108, 4112, 4130, 4268, 4269, 4292, 4313, 4315, 4317, 4340, 4582, 4583, 4587, 4589, 4590, 4591, 4593, 4596, 4597, 4600, 4605, 4607, 4608, 4610, 4615, 4619, 4621, 4622, 4625, 4630, 4635, 4638, 4646, 4650, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x² + x * y % 2» : Magma (Fin 2) where + op := memoFinOp fun x y => x*x + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x² + x * y % 2» : + ∃ (G : Type) (_ : Magma G), Facts G [1, 10, 11, 106, 109, 111, 369, 371, 378, 429, 433, 434, 442, 443, 833, 836, 842, 845, 854, 1041, 1042, 1043, 1051, 1052, 1053, 1055, 1056, 1059, 1060, 1063, 1247, 1257, 1265, 1271, 1850, 1855, 1861, 1863, 3285, 3286, 3306, 3316, 3321, 3684, 3685, 3687, 3726, 3727, 3878, 3881, 3888, 3895, 3931, 4072, 4085, 4099, 4104, 4106, 4113, 4293, 4318, 4609, 4626, 4639, 4673] [2, 3, 9, 13, 14, 16, 23, 38, 39, 43, 47, 102, 114, 115, 117, 118, 124, 125, 127, 151, 203, 255, 307, 331, 362, 364, 374, 375, 377, 384, 385, 407, 412, 416, 417, 419, 420, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 614, 822, 825, 826, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1026, 1029, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1232, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1426, 1629, 1833, 1837, 1838, 1840, 1841, 1848, 1858, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3281, 3308, 3309, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3456, 3543, 3664, 3667, 3668, 3674, 3675, 3678, 3712, 3714, 3715, 3722, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3868, 3871, 3877, 3880, 3890, 3917, 3918, 3924, 3927, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4074, 4080, 4118, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4585, 4587, 4599, 4605, 4629, 4635, 4658, 4683, 4688] := + ⟨Fin 2, «FinitePoly x² + x * y % 2», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation84.lean b/equational_theories/Generated/FinitePoly/Refutation84.lean new file mode 100644 index 00000000..87aee070 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation84.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 39, 306, 309, 311, 315, 319, 3252, 3255, 3257, 3261, 3265, 3267, 3271, 3275, 3277, 3281, 3285, 3287, 3292, 3297, 3302, 3658, 3661, 3663, 3664, 3667, 3671, 3673, 3676, 3677, 3681, 3683, 3687, 3691, 3693, 3698, 3699, 3703, 3708, 4269, 4271, 4275, 4279, 4340, 4342, 4345, 4350, 4354, 4589, 4621) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + x * y % 3» : Magma (Fin 3) where + op := memoFinOp fun x y => 2 * y*y + x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + x * y % 3» : + ∃ (G : Type) (_ : Magma G), Facts G [320, 3303, 3662, 3668, 3678, 3700, 4346, 4622] [323, 3306] := + ⟨Fin 3, «FinitePoly 2 * y² + x * y % 3», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation88.lean b/equational_theories/Generated/FinitePoly/Refutation88.lean new file mode 100644 index 00000000..0ab54199 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation88.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(2 * x**2 + 3 * y**2 + 1 * x + 2 * y + 0 * x * y) % 4' (0, 22, 25, 1425, 1428, 1431, 1433, 1441, 1443, 1450, 1454, 1458, 1466, 1469, 1628, 1631, 1634, 1636, 1644, 1646, 1653, 1657, 1661, 1669, 1672, 1831, 1834, 1837, 1839, 1847, 1849, 1856, 1860, 1864, 1872, 1875, 2237, 2240, 2243, 2245, 2253, 2255, 2262, 2266, 2270, 2278, 2281, 2440, 2443, 2446, 2448, 2456, 2458, 2465, 2469, 2473, 2481, 2484, 2643, 2651, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3661, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4269, 4282, 4340, 4357, 4584, 4655) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * x² + 3 * y² + x + 2 * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * x*x + 3 * y*y + x + 2 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * x² + 3 * y² + x + 2 * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [26, 1459, 1467, 1470, 1632, 1654, 1670, 1673, 1838, 1850, 1865, 1876, 2271, 2279, 2282, 2449, 2457, 2474, 2482, 2652, 3053, 3058, 3066, 3075, 3079, 3323, 3331, 3334, 3459, 3518, 3534, 3537, 3662, 4073, 4341, 4358, 4585] [2, 3, 8, 24, 25, 28, 29, 31, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1427, 1428, 1431, 1435, 1441, 1445, 1452, 1454, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1634, 1638, 1644, 1648, 1655, 1657, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1837, 1841, 1847, 1851, 1858, 1860, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2035, 2239, 2240, 2243, 2247, 2253, 2257, 2264, 2266, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2446, 2450, 2456, 2460, 2467, 2469, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2847, 3051, 3052, 3055, 3056, 3059, 3065, 3068, 3069, 3076, 3078, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3258, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3309, 3316, 3318, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3461, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3512, 3519, 3521, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3862, 4055, 4066, 4067, 4070, 4071, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4120, 4121, 4128, 4130, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4272, 4273, 4275, 4276, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4587, 4588, 4590, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * x² + 3 * y² + x + 2 * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation90.lean b/equational_theories/Generated/FinitePoly/Refutation90.lean new file mode 100644 index 00000000..70f0705d --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation90.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(3 * x**2 + 0 * y**2 + 0 * x + 1 * y + 2 * x * y) % 4' (0, 7, 15, 22, 30, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 621, 631, 638, 668, 675, 702, 715, 730, 764, 777, 816, 824, 834, 841, 871, 878, 905, 918, 933, 967, 980, 1019, 1027, 1037, 1044, 1074, 1081, 1108, 1121, 1136, 1170, 1183, 1222, 1230, 1240, 1247, 1277, 1284, 1311, 1324, 1339, 1373, 1386, 1425, 1433, 1443, 1450, 1480, 1487, 1514, 1527, 1542, 1576, 1589, 1628, 1636, 1646, 1653, 1683, 1690, 1717, 1730, 1745, 1779, 1792, 1831, 1839, 1849, 1856, 1886, 1893, 1920, 1933, 1948, 1982, 1995, 2034, 2042, 2052, 2059, 2089, 2096, 2123, 2136, 2151, 2185, 2198, 2237, 2245, 2255, 2262, 2292, 2299, 2326, 2339, 2354, 2388, 2401, 2440, 2448, 2458, 2465, 2495, 2502, 2529, 2542, 2557, 2591, 2604, 2643, 2651, 2661, 2668, 2698, 2705, 2732, 2745, 2760, 2794, 2807, 2846, 2854, 2864, 2871, 2901, 2908, 2935, 2948, 2963, 2997, 3010, 3049, 3057, 3067, 3074, 3104, 3111, 3138, 3151, 3166, 3200, 3213, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3463, 3473, 3480, 3508, 3521, 3536, 3548, 3555, 3590, 3616, 3658, 3666, 3676, 3683, 3711, 3724, 3739, 3751, 3758, 3793, 3819, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4082, 4089, 4117, 4130, 4145, 4157, 4164, 4199, 4225, 4274, 4306, 4319, 4361, 4379, 4387, 4395, 4408, 4423, 4434, 4441, 4472, 4479, 4511, 4524, 4589, 4621, 4634, 4676) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 3 * x² + y + 2 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 3 * x*x + y + 2 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 3 * x² + y + 2 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [16, 31, 419, 436, 466, 500, 562, 731, 765, 778, 934, 968, 981, 1045, 1075, 1137, 1171, 1340, 1374, 1387, 1543, 1577, 1590, 1637, 1718, 1793, 1840, 1921, 1983, 1996, 2152, 2186, 2199, 2355, 2389, 2402, 2466, 2496, 2558, 2592, 2652, 2662, 2706, 2733, 2808, 2964, 2998, 3011, 3058, 3139, 3201, 3214, 3261, 3388, 3464, 3591, 3617, 3740, 3794, 3887, 3943, 3962, 3997, 4090, 4146, 4165, 4200, 4362, 4424, 4512, 4525, 4590, 4677] [2, 3, 9, 10, 11, 13, 14, 24, 25, 26, 28, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 412, 413, 414, 416, 417, 420, 426, 427, 430, 437, 439, 440, 463, 464, 467, 474, 476, 477, 501, 503, 504, 510, 511, 615, 616, 617, 619, 620, 623, 629, 630, 633, 640, 642, 643, 666, 667, 670, 677, 679, 680, 704, 706, 707, 713, 714, 818, 819, 820, 822, 823, 826, 832, 833, 836, 843, 845, 846, 869, 870, 873, 880, 882, 883, 907, 909, 910, 916, 917, 1021, 1022, 1023, 1025, 1026, 1029, 1035, 1036, 1039, 1046, 1048, 1049, 1072, 1073, 1076, 1083, 1085, 1086, 1110, 1112, 1113, 1119, 1120, 1224, 1225, 1226, 1228, 1229, 1232, 1238, 1239, 1242, 1249, 1251, 1252, 1275, 1276, 1279, 1286, 1288, 1289, 1313, 1315, 1316, 1322, 1323, 1427, 1428, 1429, 1431, 1432, 1435, 1441, 1442, 1445, 1452, 1454, 1455, 1478, 1479, 1482, 1489, 1491, 1492, 1516, 1518, 1519, 1525, 1526, 1630, 1631, 1632, 1634, 1635, 1638, 1644, 1645, 1648, 1655, 1657, 1658, 1681, 1682, 1685, 1692, 1694, 1695, 1719, 1721, 1722, 1728, 1729, 1833, 1834, 1835, 1837, 1838, 1841, 1847, 1848, 1851, 1858, 1860, 1861, 1884, 1885, 1888, 1895, 1897, 1898, 1922, 1924, 1925, 1931, 1932, 2036, 2037, 2038, 2040, 2041, 2044, 2050, 2051, 2054, 2061, 2063, 2064, 2087, 2088, 2091, 2098, 2100, 2101, 2125, 2127, 2128, 2134, 2135, 2239, 2240, 2241, 2243, 2244, 2247, 2253, 2254, 2257, 2264, 2266, 2267, 2290, 2291, 2294, 2301, 2303, 2304, 2328, 2330, 2331, 2337, 2338, 2442, 2443, 2444, 2446, 2447, 2450, 2456, 2457, 2460, 2467, 2469, 2470, 2493, 2494, 2497, 2504, 2506, 2507, 2531, 2533, 2534, 2540, 2541, 2645, 2646, 2647, 2649, 2650, 2653, 2659, 2660, 2663, 2670, 2672, 2673, 2696, 2697, 2700, 2707, 2709, 2710, 2734, 2736, 2737, 2743, 2744, 2848, 2849, 2850, 2852, 2853, 2856, 2862, 2863, 2866, 2873, 2875, 2876, 2899, 2900, 2903, 2910, 2912, 2913, 2937, 2939, 2940, 2946, 2947, 3051, 3052, 3053, 3055, 3056, 3059, 3065, 3066, 3069, 3076, 3078, 3079, 3102, 3103, 3106, 3113, 3115, 3116, 3140, 3142, 3143, 3149, 3150, 3254, 3255, 3256, 3258, 3259, 3262, 3268, 3269, 3272, 3279, 3281, 3308, 3309, 3315, 3316, 3318, 3337, 3342, 3343, 3345, 3352, 3355, 3457, 3458, 3459, 3461, 3462, 3465, 3471, 3472, 3475, 3482, 3484, 3511, 3512, 3518, 3519, 3521, 3543, 3545, 3546, 3548, 3555, 3558, 3660, 3661, 3662, 3664, 3665, 3668, 3674, 3675, 3678, 3685, 3687, 3714, 3715, 3721, 3722, 3724, 3748, 3749, 3751, 3758, 3761, 3863, 3864, 3865, 3867, 3868, 3871, 3877, 3878, 3881, 3888, 3890, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3961, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4074, 4080, 4081, 4084, 4091, 4093, 4120, 4121, 4127, 4128, 4130, 4154, 4155, 4157, 4164, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4398, 4399, 4405, 4406, 4408, 4433, 4436, 4443, 4445, 4470, 4472, 4479, 4482, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4591, 4598, 4599, 4605, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 3 * x² + y + 2 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation92.lean b/equational_theories/Generated/FinitePoly/Refutation92.lean new file mode 100644 index 00000000..06f11bbe --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation92.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 4 * y**2 + 1 * x + 3 * y + 0 * x * y) % 5' (0, 816, 845, 1019, 1048, 4597, 4672) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 4 * y² + x + 3 * y % 5» : Magma (Fin 5) where + op := memoFinOp fun x y => 4 * y*y + x + 3 * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 4 * y² + x + 3 * y % 5» : + ∃ (G : Type) (_ : Magma G), Facts G [846, 1049, 4673] [2, 3, 8, 23, 38, 39, 40, 43, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3253, 3337, 3456, 3543, 3659, 3862, 4055, 4065, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4283, 4284, 4290, 4291, 4293, 4314, 4320, 4321, 4343, 4368, 4373, 4380, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4599, 4605, 4606, 4608, 4629, 4635, 4636, 4658, 4683, 4688] := + ⟨Fin 5, «FinitePoly 4 * y² + x + 3 * y % 5», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation94.lean b/equational_theories/Generated/FinitePoly/Refutation94.lean new file mode 100644 index 00000000..e14adb09 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation94.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 2 * y**2 + 0 * x + 2 * y + 3 * x * y) % 4' (0, 42, 3252, 3455, 3658, 3861, 4064, 4282, 4289, 4319, 4357, 4361, 4363, 4368, 4379, 4395, 4397, 4404, 4432, 4434, 4441, 4472, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4597, 4604, 4634, 4672, 4676, 4678, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly 2 * y² + 2 * y + 3 * x * y % 4» : Magma (Fin 4) where + op := memoFinOp fun x y => 2 * y*y + 2 * y + 3 * x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly 2 * y² + 2 * y + 3 * x * y % 4» : + ∃ (G : Type) (_ : Magma G), Facts G [43, 3253, 3456, 3659, 3862, 4065, 4358, 4362, 4364, 4369, 4512, 4515, 4525, 4541, 4544, 4673, 4679, 4684] [2, 3, 8, 23, 38, 39, 40, 47, 99, 151, 203, 255, 307, 331, 359, 407, 411, 614, 817, 1020, 1223, 1426, 1629, 1832, 2035, 2238, 2441, 2644, 2847, 3050, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3306, 3308, 3309, 3315, 3316, 3318, 3319, 3337, 3342, 3343, 3345, 3346, 3352, 3353, 3355, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3509, 3511, 3512, 3518, 3519, 3521, 3522, 3543, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3712, 3714, 3715, 3721, 3722, 3724, 3725, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 3915, 3917, 3918, 3924, 3925, 3927, 3928, 3951, 3952, 3954, 3955, 3961, 3962, 3964, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4118, 4120, 4121, 4127, 4128, 4130, 4131, 4154, 4155, 4157, 4158, 4164, 4165, 4167, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4284, 4291, 4293, 4314, 4321, 4343, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4399, 4406, 4408, 4436, 4443, 4445, 4470, 4472, 4479, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4599, 4606, 4608, 4629, 4636, 4658, 4683, 4688] := + ⟨Fin 4, «FinitePoly 2 * y² + 2 * y + 3 * x * y % 4», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/Refutation96.lean b/equational_theories/Generated/FinitePoly/Refutation96.lean new file mode 100644 index 00000000..00ff6ea3 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/Refutation96.lean @@ -0,0 +1,23 @@ + +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +'(0 * x**2 + 0 * y**2 + 0 * x + 0 * y + 1 * x * y) % 2' (0, 2, 7, 22, 42, 46, 98, 150, 202, 254, 306, 322, 324, 325, 331, 332, 334, 358, 374, 376, 377, 383, 384, 386, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3305, 3307, 3308, 3314, 3315, 3317, 3318, 3341, 3342, 3344, 3345, 3351, 3352, 3354, 3455, 3508, 3510, 3511, 3517, 3518, 3520, 3521, 3544, 3545, 3547, 3548, 3554, 3555, 3557, 3658, 3711, 3713, 3714, 3720, 3721, 3723, 3724, 3747, 3748, 3750, 3751, 3757, 3758, 3760, 3861, 3914, 3916, 3917, 3923, 3924, 3926, 3927, 3950, 3951, 3953, 3954, 3960, 3961, 3963, 4064, 4117, 4119, 4120, 4126, 4127, 4129, 4130, 4153, 4154, 4156, 4157, 4163, 4164, 4166, 4282, 4283, 4289, 4290, 4292, 4313, 4319, 4320, 4342, 4357, 4361, 4363, 4368, 4379, 4395, 4397, 4398, 4404, 4405, 4407, 4432, 4434, 4435, 4441, 4442, 4444, 4469, 4471, 4472, 4478, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4597, 4598, 4604, 4605, 4607, 4628, 4634, 4635, 4657, 4672, 4676, 4678, 4683) +-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «FinitePoly x * y % 2» : Magma (Fin 2) where + op := memoFinOp fun x y => x * y + +/-! The facts -/ +@[equational_result] +theorem «Facts from FinitePoly x * y % 2» : + ∃ (G : Type) (_ : Magma G), Facts G [323, 325, 332, 333, 335, 377, 384, 385, 387, 3308, 3309, 3315, 3318, 3345, 3346, 3352, 3355, 3509, 3511, 3512, 3519, 3521, 3545, 3546, 3548, 3549, 3555, 3556, 3558, 3712, 3714, 3721, 3724, 3748, 3749, 3751, 3752, 3758, 3759, 3761, 3917, 3918, 3924, 3925, 3927, 3951, 3952, 3954, 3955, 3961, 3964, 4120, 4154, 4155, 4157, 4158, 4164, 4165, 4284, 4291, 4293, 4314, 4321, 4343, 4358, 4362, 4364, 4369, 4399, 4406, 4408, 4436, 4443, 4445, 4472, 4479, 4512, 4515, 4525, 4541, 4544, 4606, 4608, 4629, 4636, 4658, 4673, 4679, 4684] [2, 4, 5, 9, 10, 11, 13, 14, 16, 24, 25, 26, 28, 31, 38, 39, 40, 48, 49, 50, 52, 53, 55, 56, 62, 63, 65, 66, 72, 73, 75, 100, 101, 102, 104, 105, 107, 108, 114, 115, 117, 118, 124, 125, 127, 152, 153, 154, 156, 157, 159, 160, 166, 167, 169, 170, 176, 177, 179, 204, 205, 206, 208, 209, 211, 212, 218, 219, 221, 222, 228, 229, 231, 256, 257, 258, 260, 261, 263, 264, 270, 271, 273, 274, 280, 281, 283, 308, 309, 310, 312, 313, 315, 316, 331, 336, 360, 361, 362, 364, 365, 367, 368, 374, 407, 412, 413, 414, 416, 417, 419, 420, 426, 427, 429, 430, 436, 437, 439, 440, 463, 464, 466, 467, 473, 474, 476, 477, 500, 501, 503, 504, 510, 511, 513, 615, 616, 617, 619, 620, 622, 623, 629, 630, 632, 633, 639, 640, 642, 643, 666, 667, 669, 670, 676, 677, 679, 680, 703, 704, 706, 707, 713, 714, 716, 818, 819, 820, 822, 823, 825, 826, 832, 833, 835, 836, 842, 843, 845, 846, 869, 870, 872, 873, 879, 880, 882, 883, 906, 907, 909, 910, 916, 917, 919, 1021, 1022, 1023, 1025, 1026, 1028, 1029, 1035, 1036, 1038, 1039, 1045, 1046, 1048, 1049, 1072, 1073, 1075, 1076, 1082, 1083, 1085, 1086, 1109, 1110, 1112, 1113, 1119, 1120, 1122, 1224, 1225, 1226, 1228, 1229, 1231, 1232, 1238, 1239, 1241, 1242, 1248, 1249, 1251, 1252, 1275, 1276, 1278, 1279, 1285, 1286, 1288, 1289, 1312, 1313, 1315, 1316, 1322, 1323, 1325, 1427, 1428, 1429, 1431, 1432, 1434, 1435, 1441, 1442, 1444, 1445, 1451, 1452, 1454, 1455, 1478, 1479, 1481, 1482, 1488, 1489, 1491, 1492, 1515, 1516, 1518, 1519, 1525, 1526, 1528, 1630, 1631, 1632, 1634, 1635, 1637, 1638, 1644, 1645, 1647, 1648, 1654, 1655, 1657, 1658, 1681, 1682, 1684, 1685, 1691, 1692, 1694, 1695, 1718, 1719, 1721, 1722, 1728, 1729, 1731, 1833, 1834, 1835, 1837, 1838, 1840, 1841, 1847, 1848, 1850, 1851, 1857, 1858, 1860, 1861, 1884, 1885, 1887, 1888, 1894, 1895, 1897, 1898, 1921, 1922, 1924, 1925, 1931, 1932, 1934, 2036, 2037, 2038, 2040, 2041, 2043, 2044, 2050, 2051, 2053, 2054, 2060, 2061, 2063, 2064, 2087, 2088, 2090, 2091, 2097, 2098, 2100, 2101, 2124, 2125, 2127, 2128, 2134, 2135, 2137, 2239, 2240, 2241, 2243, 2244, 2246, 2247, 2253, 2254, 2256, 2257, 2263, 2264, 2266, 2267, 2290, 2291, 2293, 2294, 2300, 2301, 2303, 2304, 2327, 2328, 2330, 2331, 2337, 2338, 2340, 2442, 2443, 2444, 2446, 2447, 2449, 2450, 2456, 2457, 2459, 2460, 2466, 2467, 2469, 2470, 2493, 2494, 2496, 2497, 2503, 2504, 2506, 2507, 2530, 2531, 2533, 2534, 2540, 2541, 2543, 2645, 2646, 2647, 2649, 2650, 2652, 2653, 2659, 2660, 2662, 2663, 2669, 2670, 2672, 2673, 2696, 2697, 2699, 2700, 2706, 2707, 2709, 2710, 2733, 2734, 2736, 2737, 2743, 2744, 2746, 2848, 2849, 2850, 2852, 2853, 2855, 2856, 2862, 2863, 2865, 2866, 2872, 2873, 2875, 2876, 2899, 2900, 2902, 2903, 2909, 2910, 2912, 2913, 2936, 2937, 2939, 2940, 2946, 2947, 2949, 3051, 3052, 3053, 3055, 3056, 3058, 3059, 3065, 3066, 3068, 3069, 3075, 3076, 3078, 3079, 3102, 3103, 3105, 3106, 3112, 3113, 3115, 3116, 3139, 3140, 3142, 3143, 3149, 3150, 3152, 3254, 3255, 3256, 3258, 3259, 3261, 3262, 3268, 3269, 3271, 3272, 3278, 3279, 3281, 3337, 3457, 3458, 3459, 3461, 3462, 3464, 3465, 3471, 3472, 3474, 3475, 3481, 3482, 3484, 3543, 3660, 3661, 3662, 3664, 3665, 3667, 3668, 3674, 3675, 3677, 3678, 3684, 3685, 3687, 3863, 3864, 3865, 3867, 3868, 3870, 3871, 3877, 3878, 3880, 3881, 3887, 3888, 3890, 4055, 4066, 4067, 4068, 4070, 4071, 4073, 4074, 4080, 4081, 4083, 4084, 4090, 4091, 4093, 4258, 4268, 4269, 4270, 4272, 4273, 4275, 4276, 4368, 4373, 4381, 4382, 4383, 4385, 4386, 4388, 4539, 4547, 4571, 4583, 4584, 4585, 4587, 4588, 4590, 4591, 4683, 4688] := + ⟨Fin 2, «FinitePoly x * y % 2», by decideFin!⟩ diff --git a/equational_theories/Generated/FinitePoly/src/finite_poly_generate_lean.py b/equational_theories/Generated/FinitePoly/src/finite_poly_generate_lean.py new file mode 100644 index 00000000..75bcda1c --- /dev/null +++ b/equational_theories/Generated/FinitePoly/src/finite_poly_generate_lean.py @@ -0,0 +1,170 @@ +#! /usr/bin/env python3 + +import ast +import re +import json +from pathlib import Path + +# +# This script reads the file `finite_poly_refutations.txt` and turns each line into a +# a file `equational_theories/Generated/FinitePoly/Refutation.lean` +# +# It also takes `implications.json` into account and prunes entries based on that. +# + +dir = Path(__file__).parent.parent + +# we have 4694 equations +full = range(1,4694+1) + +with open(f"{dir}/src/implications.json") as f: + implications = json.load(f)["implications"] +implications = [ (int(i["lhs"].removeprefix("Equation")), int(i["rhs"].removeprefix("Equation"))) for i in implications ] + +print("Number of implications:", len(implications)) + +impliedBy = { i : set() for i in full } +implying = { j : set() for j in full } + +for i, j in implications: + impliedBy[i].add(j) + impliedBy[i] |= impliedBy[j] + implying[j].add(i) + implying[j] |= implying[i] + +print("Size of transitive closure:", sum([len (s) for s in impliedBy.values()])) + +def parse_row(row): + if not row.startswith("'(") or "seen" in row: return + _, eq, nums = row.split("'") + data = set(ast.literal_eval(nums.strip())) + # the numbers are off by one, the offcial equations list is 1-indexed + satisfied = [i+1 for i in range(4694) if i in data] + refuted = [i+1 for i in range(4694) if i not in data] + + # we turn the equation as printed in the refutation file into a valid lean expression, + # and a pretty version of it for the name. We also remove trivial factors and summands + m = re.match(r"\((.*)\) % (.*)", eq) + div = int(m.group(2)) + + summands = m.group(1).split(" + ") + summands = [ s.removeprefix("1 * ") for s in summands if not s.startswith("0 * ") ] + poly = " + ".join(summands) if summands else "0" + + pretty_eq = poly + pretty_eq = pretty_eq.replace("**2", "²") + poly = poly.replace("x**2", "x*x").replace("y**2", "y*y") + return {"raw": row, "poly": poly, "pretty_eq": pretty_eq, "div": div, "satisfied": satisfied, "refuted": refuted} + + +stats = { + "total" : 0, + "removed_by_implication": 0, + "removed_by_covering": 0, +} + +notImpliedBy = { i : set() for i in full } +notImplying = { j : set() for j in full } + +def prune_row(data): + stats["total"] += len(data["satisfied"]) + len(data["refuted"]) + + # prune by implications + satisfied = set() + for i in data["satisfied"]: + # already implied + if implying[i].intersection(satisfied): + continue + # remove all implied by this + satisfied = satisfied - impliedBy[i] + satisfied.add(i) + refuted = set() + for i in data["refuted"]: + # already ruled out + if impliedBy[i].intersection(refuted): + continue + # remove all that this is ruling out + refuted = refuted - impliedBy[i] + refuted.add(i) + stats["removed_by_implication"] += len(data["satisfied"]) + len(data["refuted"]) - len(satisfied) - len(refuted) + + # prune by earlier examples + satisfied_ = {i for i in satisfied if refuted - notImpliedBy[i] } + refuted_ = {j for j in refuted if satisfied - notImplying[j] } + + stats["removed_by_covering"] += len(satisfied) + len(refuted) - len(satisfied_) - len(refuted_) + satisfied, refuted = satisfied_, refuted_ + + for i in satisfied: + for j in refuted: + notImpliedBy[i].add(j) + notImplying[j].add(i) + + data["satisfied"] = sorted(satisfied) + data["refuted"] = sorted(refuted) + return data + +def generate_lean(data): + raw = data["raw"] + poly = data["poly"] + pretty_eq = data["pretty_eq"] + div = data["div"] + satisfied = data["satisfied"] + refuted = data["refuted"] + + name = f"FinitePoly {pretty_eq} % {div}" + satname= lambda i: f"{name} satisfies Equation{i}" + refname= lambda i: f"{name} refutes Equation{i}" + + out = f""" +import equational_theories.AllEquations +import equational_theories.FactsSyntax +import equational_theories.MemoFinOp +import equational_theories.DecideBang + +/-! +This file is generated from the following refutation as produced by +random generation of polynomials: +{raw}-/ + +set_option linter.unusedVariables false + +/-! The magma definition -/ +def «{name}» : Magma (Fin {div}) where + op := memoFinOp fun x y => {poly} + +/-! The facts -/ +@[equational_result] +theorem «Facts from {name}» : + ∃ (G : Type) (_ : Magma G), Facts G {satisfied} {refuted} := + ⟨Fin {div}, «{name}», by decideFin!⟩ +""" + return out + + +with open(f"{dir}/src/finite_poly_refutations.txt") as f: + with open(f"{dir.parent}/FinitePoly.lean", "w") as main: + lines = f.readlines() + for i, line in enumerate(lines): + leanfile = f"{dir}/Refutation{i}.lean" + data = parse_row(line) + if data and data["div"] < 6: + data = prune_row(data) + print(f"Writing {leanfile}") + main.write(f"import equational_theories.Generated.FinitePoly.Refutation{i}\n") + with open(leanfile, "w") as f: + f.write(generate_lean(data)) + + +total = stats["total"] +removed_by_implication = stats["removed_by_implication"] +removed_by_covering = stats["removed_by_covering"] +remaining = total - removed_by_implication - removed_by_covering + +percentage_removed_by_implication = (removed_by_implication / total) * 100 if total > 0 else 0 +percentage_removed_by_covering = (removed_by_covering / total) * 100 if total > 0 else 0 + +print(f"Out of {total} facts to check, pruning by implication removed " + + f"{removed_by_implication} facts ({percentage_removed_by_implication:.2f}%) to check, " + + f"pruning by covering removed {removed_by_covering} facts ({percentage_removed_by_covering:.2f}%), " + + f"leaving {remaining} facts to check.") diff --git a/equational_theories/Generated/FinitePoly/src/finite_poly_refutations.txt b/equational_theories/Generated/FinitePoly/src/finite_poly_refutations.txt new file mode 100644 index 00000000..9f43ad1c --- /dev/null +++ b/equational_theories/Generated/FinitePoly/src/finite_poly_refutations.txt @@ -0,0 +1,700 @@ +'(2 * x**2 + 0 * y**2 + 3 * x + 2 * y + 2 * x * y) % 9' (0,) + +'(2 * x**2 + 3 * y**2 + 1 * x + 5 * y + 7 * x * y) % 10' (0, 4064, 4130) + +'(9 * x**2 + 5 * y**2 + 3 * x + 9 * y + 6 * x * y) % 12' (0, 3252, 3277, 3305, 3352, 3413, 3658, 3676, 3683, 3711, 3724, 3758, 3819, 4064, 4089, 4130, 4589, 4621) + +'(2 * x**2 + 0 * y**2 + 1 * x + 1 * y + 2 * x * y) % 3' (0, 22, 202, 306, 1628, 1730, 2237, 2242, 2326, 2440, 2455, 2458, 2465, 2529, 2643, 2658, 2695, 2698, 2705, 3049, 3064, 3067, 3252, 3305, 3455, 3460, 3521, 3658, 3673, 4064, 4069, 4117, 4154) + +'(1 * x**2 + 0 * y**2 + 1 * x + 1 * y + 0 * x * y) % 2' (0, 2, 4, 7, 9, 12, 15, 18, 22, 24, 27, 30, 33, 38, 44, 46, 48, 51, 54, 57, 61, 64, 67, 71, 74, 77, 81, 85, 89, 93, 98, 100, 103, 106, 109, 113, 116, 119, 123, 126, 129, 133, 137, 141, 145, 150, 152, 155, 158, 161, 165, 168, 171, 175, 178, 181, 185, 189, 193, 197, 202, 204, 207, 210, 213, 217, 220, 223, 227, 230, 233, 237, 241, 245, 249, 254, 256, 259, 262, 265, 269, 272, 275, 279, 282, 285, 289, 293, 297, 301, 306, 308, 311, 314, 317, 322, 325, 328, 332, 335, 338, 342, 346, 350, 354, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 462, 465, 468, 472, 475, 478, 482, 486, 490, 494, 499, 502, 505, 509, 512, 515, 519, 523, 527, 531, 536, 540, 544, 548, 553, 557, 561, 565, 570, 574, 578, 582, 587, 592, 597, 602, 607, 613, 615, 618, 621, 624, 628, 631, 634, 638, 641, 644, 648, 652, 656, 660, 665, 668, 671, 675, 678, 681, 685, 689, 693, 697, 702, 705, 708, 712, 715, 718, 722, 726, 730, 734, 739, 743, 747, 751, 756, 760, 764, 768, 773, 777, 781, 785, 790, 795, 800, 805, 810, 816, 818, 821, 824, 827, 831, 834, 837, 841, 844, 847, 851, 855, 859, 863, 868, 871, 874, 878, 881, 884, 888, 892, 896, 900, 905, 908, 911, 915, 918, 921, 925, 929, 933, 937, 942, 946, 950, 954, 959, 963, 967, 971, 976, 980, 984, 988, 993, 998, 1003, 1008, 1013, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1071, 1074, 1077, 1081, 1084, 1087, 1091, 1095, 1099, 1103, 1108, 1111, 1114, 1118, 1121, 1124, 1128, 1132, 1136, 1140, 1145, 1149, 1153, 1157, 1162, 1166, 1170, 1174, 1179, 1183, 1187, 1191, 1196, 1201, 1206, 1211, 1216, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1274, 1277, 1280, 1284, 1287, 1290, 1294, 1298, 1302, 1306, 1311, 1314, 1317, 1321, 1324, 1327, 1331, 1335, 1339, 1343, 1348, 1352, 1356, 1360, 1365, 1369, 1373, 1377, 1382, 1386, 1390, 1394, 1399, 1404, 1409, 1414, 1419, 1425, 1427, 1430, 1433, 1436, 1440, 1443, 1446, 1450, 1453, 1456, 1460, 1464, 1468, 1472, 1477, 1480, 1483, 1487, 1490, 1493, 1497, 1501, 1505, 1509, 1514, 1517, 1520, 1524, 1527, 1530, 1534, 1538, 1542, 1546, 1551, 1555, 1559, 1563, 1568, 1572, 1576, 1580, 1585, 1589, 1593, 1597, 1602, 1607, 1612, 1617, 1622, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1680, 1683, 1686, 1690, 1693, 1696, 1700, 1704, 1708, 1712, 1717, 1720, 1723, 1727, 1730, 1733, 1737, 1741, 1745, 1749, 1754, 1758, 1762, 1766, 1771, 1775, 1779, 1783, 1788, 1792, 1796, 1800, 1805, 1810, 1815, 1820, 1825, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 1883, 1886, 1889, 1893, 1896, 1899, 1903, 1907, 1911, 1915, 1920, 1923, 1926, 1930, 1933, 1936, 1940, 1944, 1948, 1952, 1957, 1961, 1965, 1969, 1974, 1978, 1982, 1986, 1991, 1995, 1999, 2003, 2008, 2013, 2018, 2023, 2028, 2034, 2036, 2039, 2042, 2045, 2049, 2052, 2055, 2059, 2062, 2065, 2069, 2073, 2077, 2081, 2086, 2089, 2092, 2096, 2099, 2102, 2106, 2110, 2114, 2118, 2123, 2126, 2129, 2133, 2136, 2139, 2143, 2147, 2151, 2155, 2160, 2164, 2168, 2172, 2177, 2181, 2185, 2189, 2194, 2198, 2202, 2206, 2211, 2216, 2221, 2226, 2231, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2289, 2292, 2295, 2299, 2302, 2305, 2309, 2313, 2317, 2321, 2326, 2329, 2332, 2336, 2339, 2342, 2346, 2350, 2354, 2358, 2363, 2367, 2371, 2375, 2380, 2384, 2388, 2392, 2397, 2401, 2405, 2409, 2414, 2419, 2424, 2429, 2434, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2492, 2495, 2498, 2502, 2505, 2508, 2512, 2516, 2520, 2524, 2529, 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3831, 3836, 3841, 3846, 3851, 3856, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4268, 4271, 4274, 4277, 4283, 4286, 4290, 4295, 4299, 4303, 4306, 4309, 4315, 4319, 4322, 4326, 4329, 4333, 4339, 4347, 4350, 4353, 4359, 4361, 4366, 4373, 4377, 4379, 4381, 4384, 4387, 4390, 4395, 4398, 4401, 4405, 4408, 4411, 4415, 4419, 4423, 4427, 4431, 4434, 4437, 4441, 4444, 4447, 4451, 4455, 4459, 4463, 4469, 4472, 4475, 4479, 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613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3318, 3455, 3521, 3658, 3714, 3721, 3724, 3861, 3914, 3927, 4064, 4117, 4120, 4130, 4379, 4469, 4472, 4598) + +'(11 * x**2 + 7 * y**2 + 0 * x + 9 * y + 3 * x * y) % 12' (0, 3252, 3305, 3658, 3683, 4064, 4130) + +'(0 * x**2 + 0 * y**2 + 1 * x + 0 * y + 0 * x * y) % 2' (0, 2, 3, 7, 8, 9, 10, 11, 22, 23, 24, 25, 26, 37, 41, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 358, 359, 360, 361, 362, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 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4438, 4439, 4440, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) + +'(4 * x**2 + 4 * y**2 + 0 * x + 4 * y + 2 * x * y) % 5' (0, 150, 158) + +'(8 * x**2 + 5 * y**2 + 6 * x + 4 * y + 7 * x * y) % 10' (0, 39, 1628, 1636, 1717, 1730, 1745, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 4269, 4340, 4589, 4621) + +'(4 * x**2 + 2 * y**2 + 4 * x + 2 * y + 5 * x * y) % 6' (0, 202, 358, 2440, 3252, 3305, 3658, 3711, 4064) + +'(0 * x**2 + 2 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 2, 7, 22, 46, 98, 150, 202, 254, 306, 325, 358, 374, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3318, 3455, 3521, 3658, 3714, 3721, 3861, 3914, 4064, 4117, 4130, 4379, 4469) + +'(1 * x**2 + 0 * y**2 + 3 * x + 2 * y + 0 * x * y) % 4' (0, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4382, 4394, 4398, 4402, 4431, 4435, 4439, 4468, 4472, 4476, 4505, 4510, 4515, 4520, 4584, 4597, 4655, 4672) + +'(3 * x**2 + 2 * y**2 + 3 * x + 7 * y + 0 * x * y) % 9' (0, 4586, 4605, 4614, 4644, 4665, 4688) + +'(10 * x**2 + 1 * y**2 + 5 * x + 5 * y + 6 * x * y) % 12' (0, 3252, 3305, 3318, 3455, 3458, 3508, 3510, 3517, 3521, 3525, 3861, 3914, 3916, 4064, 4072, 4117, 4119, 4126, 4130, 4145, 4379, 4397) + +'(3 * x**2 + 0 * y**2 + 3 * x + 0 * y + 0 * x * y) % 4' (0, 37, 41, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 358, 359, 360, 361, 362, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 3870, 3871, 3872, 3873, 3874, 3875, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4380, 4381, 4382, 4383, 4394, 4395, 4396, 4397, 4398, 4399, 4400, 4401, 4402, 4403, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 4440, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) + +'(4 * x**2 + 0 * y**2 + 7 * x + 5 * y + 0 * x * y) % 8' (0, 39, 1019, 1022, 1027, 1108, 1112, 1116, 1121, 1136, 1628, 1636, 1644, 1657, 1672, 1717, 1730, 1745, 1831, 1834, 1856, 1860, 1864, 1886, 1933, 1995, 2440, 2443, 2465, 2469, 2473, 2529, 2533, 2537, 3049, 3078, 3104, 3138, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 4269, 4340, 4589, 4621) + +'(6 * x**2 + 4 * y**2 + 7 * x + 1 * y + 7 * x * y) % 8' (0, 3861) + +'(1 * x**2 + 1 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 39, 42, 3658, 3661, 3664, 3666, 3674, 3676, 3683, 3687, 3691, 3699, 3702, 3711, 3713, 3720, 3724, 3728, 3747, 3751, 3755, 3758, 3760, 3819, 3822, 4269, 4282, 4340, 4357, 4379, 4387, 4397, 4404, 4434, 4441, 4468, 4481, 4496, 4530, 4543, 4589, 4621, 4634, 4676) + +'(2 * x**2 + 9 * y**2 + 4 * x + 4 * y + 4 * x * y) % 10' (0, 7, 410, 1019, 1831, 3252, 3318, 3861, 3914) + +'(2 * x**2 + 0 * y**2 + 2 * x + 2 * y + 0 * x * y) % 3' (0, 7, 15, 410, 418, 435, 465, 499, 512, 527, 574, 1019, 1044, 1074, 1121, 1183, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1920, 1933, 1948, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3861, 3886, 3914, 3961, 4022, 4274, 4306) + +'(7 * x**2 + 5 * y**2 + 6 * x + 3 * y + 2 * x * y) % 9' (0, 3252, 3455) + +'(5 * x**2 + 4 * y**2 + 3 * x + 4 * y + 1 * x * y) % 6' (0, 7, 410, 1019, 1222, 1831, 3252, 3317, 3318, 3861, 3914, 4064, 4130) + +'(2 * x**2 + 0 * y**2 + 0 * x + 2 * y + 1 * x * y) % 3' (0, 150, 1425, 1831, 3455, 4064, 4130) + +'(9 * x**2 + 5 * y**2 + 1 * x + 1 * y + 3 * x * y) % 10' (0, 2643, 3455, 4064) + +'(1 * x**2 + 1 * y**2 + 3 * x + 1 * y + 1 * x * y) % 4' (0, 3252, 3305, 3455, 3510, 3658, 3861, 3954, 4064, 4130, 4379) + +'(1 * x**2 + 3 * y**2 + 1 * x + 1 * y + 3 * x * y) % 6' (0, 22, 46, 202, 1628, 2440, 2643, 3049, 3455, 3508, 3521, 3658, 3711, 3758, 4064, 4117, 4164, 4319, 4361) + +'(4 * x**2 + 5 * y**2 + 3 * x + 5 * y + 1 * x * y) % 6' (0, 7, 410, 816, 1019, 1222, 1831, 3252, 3305, 3318, 3658, 3724, 3861, 3914, 4064, 4130) + +'(1 * x**2 + 1 * y**2 + 1 * x + 1 * y + 0 * x * y) % 2' (0, 37, 38, 39, 40, 41, 42, 43, 44, 45, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347, 3348, 3349, 3350, 3351, 3352, 3353, 3354, 3355, 3356, 3357, 3358, 3359, 3360, 3361, 3362, 3363, 3364, 3365, 3366, 3367, 3368, 3369, 3370, 3371, 3372, 3373, 3374, 3375, 3376, 3377, 3378, 3379, 3380, 3381, 3382, 3383, 3384, 3385, 3386, 3387, 3388, 3389, 3390, 3391, 3392, 3393, 3394, 3395, 3396, 3397, 3398, 3399, 3400, 3401, 3402, 3403, 3404, 3405, 3406, 3407, 3408, 3409, 3410, 3411, 3412, 3413, 3414, 3415, 3416, 3417, 3418, 3419, 3420, 3421, 3422, 3423, 3424, 3425, 3426, 3427, 3428, 3429, 3430, 3431, 3432, 3433, 3434, 3435, 3436, 3437, 3438, 3439, 3440, 3441, 3442, 3443, 3444, 3445, 3446, 3447, 3448, 3449, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 3544, 3545, 3546, 3547, 3548, 3549, 3550, 3551, 3552, 3553, 3554, 3555, 3556, 3557, 3558, 3559, 3560, 3561, 3562, 3563, 3564, 3565, 3566, 3567, 3568, 3569, 3570, 3571, 3572, 3573, 3574, 3575, 3576, 3577, 3578, 3579, 3580, 3581, 3582, 3583, 3584, 3585, 3586, 3587, 3588, 3589, 3590, 3591, 3592, 3593, 3594, 3595, 3596, 3597, 3598, 3599, 3600, 3601, 3602, 3603, 3604, 3605, 3606, 3607, 3608, 3609, 3610, 3611, 3612, 3613, 3614, 3615, 3616, 3617, 3618, 3619, 3620, 3621, 3622, 3623, 3624, 3625, 3626, 3627, 3628, 3629, 3630, 3631, 3632, 3633, 3634, 3635, 3636, 3637, 3638, 3639, 3640, 3641, 3642, 3643, 3644, 3645, 3646, 3647, 3648, 3649, 3650, 3651, 3652, 3653, 3654, 3655, 3656, 3657, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3747, 3748, 3749, 3750, 3751, 3752, 3753, 3754, 3755, 3756, 3757, 3758, 3759, 3760, 3761, 3762, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 3770, 3771, 3772, 3773, 3774, 3775, 3776, 3777, 3778, 3779, 3780, 3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3789, 3790, 3791, 3792, 3793, 3794, 3795, 3796, 3797, 3798, 3799, 3800, 3801, 3802, 3803, 3804, 3805, 3806, 3807, 3808, 3809, 3810, 3811, 3812, 3813, 3814, 3815, 3816, 3817, 3818, 3819, 3820, 3821, 3822, 3823, 3824, 3825, 3826, 3827, 3828, 3829, 3830, 3831, 3832, 3833, 3834, 3835, 3836, 3837, 3838, 3839, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 3850, 3851, 3852, 3853, 3854, 3855, 3856, 3857, 3858, 3859, 3860, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 3910, 3911, 3912, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 3950, 3951, 3952, 3953, 3954, 3955, 3956, 3957, 3958, 3959, 3960, 3961, 3962, 3963, 3964, 3965, 3966, 3967, 3968, 3969, 3970, 3971, 3972, 3973, 3974, 3975, 3976, 3977, 3978, 3979, 3980, 3981, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 3990, 3991, 3992, 3993, 3994, 3995, 3996, 3997, 3998, 3999, 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 4010, 4011, 4012, 4013, 4014, 4015, 4016, 4017, 4018, 4019, 4020, 4021, 4022, 4023, 4024, 4025, 4026, 4027, 4028, 4029, 4030, 4031, 4032, 4033, 4034, 4035, 4036, 4037, 4038, 4039, 4040, 4041, 4042, 4043, 4044, 4045, 4046, 4047, 4048, 4049, 4050, 4051, 4052, 4053, 4054, 4055, 4056, 4057, 4058, 4059, 4060, 4061, 4062, 4063, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 4110, 4111, 4112, 4113, 4114, 4115, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4153, 4154, 4155, 4156, 4157, 4158, 4159, 4160, 4161, 4162, 4163, 4164, 4165, 4166, 4167, 4168, 4169, 4170, 4171, 4172, 4173, 4174, 4175, 4176, 4177, 4178, 4179, 4180, 4181, 4182, 4183, 4184, 4185, 4186, 4187, 4188, 4189, 4190, 4191, 4192, 4193, 4194, 4195, 4196, 4197, 4198, 4199, 4200, 4201, 4202, 4203, 4204, 4205, 4206, 4207, 4208, 4209, 4210, 4211, 4212, 4213, 4214, 4215, 4216, 4217, 4218, 4219, 4220, 4221, 4222, 4223, 4224, 4225, 4226, 4227, 4228, 4229, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 4240, 4241, 4242, 4243, 4244, 4245, 4246, 4247, 4248, 4249, 4250, 4251, 4252, 4253, 4254, 4255, 4256, 4257, 4258, 4259, 4260, 4261, 4262, 4263, 4264, 4265, 4266, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4379, 4380, 4381, 4382, 4383, 4384, 4385, 4386, 4387, 4388, 4389, 4390, 4391, 4392, 4393, 4394, 4395, 4396, 4397, 4398, 4399, 4400, 4401, 4402, 4403, 4404, 4405, 4406, 4407, 4408, 4409, 4410, 4411, 4412, 4413, 4414, 4415, 4416, 4417, 4418, 4419, 4420, 4421, 4422, 4423, 4424, 4425, 4426, 4427, 4428, 4429, 4430, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 4440, 4441, 4442, 4443, 4444, 4445, 4446, 4447, 4448, 4449, 4450, 4451, 4452, 4453, 4454, 4455, 4456, 4457, 4458, 4459, 4460, 4461, 4462, 4463, 4464, 4465, 4466, 4467, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4478, 4479, 4480, 4481, 4482, 4483, 4484, 4485, 4486, 4487, 4488, 4489, 4490, 4491, 4492, 4493, 4494, 4495, 4496, 4497, 4498, 4499, 4500, 4501, 4502, 4503, 4504, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4522, 4523, 4524, 4525, 4526, 4527, 4528, 4529, 4530, 4531, 4532, 4533, 4534, 4535, 4536, 4537, 4538, 4539, 4540, 4541, 4542, 4543, 4544, 4545, 4546, 4547, 4548, 4549, 4550, 4551, 4552, 4553, 4554, 4555, 4556, 4557, 4558, 4559, 4560, 4561, 4562, 4563, 4564, 4565, 4566, 4567, 4568, 4569, 4570, 4571, 4572, 4573, 4574, 4575, 4576, 4577, 4578, 4579, 4580, 4581, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) + +'(1 * x**2 + 2 * y**2 + 1 * x + 1 * y + 2 * x * y) % 3' (0, 306, 2034, 2049, 3252, 3658, 3659) + +'(1 * x**2 + 3 * y**2 + 6 * x + 3 * y + 0 * x * y) % 8' (0, 7, 98, 150, 358, 374, 410, 418, 428, 435, 1019, 1024, 1222, 1227, 1628, 1646, 1831, 1846, 2034, 2049, 3252, 3260, 3305, 3318, 3333, 3861, 3866, 3914, 3924, 3934, 4064, 4069, 4117, 4127, 4137) + +'(0 * x**2 + 1 * y**2 + 0 * x + 1 * y + 0 * x * y) % 3' (0, 38, 44, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(1 * x**2 + 2 * y**2 + 2 * x + 2 * y + 0 * x * y) % 3' (0, 2, 7, 22, 46, 98, 100, 103, 150, 202, 204, 207, 254, 306, 325, 358, 374, 410, 613, 615, 618, 816, 821, 831, 1019, 1021, 1024, 1027, 1030, 1034, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1257, 1425, 1628, 1630, 1633, 1831, 1836, 1846, 2034, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2272, 2440, 2442, 2445, 2455, 2465, 2475, 2643, 2645, 2648, 2846, 2851, 2861, 3049, 3252, 3318, 3455, 3457, 3460, 3511, 3518, 3521, 3524, 3532, 3658, 3714, 3721, 3861, 3863, 3866, 3914, 3917, 3920, 3924, 3934, 4064, 4117, 4379, 4469) + +'(2 * x**2 + 5 * y**2 + 4 * x + 1 * y + 2 * x * y) % 6' (0, 42, 3252, 3257, 3455, 3456, 3861, 3876, 4064, 4066, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) + +'(0 * x**2 + 1 * y**2 + 0 * x + 0 * y + 1 * x * y) % 2' (0, 22, 24, 30, 39, 202, 204, 207, 210, 213, 217, 220, 223, 230, 241, 245, 306, 308, 309, 311, 312, 315, 318, 319, 322, 1628, 1630, 1636, 1643, 1646, 1649, 1656, 1671, 1717, 1720, 1723, 1730, 1745, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2289, 2292, 2295, 2299, 2302, 2305, 2309, 2313, 2317, 2321, 2326, 2329, 2332, 2339, 2350, 2354, 2363, 2367, 2371, 2375, 2384, 2388, 2401, 2405, 2419, 2424, 2429, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2495, 2505, 2516, 2529, 2532, 2535, 2542, 2553, 2557, 2570, 2587, 2604, 2622, 2643, 2645, 2651, 2658, 2661, 2664, 2671, 2686, 2695, 2698, 2701, 2705, 2708, 2711, 2723, 2732, 2735, 2738, 2745, 2760, 2769, 2773, 2777, 2781, 2790, 2794, 2811, 2835, 3049, 3051, 3057, 3064, 3067, 3070, 3077, 3092, 3104, 3114, 3138, 3141, 3144, 3151, 3166, 3179, 3196, 3252, 3254, 3255, 3257, 3258, 3260, 3261, 3263, 3264, 3265, 3267, 3268, 3270, 3271, 3273, 3274, 3275, 3277, 3278, 3281, 3284, 3285, 3287, 3288, 3289, 3292, 3293, 3296, 3297, 3300, 3301, 3302, 3305, 3455, 3457, 3458, 3460, 3463, 3466, 3471, 3474, 3477, 3480, 3481, 3484, 3487, 3488, 3491, 3495, 3499, 3503, 3508, 3518, 3521, 3524, 3528, 3536, 3658, 3661, 3663, 3664, 3667, 3671, 3673, 3676, 3677, 3681, 3683, 3687, 3691, 3693, 3698, 3699, 3703, 3708, 3711, 3748, 3758, 3768, 3785, 3819, 4064, 4067, 4069, 4083, 4089, 4093, 4097, 4104, 4117, 4127, 4130, 4137, 4154, 4164, 4174, 4225, 4268, 4269, 4271, 4272, 4275, 4278, 4279, 4313, 4315, 4317, 4319, 4320, 4323, 4324, 4326, 4330, 4331, 4335, 4336, 4340, 4342, 4345, 4350, 4354, 4361, 4583, 4589, 4605, 4610, 4621, 4630, 4657) + +'(4 * x**2 + 4 * y**2 + 1 * x + 2 * y + 0 * x * y) % 8' (0, 150, 159, 202, 211, 1425, 1426, 1453, 1454, 1455, 2237, 2239, 2263, 2266, 2269, 3049, 3078, 3455, 3458, 3517, 3521, 3525, 4597, 4672) + +'(1 * x**2 + 0 * y**2 + 0 * x + 0 * y + 1 * x * y) % 2' (0, 7, 9, 10, 39, 98, 99, 100, 103, 104, 105, 106, 107, 108, 109, 110, 358, 359, 360, 364, 366, 367, 368, 370, 377, 410, 412, 413, 425, 426, 428, 429, 431, 432, 433, 435, 436, 438, 439, 441, 442, 443, 816, 817, 818, 819, 820, 822, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 853, 857, 1019, 1021, 1022, 1024, 1027, 1030, 1034, 1035, 1037, 1038, 1040, 1041, 1042, 1044, 1045, 1047, 1048, 1050, 1051, 1052, 1054, 1055, 1058, 1059, 1062, 1063, 1066, 1067, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1233, 1237, 1238, 1239, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1269, 1270, 1831, 1833, 1834, 1846, 1849, 1850, 1852, 1854, 1856, 1859, 1860, 1862, 1864, 3252, 3254, 3255, 3277, 3278, 3281, 3284, 3285, 3305, 3314, 3315, 3317, 3318, 3320, 3321, 3322, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 3720, 3723, 3724, 3725, 3726, 3728, 3861, 3863, 3864, 3866, 3869, 3872, 3877, 3880, 3883, 3886, 3887, 3890, 3893, 3894, 3897, 3901, 3905, 3909, 3914, 3924, 3927, 3930, 3934, 3942, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4075, 4080, 4082, 4083, 4084, 4086, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4100, 4103, 4104, 4105, 4106, 4108, 4112, 4130, 4268, 4269, 4292, 4313, 4315, 4317, 4340, 4582, 4583, 4587, 4589, 4590, 4591, 4593, 4596, 4597, 4600, 4605, 4607, 4608, 4610, 4615, 4619, 4621, 4622, 4625, 4630, 4635, 4638, 4646, 4650, 4672) + +'(0 * x**2 + 2 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 39, 306, 309, 311, 315, 319, 3252, 3255, 3257, 3261, 3265, 3267, 3271, 3275, 3277, 3281, 3285, 3287, 3292, 3297, 3302, 3658, 3661, 3663, 3664, 3667, 3671, 3673, 3676, 3677, 3681, 3683, 3687, 3691, 3693, 3698, 3699, 3703, 3708, 4269, 4271, 4275, 4279, 4340, 4342, 4345, 4350, 4354, 4589, 4621) + +'(2 * x**2 + 3 * y**2 + 5 * x + 2 * y + 10 * x * y) % 12' (0, 1831, 2034, 2846, 3049, 3252, 3305, 3318, 3455, 3521, 3658, 4379) + +'(2 * x**2 + 3 * y**2 + 1 * x + 2 * y + 0 * x * y) % 4' (0, 22, 25, 1425, 1428, 1431, 1433, 1441, 1443, 1450, 1454, 1458, 1466, 1469, 1628, 1631, 1634, 1636, 1644, 1646, 1653, 1657, 1661, 1669, 1672, 1831, 1834, 1837, 1839, 1847, 1849, 1856, 1860, 1864, 1872, 1875, 2237, 2240, 2243, 2245, 2253, 2255, 2262, 2266, 2270, 2278, 2281, 2440, 2443, 2446, 2448, 2456, 2458, 2465, 2469, 2473, 2481, 2484, 2643, 2651, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3661, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4269, 4282, 4340, 4357, 4584, 4655) + +'(3 * x**2 + 0 * y**2 + 0 * x + 1 * y + 2 * x * y) % 4' (0, 7, 15, 22, 30, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 621, 631, 638, 668, 675, 702, 715, 730, 764, 777, 816, 824, 834, 841, 871, 878, 905, 918, 933, 967, 980, 1019, 1027, 1037, 1044, 1074, 1081, 1108, 1121, 1136, 1170, 1183, 1222, 1230, 1240, 1247, 1277, 1284, 1311, 1324, 1339, 1373, 1386, 1425, 1433, 1443, 1450, 1480, 1487, 1514, 1527, 1542, 1576, 1589, 1628, 1636, 1646, 1653, 1683, 1690, 1717, 1730, 1745, 1779, 1792, 1831, 1839, 1849, 1856, 1886, 1893, 1920, 1933, 1948, 1982, 1995, 2034, 2042, 2052, 2059, 2089, 2096, 2123, 2136, 2151, 2185, 2198, 2237, 2245, 2255, 2262, 2292, 2299, 2326, 2339, 2354, 2388, 2401, 2440, 2448, 2458, 2465, 2495, 2502, 2529, 2542, 2557, 2591, 2604, 2643, 2651, 2661, 2668, 2698, 2705, 2732, 2745, 2760, 2794, 2807, 2846, 2854, 2864, 2871, 2901, 2908, 2935, 2948, 2963, 2997, 3010, 3049, 3057, 3067, 3074, 3104, 3111, 3138, 3151, 3166, 3200, 3213, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3463, 3473, 3480, 3508, 3521, 3536, 3548, 3555, 3590, 3616, 3658, 3666, 3676, 3683, 3711, 3724, 3739, 3751, 3758, 3793, 3819, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4082, 4089, 4117, 4130, 4145, 4157, 4164, 4199, 4225, 4274, 4306, 4319, 4361, 4379, 4387, 4395, 4408, 4423, 4434, 4441, 4472, 4479, 4511, 4524, 4589, 4621, 4634, 4676) + +'(0 * x**2 + 4 * y**2 + 1 * x + 3 * y + 0 * x * y) % 5' (0, 816, 845, 1019, 1048, 4597, 4672) + +'(0 * x**2 + 2 * y**2 + 0 * x + 2 * y + 3 * x * y) % 4' (0, 42, 3252, 3455, 3658, 3861, 4064, 4282, 4289, 4319, 4357, 4361, 4363, 4368, 4379, 4395, 4397, 4404, 4432, 4434, 4441, 4472, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4597, 4604, 4634, 4672, 4676, 4678, 4683) + +'(0 * x**2 + 0 * y**2 + 0 * x + 0 * y + 1 * x * y) % 2' (0, 2, 7, 22, 42, 46, 98, 150, 202, 254, 306, 322, 324, 325, 331, 332, 334, 358, 374, 376, 377, 383, 384, 386, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3305, 3307, 3308, 3314, 3315, 3317, 3318, 3341, 3342, 3344, 3345, 3351, 3352, 3354, 3455, 3508, 3510, 3511, 3517, 3518, 3520, 3521, 3544, 3545, 3547, 3548, 3554, 3555, 3557, 3658, 3711, 3713, 3714, 3720, 3721, 3723, 3724, 3747, 3748, 3750, 3751, 3757, 3758, 3760, 3861, 3914, 3916, 3917, 3923, 3924, 3926, 3927, 3950, 3951, 3953, 3954, 3960, 3961, 3963, 4064, 4117, 4119, 4120, 4126, 4127, 4129, 4130, 4153, 4154, 4156, 4157, 4163, 4164, 4166, 4282, 4283, 4289, 4290, 4292, 4313, 4319, 4320, 4342, 4357, 4361, 4363, 4368, 4379, 4395, 4397, 4398, 4404, 4405, 4407, 4432, 4434, 4435, 4441, 4442, 4444, 4469, 4471, 4472, 4478, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4597, 4598, 4604, 4605, 4607, 4628, 4634, 4635, 4657, 4672, 4676, 4678, 4683) + +'(6 * x**2 + 0 * y**2 + 5 * x + 2 * y + 2 * x * y) % 8' (0, 22, 150, 202, 306, 1425, 1426, 1628, 1631, 1831, 1837, 2237, 2239, 2440, 2448, 3049, 3055, 3067, 3078, 3090, 3252, 3253, 3455, 3458, 3517, 3518, 3520, 3521, 3525, 4064, 4070, 4117, 4126, 4313) + +'(5 * x**2 + 6 * y**2 + 0 * x + 2 * y + 0 * x * y) % 8' (0, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4583, 4598, 4601, 4630, 4654, 4674) + +'(5 * x**2 + 0 * y**2 + 3 * x + 1 * y + 1 * x * y) % 8' (0, 1628, 1730, 2237, 2643, 2745, 3455, 4064) + +'(1 * x**2 + 0 * y**2 + 7 * x + 3 * y + 2 * x * y) % 8' (0, 410, 512, 816, 1019, 1121, 1628, 1730, 1831, 1933, 2440, 3049) + +'(0 * x**2 + 4 * y**2 + 2 * x + 6 * y + 6 * x * y) % 8' (0, 42, 4282, 4283, 4313, 4357, 4379, 4397, 4404, 4407, 4434, 4441, 4444, 4471, 4478, 4481, 4530, 4543, 4598, 4605, 4634, 4676) + +'(1 * x**2 + 1 * y**2 + 0 * x + 0 * y + 0 * x * y) % 2' (0, 7, 10, 13, 15, 22, 25, 28, 30, 39, 42, 410, 413, 416, 418, 426, 428, 435, 439, 443, 451, 454, 463, 465, 472, 476, 480, 488, 491, 499, 503, 507, 510, 512, 521, 527, 542, 545, 555, 561, 571, 574, 613, 616, 619, 621, 629, 631, 638, 642, 646, 654, 657, 666, 668, 675, 679, 683, 691, 694, 702, 706, 710, 713, 715, 724, 730, 745, 748, 758, 764, 774, 777, 816, 819, 822, 824, 832, 834, 841, 845, 849, 857, 860, 869, 871, 878, 882, 886, 894, 897, 905, 909, 913, 916, 918, 927, 933, 948, 951, 961, 967, 977, 980, 1019, 1022, 1025, 1027, 1035, 1037, 1044, 1048, 1052, 1060, 1063, 1072, 1074, 1081, 1085, 1089, 1097, 1100, 1108, 1112, 1116, 1119, 1121, 1130, 1136, 1151, 1154, 1164, 1170, 1180, 1183, 1222, 1225, 1228, 1230, 1238, 1240, 1247, 1251, 1255, 1263, 1266, 1275, 1277, 1284, 1288, 1292, 1300, 1303, 1311, 1315, 1319, 1322, 1324, 1333, 1339, 1354, 1357, 1367, 1373, 1383, 1386, 1425, 1428, 1431, 1433, 1441, 1443, 1450, 1454, 1458, 1466, 1469, 1478, 1480, 1487, 1491, 1495, 1503, 1506, 1514, 1518, 1522, 1525, 1527, 1536, 1542, 1557, 1560, 1570, 1576, 1586, 1589, 1628, 1631, 1634, 1636, 1644, 1646, 1653, 1657, 1661, 1669, 1672, 1681, 1683, 1690, 1694, 1698, 1706, 1709, 1717, 1721, 1725, 1728, 1730, 1739, 1745, 1760, 1763, 1773, 1779, 1789, 1792, 1831, 1834, 1837, 1839, 1847, 1849, 1856, 1860, 1864, 1872, 1875, 1884, 1886, 1893, 1897, 1901, 1909, 1912, 1920, 1924, 1928, 1931, 1933, 1942, 1948, 1963, 1966, 1976, 1982, 1992, 1995, 2034, 2037, 2040, 2042, 2050, 2052, 2059, 2063, 2067, 2075, 2078, 2087, 2089, 2096, 2100, 2104, 2112, 2115, 2123, 2127, 2131, 2134, 2136, 2145, 2151, 2166, 2169, 2179, 2185, 2195, 2198, 2237, 2240, 2243, 2245, 2253, 2255, 2262, 2266, 2270, 2278, 2281, 2290, 2292, 2299, 2303, 2307, 2315, 2318, 2326, 2330, 2334, 2337, 2339, 2348, 2354, 2369, 2372, 2382, 2388, 2398, 2401, 2440, 2443, 2446, 2448, 2456, 2458, 2465, 2469, 2473, 2481, 2484, 2493, 2495, 2502, 2506, 2510, 2518, 2521, 2529, 2533, 2537, 2540, 2542, 2551, 2557, 2572, 2575, 2585, 2591, 2601, 2604, 2643, 2646, 2649, 2651, 2659, 2661, 2668, 2672, 2676, 2684, 2687, 2696, 2698, 2705, 2709, 2713, 2721, 2724, 2732, 2736, 2740, 2743, 2745, 2754, 2760, 2775, 2778, 2788, 2794, 2804, 2807, 2846, 2849, 2852, 2854, 2862, 2864, 2871, 2875, 2879, 2887, 2890, 2899, 2901, 2908, 2912, 2916, 2924, 2927, 2935, 2939, 2943, 2946, 2948, 2957, 2963, 2978, 2981, 2991, 2997, 3007, 3010, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3102, 3104, 3111, 3115, 3119, 3127, 3130, 3138, 3142, 3146, 3149, 3151, 3160, 3166, 3181, 3184, 3194, 3200, 3210, 3213, 3252, 3255, 3258, 3260, 3268, 3270, 3277, 3281, 3285, 3293, 3296, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3341, 3345, 3349, 3352, 3354, 3363, 3369, 3384, 3387, 3397, 3403, 3413, 3416, 3455, 3458, 3461, 3463, 3471, 3473, 3480, 3484, 3488, 3496, 3499, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3544, 3548, 3552, 3555, 3557, 3566, 3572, 3587, 3590, 3600, 3606, 3616, 3619, 3658, 3661, 3664, 3666, 3674, 3676, 3683, 3687, 3691, 3699, 3702, 3711, 3713, 3720, 3724, 3728, 3736, 3739, 3747, 3751, 3755, 3758, 3760, 3769, 3775, 3790, 3793, 3803, 3809, 3819, 3822, 3861, 3864, 3867, 3869, 3877, 3879, 3886, 3890, 3894, 3902, 3905, 3914, 3916, 3923, 3927, 3931, 3939, 3942, 3950, 3954, 3958, 3961, 3963, 3972, 3978, 3993, 3996, 4006, 4012, 4022, 4025, 4064, 4067, 4070, 4072, 4080, 4082, 4089, 4093, 4097, 4105, 4108, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4153, 4157, 4161, 4164, 4166, 4175, 4181, 4196, 4199, 4209, 4215, 4225, 4228, 4269, 4272, 4274, 4282, 4289, 4296, 4304, 4306, 4319, 4324, 4331, 4340, 4357, 4361, 4363, 4368, 4379, 4382, 4385, 4387, 4395, 4397, 4404, 4408, 4412, 4420, 4423, 4432, 4434, 4441, 4445, 4449, 4457, 4460, 4468, 4472, 4476, 4479, 4481, 4490, 4496, 4511, 4514, 4524, 4530, 4540, 4543, 4584, 4587, 4589, 4597, 4604, 4611, 4619, 4621, 4634, 4639, 4646, 4655, 4672, 4676, 4678, 4683) + +'(3 * x**2 + 1 * y**2 + 1 * x + 8 * y + 5 * x * y) % 12' (0, 3252, 3305, 3658, 3661, 4064, 4130) + +'(2 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 4' (0, 22, 23, 24, 25, 26, 37, 41, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 1425, 1426, 1427, 1428, 1429, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 2237, 2238, 2239, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 2490, 2491, 3049, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 3100, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 4150, 4151, 4152, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) + +'(3 * x**2 + 0 * y**2 + 1 * x + 1 * y + 3 * x * y) % 4' (0, 22, 30, 39, 1628, 1636, 1717, 1730, 1745, 2237, 2245, 2292, 2440, 2465, 2495, 2542, 2604, 2643, 2651, 2661, 2705, 2732, 2745, 2760, 2794, 3049, 3057, 3138, 3151, 3166, 3455, 3463, 3471, 3484, 3499, 3508, 3521, 3536, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3711, 3758, 3819, 4064, 4067, 4089, 4093, 4097, 4117, 4130, 4164, 4225, 4269, 4340, 4589, 4621) + +'(2 * x**2 + 1 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 7, 410, 1019, 1034, 1037, 1222, 1250, 1831, 3252, 3317, 3318, 3861, 3914, 4064, 4092, 4130, 4590) + +'(7 * x**2 + 5 * y**2 + 2 * x + 3 * y + 2 * x * y) % 8' (0, 358, 360, 410, 428, 3861, 3863, 3866, 3869, 3872, 3914, 3924, 3934, 4064, 4066, 4069, 4072, 4075, 4583, 4630) + +'(0 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 10, 98, 107, 254, 263, 410, 413, 435, 439, 443, 816, 819, 822, 834, 841, 845, 849, 857, 1019, 1022, 1027, 1035, 1044, 1048, 1052, 1063, 1831, 1834, 1856, 1860, 1864, 3252, 3255, 3314, 3318, 3322, 3658, 3661, 3720, 3724, 3728, 3861, 3869, 3914, 3927, 3942, 4269, 4340, 4597, 4672) + +'(3 * x**2 + 0 * y**2 + 4 * x + 7 * y + 6 * x * y) % 9' (0, 98) + +'(0 * x**2 + 1 * y**2 + 5 * x + 5 * y + 3 * x * y) % 6' (0, 1831, 1849, 1860, 4064, 4067, 4072, 4130) + +'(1 * x**2 + 0 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 15, 410, 418, 435, 465, 499, 512, 527, 574, 816, 1019, 1044, 1074, 1121, 1183, 1222, 1324, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1920, 1933, 1948, 2034, 2136, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3658, 3861, 3886, 3914, 3961, 4022, 4064, 4117, 4274, 4306) + +'(2 * x**2 + 2 * y**2 + 1 * x + 0 * y + 1 * x * y) % 4' (0, 98, 104, 106, 410, 1222, 1223, 1224, 1227, 1238, 1240, 1241, 1242, 1244, 1247, 1248, 1249, 1250, 1253, 1258, 1261, 1831, 1860, 3658, 3661, 3723, 3861, 3869, 3924, 4597, 4672) + +'(5 * x**2 + 5 * y**2 + 3 * x + 0 * y + 0 * x * y) % 6' (0, 306, 325, 358, 374, 3252, 3318, 3455, 3521, 3658, 3714, 3861, 3914, 4064, 4117, 4379, 4434, 4441, 4469, 4634, 4676) + +'(0 * x**2 + 0 * y**2 + 0 * x + 2 * y + 1 * x * y) % 3' (0, 254, 306, 1628, 1730, 2846, 3252, 3305, 3455, 3658, 4319, 4361) + +'(6 * x**2 + 5 * y**2 + 4 * x + 7 * y + 4 * x * y) % 8' (0, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4379, 4381, 4384, 4387, 4390, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(4 * x**2 + 0 * y**2 + 2 * x + 6 * y + 0 * x * y) % 8' (0, 42, 4269, 4282, 4340, 4357, 4379, 4387, 4397, 4404, 4434, 4441, 4468, 4481, 4496, 4530, 4543, 4589, 4621, 4634, 4676) + +'(2 * x**2 + 2 * y**2 + 1 * x + 0 * y + 1 * x * y) % 3' (0, 98, 103, 1019, 1037, 1222, 1227, 1237, 1247, 1257, 3252, 3315, 4586, 4665) + +'(6 * x**2 + 0 * y**2 + 7 * x + 0 * y + 6 * x * y) % 8' (0, 150, 158, 159, 202, 208, 211, 1425, 1426, 1450, 1451, 1452, 1453, 1454, 1455, 2237, 2239, 2253, 2256, 2259, 2263, 2266, 2269, 3049, 3055, 3067, 3078, 3090, 3455, 3458, 3517, 3518, 3520, 3521, 3525, 4313) + +'(0 * x**2 + 7 * y**2 + 2 * x + 1 * y + 0 * x * y) % 8' (0, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3658, 3721, 4274, 4306) + +'(1 * x**2 + 1 * y**2 + 1 * x + 2 * y + 1 * x * y) % 3' (0, 39, 3252, 3255, 3277, 3281, 3285, 3658, 3661, 3663, 3664, 3667, 3671, 3673, 3676, 3677, 3681, 3683, 3687, 3691, 3693, 3698, 3699, 3703, 3708, 3711, 3748, 3758, 3819, 4064, 4067, 4089, 4093, 4097, 4269, 4320, 4340, 4589, 4621, 4657) + +'(1 * x**2 + 1 * y**2 + 2 * x + 1 * y + 1 * x * y) % 3' (0, 39, 3252, 3255, 3277, 3281, 3285, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 3720, 3723, 3724, 3728, 4064, 4067, 4089, 4093, 4097, 4269, 4292, 4340, 4589, 4621, 4635) + +'(1 * x**2 + 1 * y**2 + 1 * x + 0 * y + 2 * x * y) % 8' (0, 22, 150, 202, 306, 325, 1425, 1427, 1628, 1831, 1849, 2237, 2242, 2440, 3049, 3252, 3254, 3315, 3318, 3321, 3455, 3518, 3521, 4064, 4117, 4130) + +'(0 * x**2 + 0 * y**2 + 2 * x + 3 * y + 3 * x * y) % 4' (0, 202, 210, 220, 1628, 1730, 2237, 2242, 2245, 2252, 2255, 2265, 2276, 2280, 2289, 2292, 2302, 2313, 2317, 2329, 2367, 2371, 3049, 3455, 3463, 3518, 3658, 3683, 3748, 4319, 4361) + +'(0 * x**2 + 0 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 10, 15, 39, 254, 263, 270, 272, 279, 410, 413, 418, 426, 435, 439, 443, 454, 465, 473, 499, 503, 507, 512, 527, 542, 574, 816, 819, 822, 834, 841, 845, 849, 857, 869, 881, 905, 909, 913, 916, 927, 951, 977, 1019, 1022, 1027, 1035, 1044, 1048, 1052, 1063, 1074, 1082, 1108, 1112, 1116, 1121, 1136, 1151, 1183, 1628, 1634, 1636, 1644, 1646, 1657, 1669, 1672, 1684, 1690, 1717, 1728, 1730, 1739, 1745, 1773, 1779, 1831, 1834, 1839, 1847, 1856, 1860, 1864, 1875, 1886, 1894, 1920, 1924, 1928, 1933, 1948, 1963, 1995, 2440, 2443, 2446, 2458, 2465, 2469, 2473, 2481, 2493, 2505, 2529, 2533, 2537, 2540, 2551, 2575, 2601, 3252, 3255, 3260, 3268, 3277, 3281, 3285, 3296, 3305, 3314, 3318, 3322, 3333, 3344, 3352, 3397, 3413, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3713, 3720, 3724, 3728, 3736, 3748, 3760, 3809, 3822, 3861, 3864, 3869, 3877, 3886, 3890, 3894, 3905, 3914, 3923, 3927, 3931, 3942, 3953, 3961, 4006, 4022, 4269, 4274, 4289, 4296, 4306, 4320, 4340, 4368, 4587, 4589, 4597, 4619, 4621, 4646, 4657, 4672) + +'(1 * x**2 + 2 * y**2 + 0 * x + 0 * y + 2 * x * y) % 4' (0, 306, 307, 324, 325, 326, 358, 360, 374, 377, 380, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3658, 3659, 3663, 3664, 3665, 3713, 3714, 3715, 3723, 3724, 3725, 3734, 3735, 3736, 3737, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4066, 4069, 4072, 4075, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4267, 4281, 4313, 4314, 4338, 4356, 4379, 4381, 4394, 4397, 4400, 4432, 4435, 4438, 4469, 4472, 4475, 4506, 4510, 4514, 4518, 4583, 4598, 4601, 4630, 4654, 4674) + +'(2 * x**2 + 7 * y**2 + 3 * x + 1 * y + 3 * x * y) % 9' (0, 254, 306, 325, 2034, 2643, 2846, 3252, 3318, 3455, 3521) + +'(6 * x**2 + 5 * y**2 + 7 * x + 5 * y + 2 * x * y) % 8' (0, 7, 410, 1019, 1628, 1646, 1831, 2440, 3049, 3078, 3252, 3305, 3318, 3861, 3914) + +'(6 * x**2 + 6 * y**2 + 4 * x + 1 * y + 6 * x * y) % 8' (0, 7, 410, 428, 472, 512, 561, 1019, 1024, 1034, 1044, 1054, 1084, 1111, 1628, 1633, 1656, 1680, 1690, 1700, 1720, 1831, 1846, 1859, 1883, 1896, 1920, 1957, 3252, 3270, 3318, 3352, 3861, 3866, 3876, 3886, 3896, 3914, 3961, 4022, 4586, 4665) + +'(8 * x**2 + 3 * y**2 + 4 * x + 10 * y + 10 * x * y) % 12' (0, 3252, 3305, 3455, 3861, 3886, 4064, 4379) + +'(4 * x**2 + 4 * y**2 + 6 * x + 3 * y + 6 * x * y) % 8' (0, 358, 410, 428, 472, 512, 561, 3861, 3886, 3914, 3924, 3951, 3961, 4022, 4064, 4079, 4605) + +'(6 * x**2 + 9 * y**2 + 3 * x + 8 * y + 6 * x * y) % 12' (0, 7, 410, 418, 428, 435, 1019, 1027, 1037, 1044, 1222, 1230, 1240, 1247, 1628, 1636, 1646, 1653, 1831, 1839, 1849, 1856, 2034, 2042, 2052, 2059, 3252, 3260, 3305, 3318, 3333, 3861, 3869, 3914, 3927, 3942, 4064, 4072, 4117, 4130, 4145) + +'(3 * x**2 + 3 * y**2 + 0 * x + 1 * y + 1 * x * y) % 7' (0, 2, 7, 22, 46, 98, 150, 202, 254, 306, 325, 358, 374, 410, 411, 412, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3318, 3455, 3521, 3658, 3714, 3721, 3861, 3914, 4064, 4117, 4130, 4379, 4469) + +'(2 * x**2 + 9 * y**2 + 9 * x + 2 * y + 8 * x * y) % 12' (0, 1425, 1628, 3658) + +'(1 * x**2 + 0 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 7, 15, 22, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 638, 675, 702, 816, 834, 871, 905, 1019, 1044, 1074, 1081, 1108, 1121, 1183, 1222, 1311, 1324, 1425, 1433, 1480, 1487, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1849, 1886, 1920, 1933, 1948, 2034, 2089, 2136, 2237, 2262, 2299, 2326, 2440, 2458, 2529, 2643, 2698, 2705, 2846, 2935, 3049, 3067, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3480, 3521, 3548, 3658, 3676, 3724, 3758, 3861, 3886, 3914, 3927, 3954, 3961, 4022, 4064, 4117, 4130, 4274, 4306, 4319, 4361, 4379, 4408, 4441, 4472) + +'(3 * x**2 + 2 * y**2 + 1 * x + 3 * y + 1 * x * y) % 4' (0, 22, 1628, 1730, 2237, 2440, 2643, 2705, 2745, 3049, 3455, 3508, 3521, 4064, 4117, 4130, 4164) + +'(1 * x**2 + 1 * y**2 + 0 * x + 1 * y + 2 * x * y) % 3' (0, 202, 204, 2237, 2239, 2242, 2245, 2248, 2440, 2458, 4064, 4127, 4267, 4281) + +'(2 * x**2 + 3 * y**2 + 0 * x + 2 * y + 3 * x * y) % 4' (0, 3252, 3257, 3261, 3305, 4275) + +'(2 * x**2 + 2 * y**2 + 5 * x + 4 * y + 4 * x * y) % 8' (0, 2, 7, 8, 22, 46, 47, 48, 49, 50, 98, 99, 100, 101, 102, 150, 151, 202, 204, 254, 306, 307, 324, 325, 326, 358, 374, 376, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1425, 1426, 1427, 1428, 1429, 1628, 1629, 1630, 1631, 1632, 1831, 1832, 1836, 1837, 1838, 2034, 2035, 2237, 2239, 2242, 2245, 2248, 2440, 2442, 2445, 2448, 2451, 2643, 2645, 2846, 2851, 3049, 3078, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3658, 3659, 3713, 3714, 3715, 3720, 3721, 3722, 3861, 3863, 3914, 3917, 3920, 3923, 3926, 3929, 4064, 4117, 4119, 4126, 4267, 4281, 4313, 4314, 4338, 4356, 4379, 4394, 4432, 4434, 4469, 4471, 4506, 4509, 4597, 4672) + +'(10 * x**2 + 3 * y**2 + 8 * x + 10 * y + 8 * x * y) % 12' (0, 3252, 3305, 3455, 3463, 3508, 3521, 3536, 3658, 3676, 3711, 4064, 4089, 4117, 4164, 4225) + +'(0 * x**2 + 2 * y**2 + 3 * x + 1 * y + 0 * x * y) % 4' (0, 7, 13, 15, 22, 25, 28, 42, 410, 416, 418, 435, 463, 465, 476, 488, 491, 499, 510, 512, 521, 527, 571, 574, 613, 616, 619, 629, 668, 675, 679, 683, 691, 702, 706, 710, 713, 724, 745, 758, 1019, 1035, 1037, 1044, 1072, 1074, 1081, 1112, 1119, 1121, 1151, 1154, 1164, 1170, 1180, 1183, 1222, 1225, 1230, 1240, 1275, 1284, 1288, 1292, 1303, 1311, 1315, 1319, 1324, 1339, 1357, 1373, 1425, 1431, 1433, 1441, 1443, 1454, 1466, 1469, 1478, 1480, 1491, 1503, 1506, 1518, 1557, 1560, 1628, 1631, 1634, 1646, 1653, 1657, 1661, 1669, 1683, 1690, 1694, 1698, 1706, 1730, 1779, 1792, 1831, 1837, 1839, 1847, 1849, 1860, 1872, 1875, 1893, 1920, 1931, 1933, 1942, 1948, 1976, 1982, 2034, 2050, 2052, 2059, 2087, 2089, 2096, 2127, 2134, 2136, 2166, 2169, 2179, 2185, 2195, 2198, 2237, 2240, 2243, 2255, 2262, 2266, 2270, 2278, 2290, 2326, 2330, 2334, 2337, 2348, 2372, 2398, 2440, 2446, 2448, 2456, 2458, 2469, 2481, 2484, 2493, 2495, 2506, 2518, 2521, 2533, 2572, 2575, 2846, 2849, 2852, 2862, 2901, 2908, 2912, 2916, 2924, 2935, 2939, 2943, 2946, 2957, 2978, 2991, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3102, 3111, 3115, 3119, 3130, 3149, 3194, 3210, 3252, 3258, 3260, 3277, 3305, 3307, 3318, 3330, 3333, 3341, 3352, 3354, 3363, 3369, 3413, 3416, 3455, 3458, 3461, 3471, 3510, 3517, 3521, 3525, 3533, 3544, 3548, 3552, 3555, 3566, 3587, 3600, 3861, 3877, 3879, 3886, 3914, 3916, 3923, 3954, 3961, 3963, 3993, 3996, 4006, 4012, 4022, 4025, 4064, 4067, 4072, 4082, 4117, 4126, 4130, 4134, 4145, 4153, 4157, 4161, 4166, 4181, 4199, 4215, 4272, 4274, 4282, 4304, 4306, 4331, 4357, 4379, 4382, 4385, 4397, 4404, 4408, 4412, 4420, 4434, 4441, 4445, 4449, 4457, 4481, 4530, 4543, 4584, 4587, 4634, 4639, 4646, 4655, 4676) + +'(5 * x**2 + 7 * y**2 + 5 * x + 1 * y + 0 * x * y) % 10' (0, 38, 44, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 3252, 3254, 3257, 3260, 3263, 3267, 3270, 3273, 3277, 3280, 3283, 3287, 3291, 3295, 3299, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3342, 3345, 3348, 3352, 3355, 3358, 3362, 3366, 3370, 3374, 3379, 3383, 3387, 3391, 3396, 3400, 3404, 3408, 3413, 3417, 3421, 3425, 3430, 3435, 3440, 3445, 3450, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4268, 4271, 4274, 4277, 4283, 4286, 4290, 4295, 4299, 4303, 4306, 4309, 4315, 4319, 4322, 4326, 4329, 4333, 4339, 4347, 4350, 4353, 4359, 4361, 4366, 4373, 4377, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(4 * x**2 + 4 * y**2 + 5 * x + 3 * y + 6 * x * y) % 7' (0, 2, 7, 22, 46, 98, 150, 202, 254, 306, 325, 358, 374, 410, 613, 615, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3318, 3455, 3521, 3658, 3714, 3721, 3861, 3914, 4064, 4117, 4379, 4469) + +'(2 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 7, 410, 418, 428, 435, 613, 621, 816, 841, 1019, 1831, 3252, 3260, 3305, 3318, 3333, 3455, 3463, 3508, 3521, 3536, 3658, 3683, 3861, 3914, 4589, 4621) + +'(4 * x**2 + 0 * y**2 + 0 * x + 1 * y + 6 * x * y) % 9' (0, 2440, 2542, 2643, 2745) + +'(1 * x**2 + 0 * y**2 + 2 * x + 0 * y + 1 * x * y) % 4' (0, 39, 358, 359, 366, 367, 368, 377, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 4064, 4065, 4066, 4067, 4068, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4130, 4269, 4340, 4582, 4589, 4590, 4591, 4596, 4607, 4608, 4621, 4622) + +'(0 * x**2 + 1 * y**2 + 4 * x + 1 * y + 3 * x * y) % 5' (0, 816, 3252, 3861) + +'(1 * x**2 + 0 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 46, 98, 1019, 1222, 1425, 1628, 3658, 3723, 3724, 4379) + +'(0 * x**2 + 0 * y**2 + 3 * x + 1 * y + 3 * x * y) % 4' (0, 3252, 3455, 3658, 3861, 4064, 4319, 4361, 4379, 4404, 4434, 4479) + +'(3 * x**2 + 3 * y**2 + 0 * x + 11 * y + 0 * x * y) % 12' (0, 7, 9, 98, 100, 103, 106, 109, 150, 152, 155, 158, 161, 358, 360, 374, 377, 380, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 2034, 2036, 2039, 2042, 2045, 2049, 2052, 2055, 2059, 2062, 2065, 2069, 2073, 2077, 2081, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4066, 4069, 4072, 4075, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4268, 4283, 4286, 4315, 4339, 4359, 4583, 4598, 4601, 4630, 4654, 4674) + +'(0 * x**2 + 8 * y**2 + 3 * x + 3 * y + 3 * x * y) % 9' (0, 3252, 3257, 3305, 3315, 3325, 4586, 4605, 4614, 4644, 4665, 4688) + +'(2 * x**2 + 2 * y**2 + 0 * x + 3 * y + 0 * x * y) % 4' (0, 7, 15, 98, 103, 116, 126, 137, 150, 158, 165, 178, 193, 358, 363, 374, 384, 394, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 1019, 1024, 1034, 1044, 1054, 1074, 1084, 1095, 1111, 1121, 1132, 1149, 1166, 1183, 1201, 1222, 1227, 1237, 1247, 1257, 1277, 1287, 1298, 1314, 1324, 1335, 1352, 1369, 1386, 1404, 1628, 1633, 1646, 1656, 1667, 1680, 1690, 1700, 1720, 1730, 1741, 1762, 1779, 1796, 1815, 1831, 1839, 1846, 1859, 1874, 1883, 1896, 1911, 1920, 1933, 1948, 1957, 1978, 1999, 2023, 2034, 2042, 2049, 2062, 2077, 2086, 2099, 2114, 2123, 2136, 2151, 2160, 2181, 2202, 2226, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4274, 4306, 4319, 4361, 4586, 4605, 4614, 4644, 4665, 4688) + +'(1 * x**2 + 0 * y**2 + 2 * x + 1 * y + 0 * x * y) % 3' (0, 22, 30, 46, 74, 202, 230, 1628, 1636, 1717, 1730, 1745, 2440, 2448, 2465, 2495, 2529, 2542, 2557, 2604, 2643, 2651, 2661, 2705, 2732, 2745, 2760, 2794, 3049, 3057, 3138, 3151, 3166, 3455, 3463, 3508, 3521, 3536, 3658, 3683, 3711, 3758, 3819, 4064, 4089, 4117, 4164, 4225, 4319, 4361, 4589, 4621) + +'(4 * x**2 + 1 * y**2 + 1 * x + 3 * y + 1 * x * y) % 6' (0, 7, 98, 103, 358, 410, 816, 831, 1019, 1034, 1044, 1222, 1227, 1237, 1247, 1257, 1831, 3252, 3305, 3318, 3658, 3861, 3886, 3914, 3924, 4064, 4069, 4089) + +'(0 * x**2 + 3 * y**2 + 3 * x + 2 * y + 1 * x * y) % 4' (0, 2, 7, 22, 46, 98, 150, 202, 254, 306, 322, 325, 358, 374, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3305, 3308, 3318, 3455, 3508, 3521, 3658, 3711, 3714, 3721, 3861, 3914, 4064, 4117, 4283, 4379, 4395, 4469) + +'(1 * x**2 + 2 * y**2 + 2 * x + 2 * y + 2 * x * y) % 3' (0, 306, 3252, 3254, 3455, 3457, 4064, 4130) + +'(0 * x**2 + 2 * y**2 + 1 * x + 0 * y + 0 * x * y) % 3' (0, 254, 263, 816, 845, 1019, 1048, 3252, 3318, 4597, 4672) + +'(1 * x**2 + 2 * y**2 + 1 * x + 2 * y + 0 * x * y) % 3' (0, 39, 3455, 3457, 3463, 3471, 3481, 3484, 3487, 3499, 3508, 3518, 3521, 3524, 3536, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3748, 4064, 4067, 4069, 4083, 4089, 4093, 4097, 4104, 4117, 4127, 4137, 4164, 4225, 4269, 4320, 4340, 4589, 4621, 4657) + +'(1 * x**2 + 2 * y**2 + 1 * x + 1 * y + 3 * x * y) % 4' (0, 39, 1628, 1636, 1717, 1730, 1745, 3455, 3463, 3471, 3484, 3499, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 4064, 4067, 4089, 4093, 4097, 4130, 4269, 4340, 4589, 4621) + +'(0 * x**2 + 1 * y**2 + 1 * x + 2 * y + 2 * x * y) % 6' (0, 7, 10, 39, 410, 413, 435, 439, 443, 816, 819, 822, 834, 841, 845, 849, 857, 1019, 1022, 1027, 1035, 1048, 1063, 1222, 1225, 1228, 1238, 1247, 1251, 1255, 1831, 1834, 1856, 1860, 1864, 3252, 3255, 3277, 3281, 3285, 3305, 3314, 3318, 3322, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3720, 3724, 3728, 3861, 3869, 3877, 3890, 3905, 3914, 3927, 3942, 4064, 4067, 4089, 4093, 4097, 4130, 4269, 4340, 4589, 4621) + +'(5 * x**2 + 3 * y**2 + 11 * x + 5 * y + 3 * x * y) % 12' (0, 3252, 3305, 3352, 3861, 3961) + +'(1 * x**2 + 4 * y**2 + 2 * x + 1 * y + 0 * x * y) % 5' (0, 816, 4607) + +'(3 * x**2 + 1 * y**2 + 1 * x + 4 * y + 4 * x * y) % 6' (0, 7, 98, 358, 410, 412, 428, 816, 818, 1019, 1021, 1027, 1037, 1222, 1227, 1831, 3252, 3254, 3318, 3658, 3861, 3863, 3914, 4064, 4130) + +'(2 * x**2 + 8 * y**2 + 1 * x + 6 * y + 8 * x * y) % 9' (0, 254, 306, 2034, 2643, 2846, 3252, 3305, 3455, 3460) + +'(1 * x**2 + 2 * y**2 + 2 * x + 2 * y + 1 * x * y) % 3' (0, 358, 3252, 3305, 3861, 3866, 4064, 4069) + +'(1 * x**2 + 1 * y**2 + 2 * x + 2 * y + 1 * x * y) % 3' (0, 2, 7, 22, 42, 46, 98, 150, 202, 254, 306, 322, 324, 325, 331, 332, 334, 358, 374, 376, 377, 383, 384, 386, 410, 613, 816, 1019, 1222, 1425, 1628, 1831, 2034, 2237, 2440, 2643, 2846, 3049, 3252, 3305, 3307, 3308, 3314, 3315, 3317, 3318, 3341, 3342, 3344, 3345, 3351, 3352, 3354, 3455, 3508, 3510, 3511, 3517, 3518, 3520, 3521, 3544, 3545, 3547, 3548, 3554, 3555, 3557, 3658, 3711, 3713, 3714, 3720, 3721, 3723, 3724, 3747, 3748, 3750, 3751, 3757, 3758, 3760, 3861, 3914, 3916, 3917, 3923, 3924, 3926, 3927, 3950, 3951, 3953, 3954, 3960, 3961, 3963, 4064, 4117, 4119, 4120, 4126, 4127, 4129, 4130, 4153, 4154, 4156, 4157, 4163, 4164, 4166, 4282, 4283, 4289, 4290, 4292, 4313, 4319, 4320, 4342, 4357, 4379, 4395, 4397, 4398, 4404, 4405, 4407, 4432, 4434, 4435, 4441, 4442, 4444, 4469, 4471, 4472, 4478, 4479, 4481, 4530, 4543, 4597, 4598, 4604, 4605, 4607, 4628, 4634, 4635, 4657, 4676) + +'(0 * x**2 + 1 * y**2 + 2 * x + 2 * y + 1 * x * y) % 3' (0, 3252, 3305, 4590) + +'(4 * x**2 + 4 * y**2 + 3 * x + 2 * y + 3 * x * y) % 5' (0, 98, 103, 1019, 1037, 1222, 1227, 1237, 1247, 1257) + +'(0 * x**2 + 3 * y**2 + 5 * x + 3 * y + 4 * x * y) % 6' (0, 46, 358, 613, 1831, 1860, 3658, 3861, 4064, 4130, 4597, 4672) + +'(9 * x**2 + 9 * y**2 + 9 * x + 2 * y + 2 * x * y) % 10' (0, 2, 7, 22, 46, 48, 98, 150, 202, 254, 306, 325, 358, 374, 410, 412, 415, 428, 613, 615, 618, 621, 624, 816, 818, 1019, 1222, 1425, 1427, 1628, 1831, 2034, 2237, 2242, 2440, 2643, 2698, 2846, 2861, 3049, 3252, 3254, 3318, 3455, 3521, 3658, 3714, 3721, 3861, 3914, 3917, 4064, 4117, 4379, 4469) + +'(3 * x**2 + 6 * y**2 + 6 * x + 5 * y + 6 * x * y) % 8' (0, 3658, 3683, 3861, 3869, 3879, 3886, 4064, 4072, 4082, 4089, 4379) + +'(0 * x**2 + 0 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 2440, 2442, 2542, 2643, 2645, 2745, 3252, 3305, 4319, 4361) + +'(3 * x**2 + 2 * y**2 + 2 * x + 4 * y + 2 * x * y) % 6' (0, 7, 98, 358, 410, 412, 428, 816, 817, 818, 822, 832, 1019, 1021, 1022, 1027, 1037, 1222, 1225, 1227, 1831, 1860, 3252, 3254, 3317, 3318, 3658, 3659, 3861, 3863, 3914, 4064, 4130) + +'(2 * x**2 + 0 * y**2 + 1 * x + 1 * y + 1 * x * y) % 3' (0, 150, 1425, 1628, 1633, 1831, 1846, 2034, 2049, 2086, 3252, 3305, 3455, 3861, 3886, 4064, 4379) + +'(0 * x**2 + 6 * y**2 + 1 * x + 6 * y + 1 * x * y) % 7' (0, 7, 10, 39, 410, 413, 435, 439, 443, 816, 819, 822, 834, 841, 845, 849, 857, 1019, 1027, 1035, 1048, 1063, 1831, 1834, 1856, 1860, 1864, 3252, 3255, 3277, 3281, 3285, 3314, 3318, 3322, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3720, 3724, 3728, 3861, 3869, 3877, 3890, 3905, 3914, 3927, 3942, 4269, 4340, 4589, 4621) + +'(2 * x**2 + 5 * y**2 + 0 * x + 6 * y + 2 * x * y) % 8' (0, 306, 308, 3252, 3254, 3257, 3260, 3263, 3455, 3457, 3460, 3463, 3466, 4268, 4315, 4586, 4665) + +'(1 * x**2 + 3 * y**2 + 1 * x + 0 * y + 3 * x * y) % 6' (0, 306, 308, 309, 322, 3252, 3254, 3255, 3257, 3258, 3260, 3261, 3263, 3264, 3265, 3305, 3455, 3457, 3458, 3460, 3463, 3466, 3508, 3518, 3521, 3524, 3528, 3536, 4268, 4269, 4313, 4315, 4317, 4340, 4583, 4589, 4605, 4610, 4621, 4630, 4657) + +'(7 * x**2 + 3 * y**2 + 0 * x + 1 * y + 6 * x * y) % 8' (0, 2, 7, 22, 46, 98, 150, 202, 254, 259, 306, 325, 358, 374, 410, 613, 816, 1019, 1222, 1227, 1425, 1628, 1646, 1831, 2034, 2049, 2237, 2440, 2445, 2643, 2658, 2846, 2851, 2861, 2871, 2881, 3049, 3054, 3064, 3074, 3084, 3252, 3305, 3318, 3455, 3521, 3658, 3714, 3721, 3861, 3914, 3924, 4064, 4069, 4117, 4127, 4137, 4379, 4469) + +'(5 * x**2 + 4 * y**2 + 2 * x + 4 * y + 0 * x * y) % 6' (0, 3252, 3254, 3255, 3314, 3315, 3318, 3321, 3322, 3658, 3661, 3664, 3723, 3861, 3866, 3869, 3914, 3924, 3927, 3934, 3942, 4269, 4340) + +'(0 * x**2 + 0 * y**2 + 0 * x + 2 * y + 0 * x * y) % 3' (0, 7, 9, 12, 15, 18, 38, 44, 98, 100, 103, 106, 109, 113, 116, 119, 123, 126, 129, 133, 137, 141, 145, 150, 152, 155, 158, 161, 165, 168, 171, 175, 178, 181, 185, 189, 193, 197, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 462, 465, 468, 472, 475, 478, 482, 486, 490, 494, 499, 502, 505, 509, 512, 515, 519, 523, 527, 531, 536, 540, 544, 548, 553, 557, 561, 565, 570, 574, 578, 582, 587, 592, 597, 602, 607, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1071, 1074, 1077, 1081, 1084, 1087, 1091, 1095, 1099, 1103, 1108, 1111, 1114, 1118, 1121, 1124, 1128, 1132, 1136, 1140, 1145, 1149, 1153, 1157, 1162, 1166, 1170, 1174, 1179, 1183, 1187, 1191, 1196, 1201, 1206, 1211, 1216, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1274, 1277, 1280, 1284, 1287, 1290, 1294, 1298, 1302, 1306, 1311, 1314, 1317, 1321, 1324, 1327, 1331, 1335, 1339, 1343, 1348, 1352, 1356, 1360, 1365, 1369, 1373, 1377, 1382, 1386, 1390, 1394, 1399, 1404, 1409, 1414, 1419, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1680, 1683, 1686, 1690, 1693, 1696, 1700, 1704, 1708, 1712, 1717, 1720, 1723, 1727, 1730, 1733, 1737, 1741, 1745, 1749, 1754, 1758, 1762, 1766, 1771, 1775, 1779, 1783, 1788, 1792, 1796, 1800, 1805, 1810, 1815, 1820, 1825, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 1883, 1886, 1889, 1893, 1896, 1899, 1903, 1907, 1911, 1915, 1920, 1923, 1926, 1930, 1933, 1936, 1940, 1944, 1948, 1952, 1957, 1961, 1965, 1969, 1974, 1978, 1982, 1986, 1991, 1995, 1999, 2003, 2008, 2013, 2018, 2023, 2028, 2034, 2036, 2039, 2042, 2045, 2049, 2052, 2055, 2059, 2062, 2065, 2069, 2073, 2077, 2081, 2086, 2089, 2092, 2096, 2099, 2102, 2106, 2110, 2114, 2118, 2123, 2126, 2129, 2133, 2136, 2139, 2143, 2147, 2151, 2155, 2160, 2164, 2168, 2172, 2177, 2181, 2185, 2189, 2194, 2198, 2202, 2206, 2211, 2216, 2221, 2226, 2231, 3252, 3254, 3257, 3260, 3263, 3267, 3270, 3273, 3277, 3280, 3283, 3287, 3291, 3295, 3299, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3342, 3345, 3348, 3352, 3355, 3358, 3362, 3366, 3370, 3374, 3379, 3383, 3387, 3391, 3396, 3400, 3404, 3408, 3413, 3417, 3421, 3425, 3430, 3435, 3440, 3445, 3450, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4268, 4271, 4274, 4277, 4283, 4286, 4290, 4295, 4299, 4303, 4306, 4309, 4315, 4319, 4322, 4326, 4329, 4333, 4339, 4347, 4350, 4353, 4359, 4361, 4366, 4373, 4377, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(0 * x**2 + 0 * y**2 + 1 * x + 0 * y + 2 * x * y) % 3' (0, 816, 831, 845, 1019, 1034, 1048, 4064, 4130, 4597, 4672) + +'(6 * x**2 + 1 * y**2 + 0 * x + 3 * y + 0 * x * y) % 8' (0, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4319, 4361, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(0 * x**2 + 3 * y**2 + 1 * x + 3 * y + 2 * x * y) % 4' (0, 7, 22, 25, 410, 428, 613, 616, 816, 822, 832, 1019, 1022, 1037, 1222, 1225, 1228, 1230, 1425, 1441, 1454, 1628, 1631, 1644, 1646, 1653, 1657, 1661, 1831, 1837, 1849, 1860, 1872, 2034, 2040, 2050, 2059, 2237, 2240, 2266, 2440, 2443, 2446, 2448, 2456, 2469, 2484, 2643, 2646, 2659, 2661, 2846, 2849, 2852, 2854, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3305, 3318, 3455, 3458, 3508, 3510, 3517, 3521, 3525, 3658, 3664, 3711, 3720, 3861, 3864, 3914, 3916, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4379, 4382, 4395, 4397, 4584, 4597, 4655, 4672) + +'(2 * x**2 + 2 * y**2 + 1 * x + 2 * y + 4 * x * y) % 5' (0, 202, 204, 2237, 2239, 2242, 2245, 2248, 2440, 2458) + +'(2 * x**2 + 1 * y**2 + 1 * x + 1 * y + 3 * x * y) % 4' (0, 39, 1831, 1834, 1856, 1860, 1864, 3252, 3255, 3277, 3281, 3285, 3305, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3861, 3869, 3877, 3890, 3905, 4269, 4340, 4589, 4621) + +'(0 * x**2 + 6 * y**2 + 0 * x + 0 * y + 2 * x * y) % 8' (0, 39, 306, 307, 309, 311, 314, 315, 316, 319, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 4267, 4269, 4271, 4274, 4275, 4276, 4279, 4281, 4283, 4287, 4289, 4292, 4293, 4296, 4298, 4303, 4306, 4307, 4311, 4340, 4342, 4345, 4350, 4354, 4368, 4583, 4589, 4605, 4610, 4621, 4630) + +'(1 * x**2 + 5 * y**2 + 0 * x + 2 * y + 6 * x * y) % 8' (0, 3252, 3255, 3258, 3260, 3455, 3458, 3461, 3463) + +'(1 * x**2 + 3 * y**2 + 3 * x + 4 * y + 0 * x * y) % 6' (0, 46, 74, 2440, 2542, 2643, 2745, 4064, 4117, 4319, 4361) + +'(1 * x**2 + 1 * y**2 + 2 * x + 3 * y + 2 * x * y) % 4' (0, 2, 7, 22, 24, 46, 98, 100, 150, 155, 202, 204, 207, 210, 213, 254, 256, 259, 262, 265, 306, 322, 325, 358, 360, 374, 377, 380, 410, 428, 613, 615, 816, 821, 1019, 1021, 1024, 1027, 1030, 1222, 1224, 1227, 1230, 1233, 1425, 1440, 1628, 1630, 1643, 1646, 1649, 1831, 1836, 1846, 1856, 1866, 2034, 2039, 2049, 2059, 2069, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2643, 2645, 2648, 2651, 2654, 2658, 2661, 2664, 2668, 2671, 2674, 2678, 2682, 2686, 2690, 2846, 2848, 2851, 2854, 2857, 2861, 2864, 2867, 2871, 2874, 2877, 2881, 2885, 2889, 2893, 3049, 3051, 3054, 3057, 3060, 3064, 3067, 3070, 3074, 3077, 3080, 3084, 3088, 3092, 3096, 3252, 3305, 3308, 3318, 3455, 3457, 3508, 3511, 3514, 3518, 3521, 3524, 3658, 3663, 3711, 3714, 3721, 3724, 3731, 3735, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4066, 4069, 4072, 4075, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4283, 4379, 4381, 4395, 4398, 4401, 4469, 4472, 4475, 4583, 4598, 4601, 4630, 4654, 4674) + +'(2 * x**2 + 8 * y**2 + 6 * x + 11 * y + 4 * x * y) % 12' (0, 7, 9, 98, 100, 103, 106, 109, 358, 377, 410, 412, 425, 428, 431, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1831, 1833, 1846, 1849, 1852, 3252, 3254, 3315, 3318, 3321, 3861, 3866, 3914, 3924, 3934, 4064, 4130, 4268, 4315) + +'(2 * x**2 + 1 * y**2 + 1 * x + 1 * y + 0 * x * y) % 3' (0, 150, 4275, 4379, 4388, 4590) + +'(2 * x**2 + 1 * y**2 + 2 * x + 1 * y + 2 * x * y) % 4' (0, 306, 311, 322, 332, 342, 3252, 3257, 3267, 3277, 3287, 3305, 3315, 3325, 3342, 3352, 3362, 3379, 3396, 3413, 3430, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4271, 4290, 4299, 4329, 4350, 4373, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(2 * x**2 + 7 * y**2 + 7 * x + 7 * y + 4 * x * y) % 8' (0, 22, 25, 410, 1019, 1628, 1631, 1653, 1657, 1661, 1831, 1837, 1849, 1860, 1872, 2440, 2448, 2456, 2469, 2484, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3455, 3458, 3517, 3521, 3525, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4584, 4655) + +'(0 * x**2 + 1 * y**2 + 1 * x + 1 * y + 2 * x * y) % 3' (0, 150, 1425, 1426, 1427, 1628, 1630, 1831, 1836, 2034, 3252, 3455, 3458, 3861, 4064, 4130, 4379) + +'(2 * x**2 + 3 * y**2 + 2 * x + 5 * y + 4 * x * y) % 8' (0, 358, 363, 3252, 3277, 3305, 3352, 3413, 3658, 3673, 3721, 3758, 3802, 3861, 3866, 3876, 3886, 3896, 4064, 4069, 4079, 4089, 4099, 4586, 4605, 4614, 4644, 4665, 4688) + +'(0 * x**2 + 0 * y**2 + 1 * x + 8 * y + 0 * x * y) % 10' (0, 150, 159, 202, 211, 410, 416, 428, 439, 451, 1222, 1251, 4597, 4672) + +'(4 * x**2 + 1 * y**2 + 1 * x + 2 * y + 2 * x * y) % 8' (0, 1831, 1860, 2034, 2846, 3049, 3078, 3252, 3255, 3258, 3260, 3314, 3318, 3322, 3455, 3458, 3461, 3463, 3517, 3521, 3525, 3658, 3661, 3713, 4379, 4432) + +'(2 * x**2 + 1 * y**2 + 3 * x + 0 * y + 0 * x * y) % 6' (0, 39, 3252, 3255, 3258, 3260, 3268, 3270, 3277, 3281, 3285, 3293, 3296, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3455, 3458, 3461, 3463, 3471, 3473, 3480, 3484, 3488, 3496, 3499, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3661, 3664, 3666, 3674, 3676, 3683, 3687, 3691, 3699, 3702, 3861, 3864, 3867, 3869, 3877, 3879, 3886, 3890, 3894, 3902, 3905, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4067, 4070, 4072, 4080, 4082, 4089, 4093, 4097, 4105, 4108, 4117, 4130, 4145, 4157, 4164, 4199, 4225, 4269, 4282, 4340, 4357, 4589, 4621, 4634, 4676) + +'(0 * x**2 + 0 * y**2 + 1 * x + 4 * y + 0 * x * y) % 7' (0, 46, 55, 74, 2034, 2063, 2090, 2097, 2124, 2643, 2672, 2699, 2708, 2735, 2846, 2875, 2909, 2911, 2945, 4275, 4597, 4657, 4672) + +'(3 * x**2 + 3 * y**2 + 0 * x + 3 * y + 2 * x * y) % 4' (0, 7, 9, 98, 100, 103, 106, 109, 150, 152, 155, 158, 161, 358, 360, 374, 377, 380, 410, 412, 415, 425, 428, 431, 438, 449, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 2034, 2036, 2039, 2042, 2045, 2049, 2052, 2055, 2059, 2062, 2065, 2069, 2073, 2077, 2081, 3252, 3254, 3257, 3305, 3315, 3318, 3321, 3325, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4064, 4066, 4069, 4072, 4075, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4268, 4315, 4583, 4598, 4601, 4630, 4654, 4674) + +'(2 * x**2 + 1 * y**2 + 0 * x + 7 * y + 6 * x * y) % 8' (0, 3252, 3277, 3305, 3352, 3413, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4586, 4665) + +'(6 * x**2 + 0 * y**2 + 3 * x + 2 * y + 2 * x * y) % 8' (0, 22, 150, 202, 306, 324, 325, 1425, 1426, 1628, 1631, 1831, 1837, 2237, 2239, 2440, 2448, 3049, 3055, 3067, 3078, 3090, 3252, 3253, 3314, 3315, 3316, 3317, 3318, 3319, 3455, 3458, 3517, 3518, 3520, 3521, 3525, 4064, 4070, 4117, 4126, 4313) + +'(2 * x**2 + 0 * y**2 + 4 * x + 3 * y + 0 * x * y) % 6' (0, 306, 308, 322, 325, 328, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 4268, 4283, 4286, 4315, 4339, 4359, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(3 * x**2 + 3 * y**2 + 1 * x + 1 * y + 0 * x * y) % 6' (0, 42, 4275, 4282, 4289, 4319, 4357, 4361, 4363, 4368, 4379, 4388, 4395, 4397, 4404, 4432, 4434, 4441, 4472, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4590, 4597, 4604, 4634, 4672, 4676, 4678, 4683) + +'(1 * x**2 + 1 * y**2 + 3 * x + 2 * y + 3 * x * y) % 5' (0, 39, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3723, 4269, 4292, 4340, 4589, 4621, 4635) + +'(2 * x**2 + 2 * y**2 + 2 * x + 0 * y + 1 * x * y) % 3' (0, 22, 24, 202, 204, 207, 210, 213, 306, 322, 1628, 1630, 1643, 1646, 1649, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2299, 2302, 2305, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2643, 2658, 2698, 2735, 2773, 3049, 3051, 3064, 3067, 3070, 3252, 3305, 3455, 3457, 3518, 3521, 3524, 3658, 3748, 4064, 4069, 4117, 4127, 4137, 4583, 4630) + +'(3 * x**2 + 0 * y**2 + 3 * x + 3 * y + 0 * x * y) % 4' (0, 7, 15, 22, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 638, 675, 702, 816, 834, 871, 905, 1019, 1027, 1037, 1044, 1074, 1081, 1108, 1121, 1136, 1170, 1183, 1222, 1230, 1311, 1324, 1339, 1425, 1433, 1480, 1487, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1849, 1856, 1886, 1893, 1920, 1933, 1948, 1982, 1995, 2034, 2059, 2089, 2136, 2198, 2237, 2262, 2299, 2326, 2440, 2458, 2495, 2529, 2643, 2651, 2698, 2705, 2846, 2871, 2908, 2935, 3049, 3057, 3067, 3074, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3480, 3521, 3548, 3658, 3676, 3724, 3758, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4117, 4130, 4145, 4274, 4306, 4319, 4361, 4379, 4408, 4441, 4472) + +'(2 * x**2 + 2 * y**2 + 0 * x + 0 * y + 1 * x * y) % 3' (0, 42, 3252, 3455, 3658, 3721, 3723, 3748, 3750, 3861, 4064, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) + +'(0 * x**2 + 1 * y**2 + 1 * x + 3 * y + 1 * x * y) % 4' (0, 7, 410, 816, 822, 845, 1019, 1222, 1831, 1860, 3252, 3305, 3314, 3318, 3861, 3914, 3927) + +'(9 * x**2 + 7 * y**2 + 9 * x + 6 * y + 0 * x * y) % 12' (0, 306, 308, 322, 325, 328, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 4064, 4072, 4117, 4130, 4145, 4268, 4283, 4286, 4315, 4339, 4359) + +'(7 * x**2 + 7 * y**2 + 1 * x + 0 * y + 4 * x * y) % 8' (0, 306, 325, 3049, 3057, 3067, 3074, 3252, 3254, 3315, 3318, 3321, 3455, 3521) + +'(0 * x**2 + 1 * y**2 + 2 * x + 2 * y + 2 * x * y) % 4' (0, 306, 308, 322, 325, 328, 358, 363, 374, 384, 394, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3658, 3660, 3673, 3676, 3679, 3711, 3714, 3717, 3748, 3751, 3754, 3785, 3789, 3793, 3797, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4268, 4283, 4286, 4315, 4339, 4359, 4379, 4384, 4395, 4405, 4415, 4431, 4441, 4451, 4469, 4479, 4489, 4507, 4524, 4541, 4558, 4586, 4605, 4614, 4644, 4665, 4688) + +'(3 * x**2 + 1 * y**2 + 1 * x + 1 * y + 0 * x * y) % 4' (0, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4274, 4306, 4319, 4361, 4584, 4597, 4655, 4672) + +'(1 * x**2 + 1 * y**2 + 0 * x + 1 * y + 1 * x * y) % 3' (0, 2, 7, 8, 22, 46, 47, 48, 49, 50, 98, 99, 101, 150, 151, 202, 204, 254, 306, 307, 325, 358, 374, 377, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 428, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 816, 817, 818, 819, 820, 822, 824, 825, 828, 1019, 1020, 1021, 1022, 1023, 1025, 1028, 1031, 1038, 1222, 1223, 1225, 1231, 1425, 1426, 1427, 1428, 1429, 1480, 1628, 1629, 1631, 1831, 1832, 1836, 1837, 1838, 2034, 2035, 2050, 2097, 2237, 2239, 2242, 2245, 2248, 2440, 2442, 2448, 2643, 2645, 2846, 2851, 3049, 3252, 3253, 3254, 3255, 3256, 3317, 3318, 3319, 3455, 3456, 3458, 3510, 3518, 3521, 3658, 3659, 3714, 3721, 3724, 3861, 3863, 3914, 3917, 3920, 3927, 3954, 4064, 4117, 4120, 4130, 4267, 4281, 4379, 4394, 4469, 4472, 4598, 4635) + +'(3 * x**2 + 6 * y**2 + 2 * x + 1 * y + 2 * x * y) % 8' (0, 613, 1425, 3658, 3683, 3861, 3869, 3879, 3886, 4064, 4072, 4082, 4089) + +'(1 * x**2 + 5 * y**2 + 1 * x + 4 * y + 4 * x * y) % 6' (0, 358, 1425, 1427, 3658, 3673, 4064) + +'(2 * x**2 + 4 * y**2 + 1 * x + 7 * y + 4 * x * y) % 8' (0, 7, 15, 410, 418, 435, 465, 499, 512, 527, 574, 1019, 1044, 1074, 1112, 1121, 1183, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1847, 1920, 1933, 1948, 2440, 2446, 2533, 3049, 3078, 3102, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3861, 3886, 3914, 3923, 3961, 4022, 4274, 4306) + +'(0 * x**2 + 2 * y**2 + 4 * x + 5 * y + 0 * x * y) % 8' (0, 358, 363, 374, 384, 394, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4274, 4306, 4319, 4361, 4586, 4605, 4614, 4644, 4665, 4688) + +'(2 * x**2 + 2 * y**2 + 0 * x + 2 * y + 0 * x * y) % 4' (0, 37, 41, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) + +'(2 * x**2 + 3 * y**2 + 1 * x + 3 * y + 0 * x * y) % 4' (0, 7, 22, 25, 410, 418, 428, 435, 613, 616, 619, 621, 816, 822, 832, 841, 1019, 1022, 1035, 1037, 1222, 1225, 1228, 1230, 1425, 1433, 1441, 1454, 1469, 1628, 1631, 1634, 1636, 1644, 1646, 1653, 1657, 1661, 1669, 1672, 1831, 1837, 1849, 1860, 1872, 2034, 2040, 2050, 2059, 2237, 2240, 2262, 2266, 2270, 2440, 2443, 2446, 2448, 2456, 2458, 2465, 2469, 2473, 2481, 2484, 2643, 2646, 2659, 2661, 2846, 2849, 2852, 2854, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3260, 3305, 3318, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3664, 3711, 3720, 3861, 3864, 3914, 3916, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4379, 4382, 4395, 4397, 4584, 4597, 4655, 4672) + +'(0 * x**2 + 0 * y**2 + 4 * x + 1 * y + 0 * x * y) % 5' (0, 22, 25, 30, 39, 1019, 1022, 1027, 1037, 1072, 1081, 1085, 1089, 1100, 1108, 1112, 1116, 1121, 1136, 1154, 1170, 1628, 1631, 1636, 1644, 1653, 1657, 1661, 1672, 1683, 1717, 1721, 1725, 1730, 1745, 1760, 1792, 1831, 1834, 1837, 1849, 1856, 1860, 1864, 1872, 1886, 1893, 1897, 1901, 1909, 1933, 1982, 1995, 2440, 2443, 2448, 2456, 2465, 2469, 2473, 2484, 2495, 2529, 2533, 2537, 2542, 2557, 2572, 2604, 2643, 2646, 2651, 2661, 2696, 2705, 2709, 2713, 2724, 2732, 2736, 2740, 2745, 2760, 2778, 2794, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3104, 3138, 3142, 3146, 3151, 3166, 3181, 3213, 3455, 3458, 3463, 3471, 3480, 3484, 3488, 3499, 3508, 3517, 3521, 3525, 3536, 3555, 3600, 3616, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3711, 3747, 3751, 3755, 3758, 3769, 3793, 3819, 4064, 4067, 4072, 4080, 4089, 4093, 4097, 4108, 4117, 4126, 4130, 4134, 4145, 4164, 4209, 4225, 4269, 4272, 4319, 4324, 4331, 4340, 4361, 4584, 4589, 4604, 4611, 4621, 4655, 4683) + +'(3 * x**2 + 0 * y**2 + 1 * x + 0 * y + 2 * x * y) % 4' (0, 358, 359, 376, 377, 378, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 4064, 4065, 4066, 4067, 4068, 4126, 4127, 4128, 4129, 4130, 4131, 4132, 4133, 4134, 4135, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4596, 4628, 4629, 4653, 4671) + +'(0 * x**2 + 0 * y**2 + 3 * x + 6 * y + 0 * x * y) % 9' (0, 39, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(1 * x**2 + 5 * y**2 + 1 * x + 0 * y + 4 * x * y) % 6' (0, 22, 1628, 2237, 2265, 2440, 2442, 2458, 3049, 3252, 3305, 3455, 3521, 4064, 4117, 4154) + +'(1 * x**2 + 3 * y**2 + 2 * x + 0 * y + 0 * x * y) % 4' (0, 42, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3341, 3345, 3349, 3352, 3354, 3363, 3369, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3544, 3548, 3552, 3555, 3557, 3566, 3572, 3861, 3869, 3879, 3886, 3914, 3916, 3923, 3927, 3942, 3950, 3954, 3961, 3963, 3978, 3996, 4012, 4022, 4025, 4064, 4072, 4082, 4089, 4117, 4119, 4126, 4130, 4145, 4153, 4157, 4164, 4166, 4181, 4199, 4215, 4225, 4228, 4269, 4282, 4340, 4357, 4379, 4387, 4397, 4404, 4434, 4441, 4468, 4481, 4496, 4530, 4543, 4589, 4621, 4634, 4676) + +'(1 * x**2 + 4 * y**2 + 7 * x + 0 * y + 6 * x * y) % 8' (0, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 4064, 4067, 4126, 4130, 4134, 4313) + +'(1 * x**2 + 1 * y**2 + 0 * x + 2 * y + 2 * x * y) % 3' (0, 7, 9, 98, 100, 103, 106, 109, 358, 377, 410, 412, 425, 428, 431, 816, 818, 832, 835, 838, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1228, 1230, 1233, 1237, 1240, 1243, 1247, 1248, 1250, 1253, 1257, 1259, 1261, 1265, 1269, 1831, 1833, 1846, 1849, 1852, 3252, 3254, 3315, 3318, 3321, 3658, 3723, 3861, 3866, 3914, 3924, 3934, 4064, 4130, 4268, 4315) + +'(0 * x**2 + 10 * y**2 + 5 * x + 0 * y + 10 * x * y) % 12' (0, 202, 254, 1831, 2034, 2237, 2440, 3658, 4379) + +'(0 * x**2 + 0 * y**2 + 2 * x + 0 * y + 4 * x * y) % 8' (0, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) + +'(4 * x**2 + 11 * y**2 + 10 * x + 0 * y + 1 * x * y) % 12' (0, 3252, 3261, 3305, 4275) + +'(3 * x**2 + 3 * y**2 + 3 * x + 2 * y + 2 * x * y) % 4' (0, 2, 7, 9, 22, 46, 48, 51, 54, 57, 98, 100, 103, 106, 109, 150, 152, 202, 207, 254, 306, 308, 322, 325, 328, 358, 374, 377, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 613, 615, 618, 621, 624, 628, 631, 634, 638, 641, 644, 648, 652, 656, 660, 816, 818, 821, 824, 827, 831, 834, 837, 841, 844, 847, 851, 855, 859, 863, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1425, 1427, 1430, 1433, 1436, 1628, 1630, 1633, 1636, 1639, 1831, 1833, 1846, 1849, 1852, 2034, 2036, 2237, 2242, 2252, 2262, 2272, 2440, 2445, 2455, 2465, 2475, 2643, 2648, 2846, 2861, 3049, 3067, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3658, 3660, 3711, 3714, 3717, 3721, 3724, 3727, 3861, 3866, 3914, 3917, 3924, 3927, 3934, 3938, 4064, 4117, 4120, 4130, 4268, 4283, 4286, 4315, 4339, 4359, 4379, 4395, 4398, 4431, 4469, 4472, 4507, 4515, 4598) + +'(2 * x**2 + 1 * y**2 + 0 * x + 3 * y + 0 * x * y) % 4' (0, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4274, 4306, 4319, 4361, 4379, 4381, 4384, 4387, 4390, 4395, 4398, 4401, 4405, 4408, 4411, 4415, 4419, 4423, 4427, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(2 * x**2 + 0 * y**2 + 5 * x + 3 * y + 6 * x * y) % 8' (0, 39, 1019, 1027, 1112, 1628, 1636, 1717, 1730, 1745, 2440, 2465, 2533, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 4269, 4340, 4589, 4621) + +'(1 * x**2 + 2 * y**2 + 0 * x + 3 * y + 0 * x * y) % 4' (0, 22, 30, 410, 512, 1628, 1636, 1717, 1730, 1745, 2237, 2245, 2255, 2262, 2292, 2299, 2326, 2339, 2354, 2388, 2401, 2440, 2448, 2458, 2465, 2495, 2502, 2529, 2542, 2557, 2591, 2604, 2643, 2651, 2661, 2668, 2698, 2705, 2732, 2745, 2760, 2794, 2807, 2846, 2854, 2864, 2871, 2901, 2908, 2935, 2948, 2963, 2997, 3010, 3049, 3057, 3067, 3074, 3104, 3111, 3138, 3151, 3166, 3200, 3213, 3455, 3463, 3508, 3521, 3536, 3658, 3683, 3711, 3758, 3819, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4082, 4089, 4117, 4130, 4145, 4157, 4164, 4199, 4225, 4319, 4361, 4589, 4621, 4634, 4676) + +'(7 * x**2 + 7 * y**2 + 3 * x + 0 * y + 2 * x * y) % 8' (0, 150, 202, 1425, 1427, 2237, 2242, 3049, 3067, 3455, 3457, 3518, 3521, 3524) + +'(3 * x**2 + 3 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 42, 3252, 3277, 3305, 3307, 3352, 3354, 3413, 3416, 3455, 3471, 3510, 3517, 3548, 3555, 3587, 3600, 3861, 3877, 3916, 3923, 3954, 3961, 3993, 4006, 4064, 4067, 4126, 4130, 4134, 4153, 4157, 4161, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) + +'(5 * x**2 + 8 * y**2 + 3 * x + 1 * y + 5 * x * y) % 9' (0, 46, 358, 613, 816, 1425, 3861, 3863, 4064, 4130) + +'(5 * x**2 + 3 * y**2 + 6 * x + 7 * y + 4 * x * y) % 8' (0, 2, 7, 22, 46, 98, 150, 202, 207, 254, 259, 306, 325, 358, 374, 410, 428, 613, 816, 1019, 1024, 1222, 1227, 1425, 1628, 1646, 1831, 1846, 2034, 2049, 2237, 2242, 2252, 2262, 2272, 2440, 2445, 2455, 2465, 2475, 2643, 2648, 2658, 2668, 2678, 2846, 2851, 2861, 2871, 2881, 3049, 3054, 3064, 3074, 3084, 3252, 3305, 3318, 3455, 3511, 3521, 3658, 3714, 3721, 3861, 3866, 3914, 3924, 3934, 4064, 4069, 4117, 4127, 4137, 4379, 4398, 4469) + +'(1 * x**2 + 1 * y**2 + 1 * x + 1 * y + 1 * x * y) % 3' (0, 42, 150, 151, 152, 155, 165, 1425, 1426, 1427, 1428, 1429, 1628, 1630, 1633, 1636, 1639, 1831, 1836, 1846, 1856, 1866, 2034, 2049, 2086, 2123, 2160, 3252, 3257, 3455, 3456, 3861, 3876, 4064, 4066, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) + +'(6 * x**2 + 0 * y**2 + 2 * x + 4 * y + 3 * x * y) % 9' (0, 1019, 1022, 1037, 1072, 1108, 1112, 1116, 1154, 2440, 2443, 2456, 2495, 2503, 2529, 2533, 2537, 2572, 4272, 4331, 4604, 4635, 4683) + +'(1 * x**2 + 5 * y**2 + 2 * x + 3 * y + 6 * x * y) % 8' (0, 2, 7, 22, 24, 46, 98, 100, 150, 155, 202, 204, 207, 210, 213, 254, 256, 259, 262, 265, 306, 322, 325, 358, 360, 374, 410, 613, 615, 816, 821, 1019, 1021, 1024, 1027, 1030, 1222, 1224, 1227, 1230, 1233, 1425, 1440, 1628, 1630, 1643, 1646, 1649, 1831, 1836, 1846, 1856, 1866, 2034, 2039, 2049, 2059, 2069, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 2643, 2645, 2648, 2651, 2654, 2658, 2661, 2664, 2668, 2671, 2674, 2678, 2682, 2686, 2690, 2846, 2848, 2851, 2854, 2857, 2861, 2864, 2867, 2871, 2874, 2877, 2881, 2885, 2889, 2893, 3049, 3051, 3054, 3057, 3060, 3064, 3067, 3070, 3074, 3077, 3080, 3084, 3088, 3092, 3096, 3252, 3305, 3308, 3318, 3455, 3457, 3508, 3518, 3521, 3524, 3658, 3663, 3711, 3714, 3721, 3731, 3861, 3863, 3866, 3869, 3872, 3914, 4064, 4066, 4069, 4072, 4075, 4117, 4127, 4137, 4283, 4379, 4381, 4395, 4469, 4583, 4630) + +'(1 * x**2 + 0 * y**2 + 1 * x + 2 * y + 2 * x * y) % 4' (0, 306, 307, 308, 309, 310, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 4064, 4067, 4126, 4130, 4134, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360) + +'(0 * x**2 + 0 * y**2 + 1 * x + 1 * y + 0 * x * y) % 4' (0, 42, 410, 439, 476, 503, 510, 512, 613, 642, 679, 706, 713, 715, 816, 845, 882, 909, 916, 918, 1019, 1048, 1085, 1112, 1119, 1121, 1222, 1251, 1288, 1315, 1322, 1324, 1425, 1454, 1491, 1518, 1525, 1527, 1628, 1657, 1694, 1721, 1728, 1730, 1831, 1860, 1897, 1924, 1931, 1933, 2034, 2063, 2100, 2127, 2134, 2136, 2237, 2266, 2303, 2330, 2337, 2339, 2440, 2469, 2506, 2533, 2540, 2542, 2643, 2672, 2709, 2736, 2743, 2745, 2846, 2875, 2912, 2939, 2946, 2948, 3049, 3078, 3115, 3142, 3149, 3151, 4282, 4289, 4319, 4357, 4361, 4363, 4368, 4379, 4395, 4397, 4404, 4432, 4434, 4441, 4472, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4597, 4604, 4634, 4672, 4676, 4678, 4683) + +'(2 * x**2 + 0 * y**2 + 1 * x + 0 * y + 2 * x * y) % 4' (0, 2, 7, 8, 22, 25, 46, 47, 48, 49, 50, 98, 99, 100, 101, 102, 150, 151, 158, 159, 160, 202, 204, 208, 211, 214, 254, 257, 260, 262, 306, 307, 324, 325, 326, 358, 361, 374, 376, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1425, 1426, 1427, 1428, 1429, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1628, 1629, 1630, 1631, 1632, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1831, 1832, 1836, 1837, 1838, 1849, 1850, 1851, 1859, 1860, 1861, 1870, 1871, 1872, 1873, 2034, 2035, 2042, 2043, 2044, 2052, 2053, 2054, 2059, 2060, 2061, 2237, 2239, 2242, 2245, 2248, 2253, 2256, 2259, 2263, 2266, 2269, 2273, 2277, 2281, 2285, 2440, 2442, 2445, 2448, 2451, 2456, 2459, 2462, 2466, 2469, 2472, 2476, 2480, 2484, 2488, 2643, 2645, 2649, 2652, 2655, 2659, 2662, 2665, 2668, 2671, 2674, 2846, 2849, 2851, 2855, 2859, 2862, 2864, 2872, 2874, 2882, 2885, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3658, 3659, 3666, 3667, 3668, 3713, 3714, 3715, 3720, 3721, 3722, 3861, 3863, 3867, 3870, 3873, 3914, 3917, 3920, 3923, 3926, 3929, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4267, 4281, 4313, 4314, 4338, 4356, 4379, 4382, 4394, 4398, 4402, 4432, 4434, 4469, 4471, 4506, 4509, 4584, 4597, 4655, 4672) + +'(7 * x**2 + 6 * y**2 + 2 * x + 5 * y + 4 * x * y) % 8' (0, 7, 410, 435, 512, 816, 841, 1019, 1044, 1831, 1920, 3252, 3277, 3318, 3658, 3683, 3861, 3886, 3914, 3961, 4022, 4589, 4621) + +'(0 * x**2 + 2 * y**2 + 0 * x + 2 * y + 2 * x * y) % 4' (0, 42, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4379, 4380, 4381, 4382, 4383, 4384, 4385, 4386, 4387, 4388, 4389, 4390, 4391, 4392, 4393, 4394, 4395, 4396, 4397, 4398, 4399, 4400, 4401, 4402, 4403, 4404, 4405, 4406, 4407, 4408, 4409, 4410, 4411, 4412, 4413, 4414, 4415, 4416, 4417, 4418, 4419, 4420, 4421, 4422, 4423, 4424, 4425, 4426, 4427, 4428, 4429, 4430, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 4440, 4441, 4442, 4443, 4444, 4445, 4446, 4447, 4448, 4449, 4450, 4451, 4452, 4453, 4454, 4455, 4456, 4457, 4458, 4459, 4460, 4461, 4462, 4463, 4464, 4465, 4466, 4467, 4468, 4469, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4478, 4479, 4480, 4481, 4482, 4483, 4484, 4485, 4486, 4487, 4488, 4489, 4490, 4491, 4492, 4493, 4494, 4495, 4496, 4497, 4498, 4499, 4500, 4501, 4502, 4503, 4504, 4505, 4506, 4507, 4508, 4509, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 4520, 4521, 4522, 4523, 4524, 4525, 4526, 4527, 4528, 4529, 4530, 4531, 4532, 4533, 4534, 4535, 4536, 4537, 4538, 4539, 4540, 4541, 4542, 4543, 4544, 4545, 4546, 4547, 4548, 4549, 4550, 4551, 4552, 4553, 4554, 4555, 4556, 4557, 4558, 4559, 4560, 4561, 4562, 4563, 4564, 4565, 4566, 4567, 4568, 4569, 4570, 4571, 4572, 4573, 4574, 4575, 4576, 4577, 4578, 4579, 4580, 4581, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) + +'(5 * x**2 + 5 * y**2 + 5 * x + 0 * y + 2 * x * y) % 8' (0, 2, 7, 22, 46, 48, 98, 150, 202, 254, 306, 325, 358, 374, 410, 412, 415, 418, 421, 613, 615, 618, 621, 624, 816, 818, 1019, 1024, 1222, 1425, 1427, 1628, 1831, 1849, 2034, 2237, 2242, 2440, 2643, 2846, 3049, 3252, 3254, 3315, 3318, 3321, 3455, 3518, 3521, 3658, 3714, 3721, 3861, 3914, 4064, 4117, 4130, 4379, 4469) + +'(3 * x**2 + 0 * y**2 + 3 * x + 4 * y + 0 * x * y) % 7' (0, 46, 74) + +'(2 * x**2 + 2 * y**2 + 0 * x + 0 * y + 2 * x * y) % 4' (0, 42, 306, 307, 308, 309, 310, 358, 360, 363, 366, 369, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4381, 4384, 4387, 4390, 4394, 4397, 4400, 4404, 4407, 4410, 4414, 4418, 4422, 4426, 4431, 4434, 4437, 4441, 4444, 4447, 4451, 4455, 4459, 4463, 4468, 4471, 4474, 4478, 4481, 4484, 4488, 4492, 4496, 4500, 4505, 4509, 4513, 4517, 4522, 4526, 4530, 4534, 4539, 4543, 4547, 4551, 4556, 4561, 4566, 4571, 4576, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(0 * x**2 + 0 * y**2 + 1 * x + 3 * y + 0 * x * y) % 4' (0, 7, 10, 15, 39, 410, 413, 418, 426, 435, 439, 443, 454, 465, 499, 503, 507, 512, 527, 542, 574, 816, 819, 822, 834, 841, 845, 849, 857, 869, 905, 909, 913, 916, 927, 951, 977, 1019, 1022, 1027, 1035, 1044, 1048, 1052, 1063, 1074, 1108, 1112, 1116, 1121, 1136, 1151, 1183, 1628, 1634, 1636, 1644, 1646, 1657, 1669, 1672, 1690, 1717, 1728, 1730, 1739, 1745, 1773, 1779, 1831, 1834, 1839, 1847, 1856, 1860, 1864, 1875, 1886, 1920, 1924, 1928, 1933, 1948, 1963, 1995, 2440, 2443, 2446, 2458, 2465, 2469, 2473, 2481, 2493, 2529, 2533, 2537, 2540, 2551, 2575, 2601, 3049, 3078, 3102, 3104, 3111, 3138, 3252, 3255, 3260, 3268, 3277, 3281, 3285, 3296, 3305, 3314, 3318, 3322, 3333, 3352, 3397, 3413, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3713, 3720, 3724, 3728, 3736, 3760, 3809, 3822, 3861, 3864, 3869, 3877, 3886, 3890, 3894, 3905, 3914, 3923, 3927, 3931, 3942, 3961, 4006, 4022, 4269, 4274, 4289, 4296, 4306, 4340, 4368, 4587, 4589, 4597, 4619, 4621, 4646, 4672) + +'(0 * x**2 + 2 * y**2 + 0 * x + 1 * y + 2 * x * y) % 4' (0, 2, 7, 15, 22, 27, 46, 54, 64, 71, 98, 103, 116, 126, 137, 150, 158, 165, 178, 193, 202, 207, 217, 227, 237, 254, 259, 269, 279, 289, 306, 314, 325, 332, 358, 363, 374, 384, 394, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 618, 631, 641, 652, 668, 678, 689, 702, 712, 722, 816, 824, 831, 844, 859, 871, 878, 908, 915, 946, 959, 1019, 1024, 1034, 1044, 1054, 1074, 1084, 1095, 1111, 1121, 1132, 1149, 1166, 1183, 1201, 1222, 1227, 1237, 1247, 1257, 1277, 1287, 1298, 1314, 1324, 1335, 1352, 1369, 1386, 1404, 1425, 1433, 1443, 1450, 1477, 1490, 1505, 1517, 1524, 1559, 1585, 1628, 1633, 1646, 1656, 1667, 1680, 1690, 1700, 1720, 1730, 1741, 1762, 1779, 1796, 1815, 1831, 1839, 1846, 1859, 1874, 1883, 1896, 1911, 1920, 1933, 1948, 1957, 1978, 1999, 2023, 2034, 2042, 2049, 2062, 2077, 2086, 2099, 2114, 2123, 2136, 2151, 2160, 2181, 2202, 2226, 2237, 2242, 2252, 2262, 2272, 2289, 2299, 2309, 2326, 2336, 2346, 2363, 2380, 2397, 2414, 2440, 2445, 2455, 2465, 2475, 2492, 2502, 2512, 2529, 2539, 2549, 2566, 2583, 2600, 2617, 2643, 2648, 2658, 2668, 2678, 2695, 2705, 2715, 2732, 2742, 2752, 2769, 2786, 2803, 2820, 2846, 2851, 2861, 2871, 2881, 2898, 2908, 2918, 2935, 2945, 2955, 2972, 2989, 3006, 3023, 3049, 3054, 3064, 3074, 3084, 3101, 3111, 3121, 3138, 3148, 3158, 3175, 3192, 3209, 3226, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3460, 3473, 3483, 3494, 3511, 3521, 3532, 3545, 3555, 3565, 3658, 3666, 3673, 3686, 3701, 3714, 3721, 3751, 3758, 3789, 3802, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4274, 4306, 4319, 4361, 4379, 4384, 4398, 4408, 4419, 4434, 4444, 4455, 4469, 4479, 4489, 4586, 4605, 4614, 4644, 4665, 4688) + +'(1 * x**2 + 2 * y**2 + 2 * x + 1 * y + 2 * x * y) % 4' (0, 410, 428, 472, 512, 561, 613, 621, 668, 675, 1425, 1443, 1480, 1514, 1628, 1636, 1717, 1730, 1745, 3658, 3683, 3724, 3751, 3861, 3869, 3879, 3886, 3914, 3927, 3942, 3954, 3961, 3996, 4022, 4064, 4072, 4082, 4089, 4117, 4130, 4145, 4157, 4164, 4199, 4225, 4379, 4387, 4472, 4479, 4589, 4621, 4634, 4676) + +'(0 * x**2 + 2 * y**2 + 2 * x + 1 * y + 0 * x * y) % 5' (0, 3049, 3055, 3067, 3078, 3090) + +'(2 * x**2 + 2 * y**2 + 1 * x + 0 * y + 2 * x * y) % 3' (0, 2, 7, 22, 27, 46, 98, 103, 150, 165, 202, 217, 227, 254, 259, 269, 279, 289, 306, 322, 325, 358, 363, 374, 410, 613, 618, 816, 831, 1019, 1034, 1044, 1222, 1227, 1237, 1247, 1257, 1425, 1477, 1480, 1488, 1628, 1633, 1680, 1690, 1700, 1831, 1883, 1920, 2034, 2049, 2050, 2086, 2123, 2160, 2237, 2289, 2326, 2336, 2440, 2455, 2492, 2502, 2529, 2532, 2539, 2566, 2583, 2643, 2658, 2668, 2695, 2705, 2732, 2742, 2769, 2786, 2846, 2851, 2861, 2871, 2881, 2898, 2908, 2918, 2935, 2945, 2955, 2972, 2989, 3006, 3023, 3049, 3054, 3064, 3067, 3074, 3084, 3101, 3111, 3121, 3138, 3148, 3158, 3175, 3192, 3209, 3226, 3252, 3305, 3308, 3318, 3455, 3460, 3508, 3510, 3511, 3521, 3532, 3658, 3673, 3711, 3714, 3721, 3861, 3876, 3886, 3914, 3924, 3954, 4064, 4069, 4079, 4089, 4099, 4117, 4154, 4191, 4283, 4320, 4379, 4384, 4395, 4469, 4586, 4665) + +'(3 * x**2 + 3 * y**2 + 4 * x + 1 * y + 0 * x * y) % 6' (0, 46, 55, 98, 107, 150, 159, 202, 211, 254, 263, 4282, 4357, 4379, 4395, 4397, 4432, 4434, 4472, 4511, 4514, 4597, 4672) + +'(0 * x**2 + 2 * y**2 + 0 * x + 3 * y + 2 * x * y) % 8' (0, 98, 116, 126, 150, 158, 178, 410, 428, 472, 512, 561, 1222, 1237, 1277, 1287, 1314, 1324, 1352, 1369, 2034, 2042, 2062, 2086, 2099, 2114, 2136, 2202, 3861, 3886, 3914, 3924, 3951, 3961, 4022, 4605) + +'(2 * x**2 + 4 * y**2 + 2 * x + 2 * y + 2 * x * y) % 8' (0, 4268, 4269, 4313, 4315, 4317, 4340, 4586, 4589, 4598, 4618, 4621, 4665) + +'(0 * x**2 + 3 * y**2 + 1 * x + 0 * y + 0 * x * y) % 4' (0, 7, 10, 410, 413, 416, 418, 426, 428, 435, 439, 443, 451, 454, 613, 616, 619, 621, 629, 631, 638, 642, 646, 654, 657, 816, 819, 822, 824, 832, 834, 841, 845, 849, 857, 860, 1019, 1022, 1025, 1027, 1035, 1037, 1044, 1048, 1052, 1060, 1063, 1222, 1225, 1228, 1230, 1238, 1240, 1247, 1251, 1255, 1263, 1266, 1831, 1834, 1856, 1860, 1864, 3049, 3078, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3661, 3720, 3724, 3728, 3861, 3869, 3914, 3927, 3942, 4269, 4282, 4340, 4357, 4597, 4672) + +'(0 * x**2 + 0 * y**2 + 2 * x + 4 * y + 0 * x * y) % 5' (0, 2, 7, 15, 22, 46, 54, 71, 98, 117, 126, 150, 166, 178, 202, 208, 221, 227, 254, 260, 273, 306, 314, 325, 358, 374, 383, 410, 418, 435, 465, 473, 499, 512, 527, 574, 613, 632, 641, 668, 676, 702, 816, 832, 844, 882, 908, 915, 1019, 1025, 1038, 1044, 1074, 1085, 1097, 1121, 1183, 1222, 1228, 1241, 1278, 1312, 1324, 1425, 1433, 1443, 1451, 1481, 1524, 1628, 1646, 1654, 1681, 1690, 1721, 1730, 1763, 1779, 1831, 1839, 1850, 1884, 1897, 1912, 1920, 1933, 1948, 2034, 2053, 2060, 2100, 2124, 2136, 2237, 2253, 2262, 2303, 2326, 2440, 2449, 2466, 2496, 2505, 2530, 2539, 2643, 2649, 2659, 2698, 2709, 2721, 2736, 2742, 2775, 2846, 2864, 2872, 2902, 2911, 2935, 3049, 3055, 3067, 3078, 3090, 3102, 3114, 3142, 3184, 3252, 3260, 3277, 3305, 3318, 3333, 3344, 3352, 3413, 3455, 3474, 3483, 3521, 3547, 3555, 3658, 3674, 3686, 3714, 3721, 3747, 3861, 3867, 3880, 3886, 3914, 3950, 3961, 3972, 4022, 4064, 4070, 4083, 4117, 4129, 4163, 4274, 4306, 4320, 4379, 4408, 4434, 4442, 4469, 4478, 4604, 4635, 4683) + +'(0 * x**2 + 2 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 22, 25, 410, 416, 428, 439, 451, 463, 472, 503, 512, 545, 561, 816, 824, 832, 845, 860, 871, 878, 909, 916, 948, 961, 1019, 1025, 1037, 1048, 1060, 1072, 1081, 1112, 1121, 1154, 1170, 1628, 1631, 1653, 1657, 1661, 1681, 1683, 1728, 1730, 1789, 1792, 1831, 1837, 1849, 1860, 1872, 1884, 1893, 1924, 1933, 1966, 1982, 2440, 2448, 2456, 2469, 2484, 2495, 2502, 2533, 2540, 2572, 2585, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3455, 3458, 3471, 3473, 3517, 3521, 3525, 3555, 3557, 3600, 3606, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4272, 4289, 4331, 4368, 4584, 4597, 4655, 4672) + +'(2 * x**2 + 2 * y**2 + 0 * x + 0 * y + 0 * x * y) % 3' (0, 42, 306, 325, 331, 358, 374, 386, 3252, 3318, 3341, 3455, 3521, 3544, 3658, 3714, 3757, 3861, 3914, 3963, 4064, 4117, 4166, 4282, 4342, 4357, 4379, 4397, 4404, 4434, 4441, 4469, 4481, 4530, 4543, 4607, 4634, 4676) + +'(0 * x**2 + 0 * y**2 + 2 * x + 1 * y + 0 * x * y) % 3' (0, 22, 25, 30, 39, 46, 49, 52, 62, 74, 1019, 1022, 1027, 1037, 1045, 1072, 1081, 1085, 1089, 1100, 1108, 1112, 1116, 1121, 1136, 1154, 1170, 1628, 1631, 1636, 1644, 1653, 1657, 1661, 1672, 1683, 1691, 1717, 1721, 1725, 1730, 1745, 1760, 1792, 1831, 1834, 1837, 1849, 1856, 1860, 1864, 1872, 1886, 1893, 1897, 1901, 1909, 1921, 1933, 1982, 1995, 2440, 2443, 2448, 2456, 2465, 2469, 2473, 2484, 2495, 2503, 2529, 2533, 2537, 2542, 2557, 2572, 2604, 2643, 2646, 2651, 2661, 2669, 2696, 2705, 2709, 2713, 2724, 2732, 2736, 2740, 2745, 2760, 2778, 2794, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3104, 3112, 3138, 3142, 3146, 3151, 3166, 3181, 3213, 3455, 3458, 3463, 3471, 3480, 3484, 3488, 3499, 3508, 3517, 3521, 3525, 3536, 3547, 3555, 3600, 3616, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3711, 3723, 3747, 3751, 3755, 3758, 3769, 3793, 3819, 4064, 4067, 4072, 4080, 4089, 4093, 4097, 4108, 4117, 4126, 4130, 4134, 4145, 4156, 4164, 4209, 4225, 4269, 4272, 4292, 4319, 4324, 4331, 4340, 4361, 4584, 4589, 4604, 4611, 4621, 4635, 4655, 4683) + +'(6 * x**2 + 4 * y**2 + 5 * x + 3 * y + 4 * x * y) % 8' (0, 410, 512, 1019, 1035, 1112, 1121, 1628, 1730, 1831, 1933, 2440, 2533, 3049, 3078) + +'(2 * x**2 + 4 * y**2 + 1 * x + 4 * y + 4 * x * y) % 8' (0, 306, 307, 324, 325, 326, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 4267, 4281, 4313, 4314, 4338, 4356, 4584, 4597, 4655, 4672) + +'(2 * x**2 + 1 * y**2 + 2 * x + 1 * y + 0 * x * y) % 3' (0, 39, 3252, 3254, 3255, 3277, 3278, 3281, 3284, 3285, 3314, 3315, 3318, 3321, 3322, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3723, 3861, 3866, 3869, 3877, 3880, 3890, 3901, 3905, 3914, 3924, 3927, 3934, 3942, 4269, 4292, 4340, 4589, 4621, 4635) + +'(6 * x**2 + 0 * y**2 + 2 * x + 7 * y + 4 * x * y) % 8' (0, 7, 15, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 1019, 1024, 1034, 1044, 1054, 1074, 1084, 1095, 1111, 1121, 1132, 1149, 1166, 1183, 1201, 1628, 1633, 1646, 1656, 1667, 1680, 1690, 1700, 1720, 1730, 1741, 1762, 1779, 1796, 1815, 1831, 1839, 1846, 1859, 1874, 1883, 1896, 1911, 1920, 1933, 1948, 1957, 1978, 1999, 2023, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4274, 4306, 4319, 4361, 4586, 4605, 4614, 4644, 4665, 4688) + +'(3 * x**2 + 3 * y**2 + 2 * x + 3 * y + 6 * x * y) % 7' (0, 2237, 2239) + +'(2 * x**2 + 5 * y**2 + 0 * x + 2 * y + 2 * x * y) % 6' (0, 150, 152, 158, 1628, 1630, 1633, 1636, 1639, 3252, 3257) + +'(3 * x**2 + 0 * y**2 + 6 * x + 7 * y + 6 * x * y) % 9' (0, 46, 74, 358, 363, 374, 384, 394, 613, 618, 705, 715, 726, 816, 831, 881, 918, 963, 1425, 1453, 1477, 1527, 1593, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4319, 4361, 4586, 4605, 4614, 4644, 4665, 4688) + +'(1 * x**2 + 7 * y**2 + 1 * x + 6 * y + 2 * x * y) % 8' (0, 22, 150, 152, 202, 207, 306, 308, 325, 1425, 1427, 1430, 1433, 1436, 1628, 1630, 1633, 1636, 1639, 1831, 1833, 1846, 1849, 1852, 2237, 2242, 2252, 2262, 2272, 2440, 2445, 2455, 2465, 2475, 3049, 3252, 3254, 3257, 3260, 3263, 3315, 3318, 3321, 3455, 3457, 3460, 3463, 3466, 3521, 4064, 4117, 4130, 4268, 4315) + +'(2 * x**2 + 2 * y**2 + 2 * x + 0 * y + 2 * x * y) % 3' (0, 150, 155, 158, 1831, 1836, 1846, 1856, 1866, 4064, 4066) + +'(7 * x**2 + 4 * y**2 + 9 * x + 5 * y + 0 * x * y) % 12' (0, 22, 1628, 2440, 2643, 2651, 2846, 2871, 3049, 3057, 3067, 3074, 3455, 3521, 3658, 3861, 3869, 3914, 3927, 3942, 4064, 4072, 4117, 4130, 4145) + +'(0 * x**2 + 0 * y**2 + 1 * x + 2 * y + 0 * x * y) % 7' (0, 46, 55, 74, 1222, 1251, 1312, 1314, 1321, 4275, 4597, 4672) + +'(2 * x**2 + 0 * y**2 + 2 * x + 1 * y + 1 * x * y) % 6' (0, 22, 30, 39, 1628, 1636, 1717, 1730, 1745, 2237, 2245, 2292, 2299, 2326, 2339, 2354, 2440, 2465, 2495, 2529, 2542, 2604, 2643, 2651, 2661, 2705, 2732, 2745, 2760, 2794, 3049, 3057, 3138, 3151, 3166, 3252, 3255, 3277, 3281, 3285, 3305, 3455, 3463, 3471, 3484, 3499, 3508, 3521, 3536, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3711, 3758, 3819, 4064, 4067, 4089, 4093, 4097, 4117, 4130, 4164, 4225, 4269, 4340, 4589, 4621) + +'(0 * x**2 + 0 * y**2 + 5 * x + 6 * y + 2 * x * y) % 8' (0, 22, 25, 150, 158, 159, 202, 208, 211, 306, 324, 325, 1425, 1426, 1450, 1451, 1452, 1453, 1454, 1455, 1628, 1631, 1653, 1654, 1656, 1657, 1661, 1831, 1837, 1849, 1850, 1859, 1860, 1872, 2237, 2239, 2253, 2256, 2259, 2263, 2266, 2269, 2440, 2448, 2456, 2459, 2466, 2469, 2484, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3253, 3314, 3315, 3316, 3317, 3318, 3319, 3455, 3458, 3517, 3518, 3520, 3521, 3525, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4313, 4584, 4597, 4655, 4672) + +'(0 * x**2 + 0 * y**2 + 3 * x + 1 * y + 2 * x * y) % 4' (0, 7, 15, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 1019, 1025, 1035, 1044, 1074, 1085, 1097, 1112, 1121, 1151, 1183, 1628, 1634, 1646, 1657, 1669, 1681, 1690, 1721, 1730, 1763, 1779, 1831, 1839, 1847, 1860, 1875, 1884, 1897, 1912, 1920, 1933, 1948, 2440, 2446, 2458, 2469, 2481, 2493, 2502, 2533, 2542, 2575, 2591, 2643, 2649, 2659, 2668, 2698, 2709, 2721, 2736, 2745, 2775, 2807, 3049, 3055, 3067, 3078, 3090, 3102, 3111, 3142, 3151, 3184, 3200, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3861, 3867, 3877, 3886, 3914, 3923, 3950, 3961, 3972, 4006, 4022, 4274, 4306, 4319, 4361, 4587, 4604, 4646, 4683) + +'(7 * x**2 + 5 * y**2 + 3 * x + 2 * y + 0 * x * y) % 8' (0, 2, 7, 22, 46, 48, 98, 100, 150, 202, 204, 254, 262, 306, 325, 358, 374, 410, 412, 415, 418, 421, 613, 615, 618, 621, 624, 816, 818, 821, 824, 827, 1019, 1021, 1024, 1027, 1030, 1222, 1224, 1227, 1230, 1233, 1425, 1427, 1628, 1630, 1831, 1836, 1849, 2034, 2059, 2237, 2239, 2242, 2245, 2248, 2440, 2442, 2445, 2448, 2451, 2643, 2645, 2671, 2846, 2851, 2874, 3049, 3057, 3067, 3074, 3252, 3254, 3315, 3318, 3321, 3455, 3457, 3518, 3521, 3524, 3658, 3714, 3721, 3861, 3863, 3914, 3917, 3920, 4064, 4072, 4117, 4130, 4145, 4379, 4398, 4469) + +'(6 * x**2 + 6 * y**2 + 2 * x + 5 * y + 6 * x * y) % 8' (0, 7, 98, 103, 150, 165, 358, 363, 374, 410, 428, 472, 512, 561, 1019, 1024, 1034, 1044, 1054, 1222, 1227, 1237, 1247, 1257, 1628, 1633, 1680, 1690, 1700, 1831, 1846, 1883, 1920, 1957, 2034, 2049, 2086, 2123, 2160, 3252, 3270, 3318, 3352, 3861, 3866, 3876, 3886, 3896, 3914, 3961, 4022, 4064, 4069, 4079, 4089, 4099, 4117, 4154, 4191, 4586, 4665) + +'(4 * x**2 + 2 * y**2 + 3 * x + 4 * y + 6 * x * y) % 8' (0, 150, 151, 202, 204, 1425, 1426, 1427, 1428, 1429, 2237, 2239, 2242, 2245, 2248, 3049, 3055, 3067, 3078, 3090, 3455, 3456, 3457, 3458, 3459, 3517, 3521, 3525, 4267, 4281) + +'(6 * x**2 + 3 * y**2 + 2 * x + 5 * y + 0 * x * y) % 9' (0, 7, 22, 410, 613, 668, 706, 1019, 1222, 1315, 1425, 1628, 1683, 1831, 1847, 2034, 2237, 2330, 2440, 2846, 2862, 2939, 3049, 3252, 3318, 3455, 3521, 3861, 3914, 4064, 4117, 4379) + +'(0 * x**2 + 2 * y**2 + 0 * x + 5 * y + 0 * x * y) % 8' (0, 38, 44, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 462, 465, 468, 472, 475, 478, 482, 486, 490, 494, 499, 502, 505, 509, 512, 515, 519, 523, 527, 531, 536, 540, 544, 548, 553, 557, 561, 565, 570, 574, 578, 582, 587, 592, 597, 602, 607, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4268, 4271, 4274, 4277, 4283, 4286, 4290, 4295, 4299, 4303, 4306, 4309, 4315, 4319, 4322, 4326, 4329, 4333, 4339, 4347, 4350, 4353, 4359, 4361, 4366, 4373, 4377, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(1 * x**2 + 1 * y**2 + 3 * x + 2 * y + 2 * x * y) % 8' (0, 2, 7, 9, 22, 46, 48, 51, 54, 57, 98, 100, 103, 106, 109, 150, 152, 202, 207, 254, 306, 308, 325, 358, 374, 377, 410, 412, 415, 418, 421, 425, 428, 431, 435, 438, 441, 445, 449, 453, 457, 613, 615, 618, 621, 624, 628, 631, 634, 638, 641, 644, 648, 652, 656, 660, 816, 818, 821, 824, 827, 831, 834, 837, 841, 844, 847, 851, 855, 859, 863, 1019, 1021, 1024, 1027, 1030, 1034, 1037, 1040, 1044, 1047, 1050, 1054, 1058, 1062, 1066, 1222, 1224, 1227, 1230, 1233, 1237, 1240, 1243, 1247, 1250, 1253, 1257, 1261, 1265, 1269, 1425, 1427, 1430, 1433, 1436, 1628, 1630, 1633, 1636, 1639, 1831, 1833, 1846, 1849, 1852, 2034, 2036, 2237, 2242, 2252, 2262, 2272, 2440, 2445, 2455, 2465, 2475, 2643, 2648, 2846, 2861, 3049, 3252, 3254, 3257, 3260, 3263, 3315, 3318, 3321, 3455, 3457, 3460, 3463, 3466, 3521, 3658, 3660, 3714, 3721, 3724, 3727, 3861, 3866, 3914, 3924, 3927, 3934, 4064, 4117, 4120, 4130, 4268, 4315, 4379, 4431, 4469, 4472, 4598) + +'(7 * x**2 + 1 * y**2 + 1 * x + 0 * y + 2 * x * y) % 8' (0, 22, 1628, 1630, 1653, 1656, 1659, 1831, 1836, 1849, 1859, 1870, 2440, 2442, 2445, 2448, 2451, 3049, 3067, 3455, 3457, 3518, 3521, 3524, 4064, 4117, 4130) + +'(2 * x**2 + 0 * y**2 + 2 * x + 2 * y + 2 * x * y) % 4' (0, 39, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 3300, 3301, 3302, 3303, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 4267, 4268, 4269, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(3 * x**2 + 0 * y**2 + 0 * x + 0 * y + 2 * x * y) % 5' (0, 39, 358, 359, 366, 367, 368, 3658, 3659, 3660, 3661, 3662, 3664, 3676, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3699, 4064, 4065, 4066, 4067, 4068, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4269, 4340, 4582, 4589, 4590, 4591, 4596, 4607, 4608, 4621, 4622) + +'(0 * x**2 + 3 * y**2 + 2 * x + 1 * y + 2 * x * y) % 4' (0, 358, 360, 363, 366, 369, 3252, 3277, 3305, 3352, 3413, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(0 * x**2 + 0 * y**2 + 2 * x + 2 * y + 0 * x * y) % 3' (0, 2, 7, 13, 15, 22, 25, 28, 42, 46, 52, 54, 65, 71, 98, 101, 104, 114, 126, 150, 159, 169, 176, 178, 202, 211, 218, 220, 227, 254, 257, 262, 272, 280, 306, 312, 314, 325, 331, 358, 361, 364, 374, 386, 410, 416, 418, 429, 435, 463, 465, 476, 488, 491, 499, 510, 512, 521, 527, 571, 574, 613, 616, 619, 629, 641, 668, 675, 679, 683, 691, 702, 706, 710, 713, 724, 745, 758, 816, 825, 835, 842, 844, 872, 879, 881, 906, 908, 915, 1019, 1028, 1035, 1037, 1044, 1072, 1074, 1081, 1112, 1119, 1121, 1151, 1154, 1164, 1170, 1180, 1183, 1222, 1225, 1230, 1240, 1248, 1275, 1284, 1288, 1292, 1303, 1311, 1315, 1319, 1324, 1339, 1357, 1373, 1425, 1431, 1433, 1441, 1443, 1454, 1466, 1469, 1478, 1480, 1491, 1503, 1506, 1518, 1524, 1557, 1560, 1628, 1631, 1634, 1646, 1653, 1657, 1661, 1669, 1683, 1690, 1694, 1698, 1706, 1718, 1730, 1779, 1792, 1831, 1837, 1839, 1847, 1849, 1860, 1872, 1875, 1887, 1893, 1920, 1931, 1933, 1942, 1948, 1976, 1982, 2034, 2043, 2050, 2052, 2059, 2087, 2089, 2096, 2127, 2134, 2136, 2166, 2169, 2179, 2185, 2195, 2198, 2237, 2240, 2243, 2255, 2262, 2266, 2270, 2278, 2290, 2302, 2326, 2330, 2334, 2337, 2348, 2372, 2398, 2440, 2446, 2448, 2456, 2458, 2469, 2481, 2484, 2493, 2495, 2506, 2518, 2521, 2533, 2539, 2572, 2575, 2643, 2652, 2662, 2669, 2671, 2699, 2706, 2708, 2733, 2735, 2742, 2846, 2849, 2852, 2862, 2874, 2901, 2908, 2912, 2916, 2924, 2935, 2939, 2943, 2946, 2957, 2978, 2991, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3102, 3111, 3115, 3119, 3130, 3141, 3149, 3194, 3210, 3252, 3258, 3260, 3271, 3277, 3305, 3307, 3318, 3330, 3333, 3341, 3352, 3354, 3363, 3369, 3413, 3416, 3455, 3458, 3461, 3471, 3483, 3510, 3517, 3521, 3525, 3533, 3544, 3548, 3552, 3555, 3566, 3587, 3600, 3658, 3667, 3677, 3684, 3686, 3714, 3721, 3723, 3748, 3750, 3757, 3861, 3870, 3877, 3879, 3886, 3914, 3916, 3923, 3954, 3961, 3963, 3993, 3996, 4006, 4012, 4022, 4025, 4064, 4067, 4072, 4082, 4090, 4117, 4126, 4130, 4134, 4145, 4153, 4157, 4161, 4166, 4181, 4199, 4215, 4272, 4274, 4282, 4304, 4306, 4331, 4342, 4357, 4379, 4382, 4385, 4397, 4404, 4408, 4412, 4420, 4434, 4441, 4445, 4449, 4457, 4469, 4481, 4530, 4543, 4584, 4587, 4607, 4634, 4639, 4646, 4655, 4676) + +'(4 * x**2 + 3 * y**2 + 7 * x + 0 * y + 6 * x * y) % 9' (0, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 4267, 4281, 4313, 4314, 4338, 4356) + +'(4 * x**2 + 6 * y**2 + 5 * x + 5 * y + 2 * x * y) % 8' (0, 1628, 1657, 2440, 2469, 3049, 3078, 4597, 4672) + +'(0 * x**2 + 0 * y**2 + 2 * x + 1 * y + 0 * x * y) % 5' (0, 202, 208, 218, 230, 613, 619, 632, 669, 703, 715, 816, 825, 832, 872, 879, 918, 1425, 1434, 1444, 1451, 1478, 1527, 3049, 3055, 3067, 3078, 3090, 3111, 3139, 3151, 3200, 4275, 4319, 4361, 4587, 4607, 4646) + +'(6 * x**2 + 4 * y**2 + 1 * x + 0 * y + 6 * x * y) % 8' (0, 2, 7, 22, 46, 47, 98, 101, 150, 202, 254, 260, 306, 324, 325, 358, 374, 410, 411, 412, 413, 414, 613, 614, 615, 616, 617, 816, 817, 824, 825, 826, 1019, 1021, 1025, 1028, 1031, 1222, 1225, 1228, 1230, 1425, 1426, 1628, 1631, 1831, 1837, 2034, 2052, 2053, 2060, 2237, 2239, 2440, 2448, 2643, 2659, 2846, 2855, 2862, 2872, 3049, 3055, 3067, 3078, 3090, 3252, 3253, 3314, 3315, 3316, 3317, 3318, 3319, 3455, 3458, 3517, 3518, 3520, 3521, 3525, 3658, 3713, 3714, 3721, 3861, 3914, 4064, 4070, 4117, 4126, 4313, 4379, 4398, 4432, 4469) + +'(3 * x**2 + 1 * y**2 + 4 * x + 6 * y + 6 * x * y) % 9' (0, 254, 263) + +'(3 * x**2 + 3 * y**2 + 4 * x + 2 * y + 4 * x * y) % 5' (0, 2, 7, 22, 46, 48, 98, 150, 166, 202, 254, 306, 325, 358, 374, 410, 412, 415, 428, 613, 615, 618, 621, 624, 816, 818, 832, 1019, 1222, 1425, 1427, 1481, 1628, 1681, 1831, 1884, 2034, 2087, 2124, 2237, 2242, 2440, 2643, 2698, 2846, 2861, 3049, 3252, 3254, 3318, 3455, 3521, 3658, 3674, 3714, 3721, 3861, 3914, 3917, 4064, 4117, 4379, 4469) + +'(5 * x**2 + 0 * y**2 + 8 * x + 6 * y + 0 * x * y) % 10' (0, 98, 104, 150, 2237, 2243, 2253, 3049, 3055, 3067, 3078, 3090) + +'(0 * x**2 + 0 * y**2 + 2 * x + 0 * y + 2 * x * y) % 4' (0, 39, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 3910, 3911, 3912, 4064, 4065, 4066, 4067, 4068, 4069, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 4110, 4111, 4112, 4113, 4114, 4115, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 4690, 4691, 4692, 4693) + +'(2 * x**2 + 4 * y**2 + 0 * x + 3 * y + 0 * x * y) % 8' (0, 7, 15, 98, 103, 116, 126, 137, 150, 158, 165, 178, 193, 358, 363, 374, 384, 394, 410, 418, 435, 465, 499, 512, 527, 574, 1019, 1024, 1034, 1044, 1054, 1074, 1084, 1095, 1111, 1121, 1132, 1149, 1166, 1183, 1201, 1222, 1227, 1237, 1247, 1257, 1277, 1287, 1298, 1314, 1324, 1335, 1352, 1369, 1386, 1404, 1628, 1633, 1646, 1656, 1667, 1680, 1690, 1700, 1720, 1730, 1741, 1762, 1779, 1796, 1815, 1831, 1839, 1846, 1859, 1874, 1883, 1896, 1911, 1920, 1933, 1948, 1957, 1978, 1999, 2023, 2034, 2042, 2049, 2062, 2077, 2086, 2099, 2114, 2123, 2136, 2151, 2160, 2181, 2202, 2226, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4274, 4306, 4586, 4605, 4614, 4644, 4665, 4688) + +'(5 * x**2 + 1 * y**2 + 1 * x + 6 * y + 6 * x * y) % 8' (0, 22, 150, 152, 158, 202, 204, 207, 306, 308, 1425, 1427, 1430, 1433, 1436, 1450, 1453, 1456, 1628, 1630, 1633, 1636, 1639, 1831, 1833, 1846, 1849, 1852, 2237, 2239, 2242, 2245, 2248, 2252, 2262, 2272, 2440, 2445, 2455, 2465, 2475, 3049, 3067, 3252, 3254, 3257, 3260, 3263, 3455, 3457, 3460, 3463, 3466, 3518, 3521, 3524, 4064, 4117, 4130, 4268, 4315) + +'(4 * x**2 + 0 * y**2 + 7 * x + 7 * y + 6 * x * y) % 8' (0, 613, 706, 1222, 1315, 1628, 1730, 1831, 1860, 2237, 2330, 2846, 2939) + +'(3 * x**2 + 2 * y**2 + 7 * x + 4 * y + 2 * x * y) % 8' (0, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 4064, 4067, 4126, 4130, 4134, 4267, 4281) + +'(2 * x**2 + 2 * y**2 + 1 * x + 1 * y + 2 * x * y) % 4' (0, 39, 42, 410, 413, 426, 428, 472, 476, 480, 510, 512, 555, 561, 613, 621, 631, 638, 666, 679, 694, 706, 713, 748, 774, 1019, 1022, 1025, 1027, 1108, 1112, 1116, 1119, 1121, 1130, 1136, 1222, 1228, 1238, 1247, 1277, 1288, 1300, 1315, 1324, 1354, 1386, 1425, 1428, 1450, 1454, 1458, 1487, 1491, 1495, 1514, 1518, 1522, 1628, 1636, 1644, 1657, 1672, 1681, 1694, 1709, 1717, 1730, 1745, 1831, 1834, 1856, 1860, 1864, 1884, 1886, 1931, 1933, 1992, 1995, 2034, 2037, 2040, 2042, 2123, 2127, 2131, 2134, 2136, 2145, 2151, 2237, 2245, 2253, 2266, 2281, 2292, 2299, 2330, 2337, 2369, 2382, 2440, 2443, 2465, 2469, 2473, 2502, 2506, 2510, 2529, 2533, 2537, 2846, 2854, 2864, 2871, 2899, 2912, 2927, 2939, 2946, 2981, 3007, 3049, 3055, 3067, 3078, 3090, 3104, 3115, 3127, 3138, 3149, 3160, 3658, 3661, 3664, 3666, 3674, 3676, 3683, 3687, 3691, 3699, 3702, 4269, 4282, 4340, 4357, 4379, 4387, 4397, 4404, 4434, 4441, 4468, 4481, 4496, 4530, 4543, 4589, 4621, 4634, 4676) + +'(0 * x**2 + 3 * y**2 + 4 * x + 5 * y + 6 * x * y) % 9' (0, 39, 1019, 1027, 1074, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3748, 4269, 4320, 4340, 4589, 4621, 4657) + +'(6 * x**2 + 2 * y**2 + 7 * x + 0 * y + 6 * x * y) % 8' (0, 22, 150, 151, 202, 204, 306, 307, 325, 1425, 1426, 1427, 1428, 1429, 1628, 1629, 1630, 1631, 1632, 1831, 1832, 1836, 1837, 1838, 2237, 2239, 2242, 2245, 2248, 2440, 2442, 2445, 2448, 2451, 3049, 3055, 3067, 3078, 3090, 3252, 3253, 3254, 3255, 3256, 3317, 3318, 3319, 3455, 3456, 3457, 3458, 3459, 3517, 3521, 3525, 4064, 4070, 4117, 4126, 4267, 4281) + +'(6 * x**2 + 7 * y**2 + 1 * x + 2 * y + 0 * x * y) % 8' (0, 22, 1628, 1631, 2440, 2448, 2643, 2651, 3049, 3057, 3078, 3455, 3458, 3517, 3521, 3525, 3658, 3661, 4064, 4067, 4117, 4269, 4340) + +'(2 * x**2 + 4 * y**2 + 5 * x + 4 * y + 0 * x * y) % 8' (0, 37, 41, 306, 307, 308, 309, 310, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 3049, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 3100, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3304, 3305, 3306, 3307, 3308, 3309, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 3340, 3455, 3456, 3457, 3458, 3459, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 3507, 3508, 3509, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 3540, 3541, 3542, 3543, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4582, 4583, 4584, 4585, 4596, 4597, 4598, 4599, 4600, 4601, 4602, 4603, 4628, 4629, 4630, 4631, 4632, 4633, 4653, 4654, 4655, 4656, 4671, 4672, 4673, 4674, 4675) + +'(6 * x**2 + 4 * y**2 + 7 * x + 1 * y + 0 * x * y) % 8' (0, 1019, 1112, 1121, 1831, 1860, 1933, 2440, 2533) + +'(0 * x**2 + 0 * y**2 + 3 * x + 5 * y + 0 * x * y) % 7' (0, 2, 7, 13, 22, 28, 46, 52, 65, 98, 104, 114, 150, 169, 176, 202, 218, 220, 254, 272, 280, 306, 312, 325, 358, 364, 374, 410, 416, 429, 465, 476, 488, 613, 619, 629, 668, 679, 691, 706, 745, 816, 835, 842, 872, 879, 1019, 1035, 1037, 1072, 1074, 1112, 1118, 1151, 1154, 1222, 1240, 1248, 1275, 1315, 1357, 1425, 1431, 1441, 1453, 1480, 1491, 1503, 1518, 1557, 1628, 1634, 1683, 1694, 1706, 1718, 1831, 1847, 1887, 1893, 1931, 1976, 2034, 2050, 2089, 2096, 2127, 2134, 2166, 2179, 2237, 2255, 2290, 2302, 2330, 2372, 2440, 2456, 2458, 2493, 2495, 2533, 2572, 2575, 2643, 2706, 2708, 2733, 2735, 2846, 2855, 2862, 2901, 2908, 2939, 2946, 2978, 2991, 3049, 3065, 3111, 3141, 3149, 3194, 3252, 3258, 3271, 3307, 3318, 3330, 3455, 3461, 3471, 3510, 3521, 3533, 3548, 3587, 3658, 3677, 3684, 3714, 3721, 3861, 3877, 3879, 3914, 3916, 3954, 3960, 3993, 3996, 4064, 4082, 4090, 4117, 4157, 4199, 4272, 4292, 4331, 4379, 4385, 4434, 4445, 4457, 4469, 4587, 4646) + +'(2 * x**2 + 4 * y**2 + 0 * x + 6 * y + 2 * x * y) % 8' (0, 358, 360, 363, 3861, 3863, 3866, 3869, 3872, 4064, 4069, 4079, 4089, 4099, 4282, 4283, 4313, 4357, 4583, 4586, 4630, 4634, 4641, 4665, 4676) + +'(3 * x**2 + 0 * y**2 + 2 * x + 6 * y + 0 * x * y) % 9' (0, 150, 151, 1425, 1426, 1427, 1428, 1429, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 4267, 4281, 4313, 4314, 4338, 4356, 4584, 4655) + +'(5 * x**2 + 2 * y**2 + 3 * x + 0 * y + 4 * x * y) % 8' (0, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4379, 4394, 4431, 4468, 4505) + +'(3 * x**2 + 1 * y**2 + 6 * x + 7 * y + 3 * x * y) % 9' (0, 358, 363, 4064, 4069, 4079, 4089, 4099, 4586, 4605, 4614, 4644, 4665, 4688) + +'(4 * x**2 + 0 * y**2 + 6 * x + 5 * y + 6 * x * y) % 8' (0, 7, 15, 98, 116, 126, 150, 158, 178, 358, 374, 384, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 1019, 1044, 1074, 1084, 1111, 1121, 1183, 1222, 1237, 1277, 1287, 1314, 1324, 1352, 1369, 1628, 1646, 1656, 1690, 1720, 1730, 1779, 1831, 1839, 1859, 1896, 1920, 1933, 1948, 2034, 2042, 2062, 2086, 2099, 2114, 2136, 2202, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3861, 3886, 3914, 3924, 3951, 3961, 4022, 4064, 4079, 4117, 4127, 4154, 4164, 4191, 4208, 4274, 4306, 4319, 4361, 4605) + +'(5 * x**2 + 5 * y**2 + 3 * x + 2 * y + 3 * x * y) % 7' (0, 1222, 1237) + +'(0 * x**2 + 0 * y**2 + 3 * x + 4 * y + 5 * x * y) % 10' (0, 7, 410, 429, 435, 1019, 1044, 1831, 3252, 3277, 3305, 3318, 3861, 3886, 3914, 4590) + +'(6 * x**2 + 3 * y**2 + 3 * x + 7 * y + 0 * x * y) % 9' (0, 2, 7, 22, 27, 46, 74, 98, 103, 150, 165, 202, 207, 217, 227, 237, 254, 259, 269, 279, 289, 306, 325, 332, 358, 363, 374, 384, 394, 410, 438, 475, 502, 509, 613, 618, 705, 715, 726, 816, 831, 881, 918, 963, 1019, 1024, 1034, 1044, 1054, 1222, 1227, 1237, 1247, 1257, 1425, 1453, 1477, 1527, 1593, 1628, 1633, 1680, 1690, 1700, 1831, 1846, 1883, 1920, 1957, 2034, 2049, 2086, 2123, 2160, 2237, 2242, 2252, 2262, 2272, 2289, 2299, 2309, 2326, 2336, 2346, 2363, 2380, 2397, 2414, 2440, 2445, 2455, 2465, 2475, 2492, 2502, 2512, 2529, 2539, 2549, 2566, 2583, 2600, 2617, 2643, 2648, 2658, 2668, 2678, 2695, 2705, 2715, 2732, 2742, 2752, 2769, 2786, 2803, 2820, 2846, 2851, 2861, 2871, 2881, 2898, 2908, 2918, 2935, 2945, 2955, 2972, 2989, 3006, 3023, 3049, 3054, 3064, 3074, 3084, 3101, 3111, 3121, 3138, 3148, 3158, 3175, 3192, 3209, 3226, 3252, 3280, 3318, 3345, 3352, 3455, 3460, 3511, 3521, 3532, 3545, 3555, 3565, 3658, 3673, 3714, 3721, 3751, 3758, 3789, 3802, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4064, 4069, 4079, 4089, 4099, 4117, 4127, 4137, 4154, 4164, 4174, 4191, 4208, 4225, 4242, 4319, 4361, 4379, 4384, 4434, 4444, 4455, 4469, 4479, 4489, 4586, 4605, 4614, 4644, 4665, 4688) + +'(0 * x**2 + 1 * y**2 + 3 * x + 0 * y + 2 * x * y) % 4' (0, 1831, 1834, 1856, 1860, 1864, 2034, 2037, 2050, 2052, 2846, 2852, 2862, 2871, 3049, 3055, 3067, 3078, 3090, 3252, 3255, 3258, 3260, 3305, 3307, 3314, 3318, 3322, 3330, 3333, 3455, 3458, 3461, 3463, 3508, 3510, 3517, 3521, 3525, 3533, 3536, 3658, 3661, 3711, 3713, 4269, 4282, 4340, 4357, 4379, 4395, 4432, 4468) + +'(4 * x**2 + 4 * y**2 + 3 * x + 6 * y + 0 * x * y) % 8' (0, 2, 7, 22, 25, 46, 47, 98, 101, 150, 159, 202, 211, 254, 257, 262, 306, 325, 358, 361, 374, 410, 411, 412, 413, 414, 613, 614, 615, 616, 617, 816, 817, 824, 825, 826, 1019, 1021, 1025, 1028, 1031, 1222, 1225, 1228, 1230, 1425, 1426, 1453, 1454, 1455, 1628, 1631, 1653, 1657, 1661, 1831, 1837, 1849, 1860, 1872, 2034, 2043, 2052, 2059, 2237, 2239, 2263, 2266, 2269, 2440, 2448, 2456, 2469, 2484, 2643, 2652, 2662, 2671, 2846, 2849, 2862, 2874, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3252, 3253, 3317, 3318, 3319, 3455, 3458, 3517, 3521, 3525, 3658, 3667, 3714, 3721, 3861, 3870, 3914, 3923, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4379, 4382, 4434, 4469, 4584, 4655) + +'(0 * x**2 + 0 * y**2 + 8 * x + 4 * y + 0 * x * y) % 9' (0, 22, 25, 1628, 1631, 1653, 1657, 1661, 1831, 1837, 1849, 1860, 1872, 2440, 2448, 2456, 2469, 2484, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3112, 3455, 3458, 3517, 3521, 3525, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4156, 4584, 4635, 4655) + +'(4 * x**2 + 1 * y**2 + 7 * x + 2 * y + 0 * x * y) % 8' (0, 1425, 1428, 1450, 1454, 1458, 1831, 1834, 1856, 1860, 1864, 2237, 2245, 2253, 2266, 2281, 3049, 3078, 3455, 3458, 3517, 3521, 3525, 4269, 4340) + +'(0 * x**2 + 0 * y**2 + 6 * x + 2 * y + 0 * x * y) % 7' (0, 2, 7, 22, 25, 46, 62, 74, 98, 101, 150, 159, 202, 211, 254, 257, 262, 306, 325, 358, 361, 374, 410, 426, 438, 466, 509, 613, 616, 666, 715, 816, 825, 869, 918, 1019, 1028, 1082, 1111, 1222, 1225, 1230, 1285, 1314, 1425, 1454, 1488, 1515, 1527, 1628, 1631, 1653, 1657, 1661, 1691, 1831, 1837, 1849, 1860, 1872, 1921, 2034, 2043, 2052, 2059, 2237, 2266, 2292, 2300, 2336, 2440, 2448, 2456, 2469, 2484, 2503, 2643, 2652, 2662, 2671, 2846, 2849, 2862, 2874, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3252, 3268, 3280, 3318, 3344, 3455, 3458, 3517, 3521, 3525, 3547, 3658, 3667, 3714, 3721, 3861, 3870, 3914, 3923, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4292, 4379, 4382, 4434, 4469, 4584, 4655) + +'(0 * x**2 + 4 * y**2 + 1 * x + 0 * y + 6 * x * y) % 8' (0, 22, 25, 1628, 1631, 1653, 1654, 1656, 1657, 1661, 1831, 1837, 1849, 1850, 1859, 1860, 1872, 2440, 2448, 2456, 2459, 2466, 2469, 2484, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3455, 3458, 3517, 3518, 3520, 3521, 3525, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4313, 4584, 4597, 4655, 4672) + +'(5 * x**2 + 1 * y**2 + 2 * x + 1 * y + 2 * x * y) % 8' (0, 7, 98, 100, 150, 155, 358, 360, 410, 428, 1019, 1021, 1024, 1027, 1030, 1222, 1224, 1227, 1230, 1233, 1628, 1630, 1643, 1646, 1649, 1831, 1836, 1846, 1856, 1866, 2034, 2039, 2049, 2059, 2069, 3252, 3305, 3318, 3861, 3863, 3866, 3869, 3872, 3914, 3924, 3934, 4064, 4066, 4069, 4072, 4075, 4583, 4630) + +'(0 * x**2 + 0 * y**2 + 2 * x + 3 * y + 0 * x * y) % 7' (0, 254, 263, 272, 1019, 1022, 1035, 1074, 1108, 1112, 1116, 1151, 2440, 2443, 2458, 2466, 2493, 2529, 2533, 2537, 2575, 4289, 4368, 4587, 4607, 4646) + +'(6 * x**2 + 6 * y**2 + 4 * x + 6 * y + 6 * x * y) % 8' (0, 358, 363, 366, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4267, 4269, 4281, 4283, 4287, 4340, 4586, 4589, 4598, 4618, 4621, 4665) + +'(1 * x**2 + 1 * y**2 + 3 * x + 0 * y + 2 * x * y) % 4' (0, 22, 24, 150, 152, 155, 158, 161, 202, 204, 207, 210, 213, 306, 308, 322, 325, 328, 1425, 1427, 1430, 1433, 1436, 1440, 1443, 1446, 1450, 1453, 1456, 1460, 1464, 1468, 1472, 1628, 1630, 1633, 1636, 1639, 1643, 1646, 1649, 1653, 1656, 1659, 1663, 1667, 1671, 1675, 1831, 1833, 1836, 1839, 1842, 1846, 1849, 1852, 1856, 1859, 1862, 1866, 1870, 1874, 1878, 2237, 2239, 2242, 2245, 2248, 2252, 2255, 2258, 2262, 2265, 2268, 2272, 2276, 2280, 2284, 2440, 2442, 2445, 2448, 2451, 2455, 2458, 2461, 2465, 2468, 2471, 2475, 2479, 2483, 2487, 3049, 3051, 3054, 3064, 3067, 3070, 3077, 3088, 3252, 3254, 3257, 3260, 3263, 3305, 3308, 3311, 3315, 3318, 3321, 3325, 3329, 3333, 3337, 3455, 3457, 3460, 3463, 3466, 3508, 3511, 3514, 3518, 3521, 3524, 3528, 3532, 3536, 3540, 4064, 4066, 4069, 4117, 4127, 4130, 4133, 4137, 4268, 4283, 4286, 4315, 4339, 4359, 4583, 4630) + +'(1 * x**2 + 7 * y**2 + 2 * x + 5 * y + 4 * x * y) % 8' (0, 98, 150, 410, 418, 428, 435, 1222, 1227, 2034, 2049, 3861, 3914) + +'(2 * x**2 + 4 * y**2 + 2 * x + 5 * y + 6 * x * y) % 8' (0, 7, 15, 98, 103, 116, 150, 158, 165, 358, 363, 384, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 1019, 1024, 1034, 1044, 1054, 1074, 1121, 1183, 1222, 1227, 1237, 1247, 1257, 1277, 1314, 1352, 1628, 1633, 1646, 1680, 1690, 1700, 1730, 1779, 1831, 1839, 1846, 1883, 1920, 1933, 1948, 1957, 2034, 2042, 2049, 2086, 2099, 2114, 2123, 2160, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3861, 3866, 3876, 3886, 3896, 3914, 3961, 4022, 4064, 4069, 4079, 4089, 4099, 4127, 4164, 4208, 4274, 4306, 4319, 4361, 4586, 4665) + +'(3 * x**2 + 6 * y**2 + 4 * x + 1 * y + 4 * x * y) % 8' (0, 7, 410, 435, 512, 1019, 1044, 1222, 1247, 1831, 1920, 2034, 2123, 3252, 3277, 3318, 3861, 3886, 3914, 3961, 4022, 4064, 4089, 4117, 4164, 4225) + +'(0 * x**2 + 6 * y**2 + 7 * x + 3 * y + 3 * x * y) % 9' (0, 2, 7, 8, 22, 46, 47, 48, 49, 50, 98, 99, 100, 101, 102, 150, 151, 202, 204, 254, 263, 306, 307, 324, 325, 326, 358, 374, 376, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1425, 1426, 1427, 1428, 1429, 1628, 1629, 1630, 1631, 1632, 1831, 1832, 1836, 1837, 1838, 2034, 2035, 2062, 2063, 2064, 2237, 2239, 2242, 2245, 2248, 2440, 2442, 2445, 2448, 2451, 2643, 2645, 2669, 2672, 2675, 2846, 2851, 2865, 2875, 2886, 3049, 3058, 3068, 3075, 3077, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3658, 3659, 3713, 3714, 3715, 3720, 3721, 3722, 3861, 3863, 3914, 3917, 3920, 3923, 3926, 3929, 4064, 4073, 4117, 4119, 4126, 4267, 4281, 4313, 4314, 4338, 4356, 4379, 4394, 4432, 4434, 4469, 4471, 4506, 4509, 4597, 4672) + +'(3 * x**2 + 3 * y**2 + 6 * x + 2 * y + 3 * x * y) % 9' (0, 150, 165, 2034, 2049, 2086, 2123, 2160, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4586, 4605, 4614, 4644, 4665, 4688) + +'(0 * x**2 + 0 * y**2 + 4 * x + 6 * y + 0 * x * y) % 8' (0, 4268, 4272, 4275, 4278, 4283, 4286, 4289, 4292, 4294, 4315, 4320, 4323, 4331, 4335, 4339, 4342, 4344, 4359, 4368, 4370, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(4 * x**2 + 2 * y**2 + 4 * x + 1 * y + 6 * x * y) % 8' (0, 2, 7, 22, 46, 64, 98, 150, 202, 227, 254, 269, 306, 325, 358, 374, 384, 410, 428, 472, 512, 561, 613, 668, 678, 712, 816, 871, 1019, 1044, 1222, 1237, 1425, 1443, 1490, 1517, 1628, 1690, 1831, 1920, 2034, 2086, 2237, 2262, 2299, 2326, 2440, 2455, 2502, 2539, 2583, 2643, 2668, 2695, 2742, 2803, 2846, 2861, 2898, 2935, 2972, 3049, 3064, 3101, 3138, 3175, 3252, 3270, 3318, 3352, 3455, 3521, 3658, 3714, 3721, 3751, 3861, 3886, 3914, 3924, 3951, 3961, 4022, 4064, 4079, 4117, 4127, 4154, 4164, 4191, 4208, 4379, 4398, 4469, 4479, 4605) + +'(2 * x**2 + 1 * y**2 + 3 * x + 4 * y + 0 * x * y) % 8' (0, 7, 410, 413, 416, 418, 613, 616, 619, 621, 816, 819, 1019, 1027, 1831, 1860, 3252, 3255, 3314, 3318, 3322, 3455, 3521, 3658, 3861, 3914) + +'(0 * x**2 + 0 * y**2 + 1 * x + 1 * y + 0 * x * y) % 3' (0, 42, 46, 55, 65, 72, 74, 98, 107, 117, 124, 126, 150, 159, 169, 176, 178, 202, 211, 221, 228, 230, 254, 263, 273, 280, 282, 4275, 4282, 4289, 4319, 4357, 4361, 4363, 4368, 4379, 4388, 4395, 4397, 4404, 4432, 4434, 4441, 4472, 4479, 4481, 4511, 4514, 4524, 4530, 4540, 4543, 4590, 4597, 4604, 4634, 4672, 4676, 4678, 4683) + +'(0 * x**2 + 0 * y**2 + 2 * x + 3 * y + 4 * x * y) % 8' (0, 2, 7, 15, 22, 46, 54, 71, 98, 126, 150, 178, 202, 227, 254, 269, 306, 314, 325, 358, 374, 410, 418, 435, 465, 499, 512, 527, 574, 613, 641, 668, 702, 816, 844, 908, 915, 1019, 1044, 1074, 1121, 1183, 1222, 1237, 1287, 1324, 1369, 1425, 1433, 1443, 1524, 1628, 1646, 1690, 1730, 1779, 1831, 1839, 1920, 1933, 1948, 2034, 2062, 2086, 2136, 2202, 2237, 2262, 2299, 2326, 2440, 2455, 2502, 2539, 2583, 2643, 2668, 2695, 2742, 2803, 2846, 2861, 2898, 2935, 2972, 3049, 3064, 3101, 3138, 3175, 3252, 3260, 3277, 3305, 3318, 3333, 3352, 3413, 3455, 3483, 3521, 3555, 3658, 3686, 3714, 3721, 3861, 3886, 3914, 3961, 4022, 4064, 4079, 4117, 4154, 4191, 4274, 4306, 4379, 4408, 4434, 4469) + +'(6 * x**2 + 6 * y**2 + 1 * x + 0 * y + 3 * x * y) % 9' (0, 254, 263, 306, 307, 324, 325, 326, 2034, 2035, 2062, 2063, 2064, 2643, 2645, 2669, 2672, 2675, 2846, 2851, 2865, 2875, 2886, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 4267, 4281, 4313, 4314, 4338, 4356, 4597, 4672) + +'(0 * x**2 + 2 * y**2 + 0 * x + 6 * y + 6 * x * y) % 8' (0, 4267, 4268, 4272, 4274, 4275, 4276, 4278, 4281, 4282, 4285, 4290, 4292, 4293, 4295, 4300, 4304, 4306, 4307, 4310, 4315, 4320, 4323, 4331, 4335, 4357, 4598, 4605, 4634, 4676) + +'(4 * x**2 + 6 * y**2 + 7 * x + 4 * y + 4 * x * y) % 8' (0, 22, 25, 150, 151, 158, 159, 160, 202, 204, 208, 211, 214, 306, 307, 324, 325, 326, 1425, 1426, 1427, 1428, 1429, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1628, 1629, 1630, 1631, 1632, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1831, 1832, 1836, 1837, 1838, 1849, 1850, 1851, 1859, 1860, 1861, 1870, 1871, 1872, 1873, 2237, 2239, 2242, 2245, 2248, 2253, 2256, 2259, 2263, 2266, 2269, 2273, 2277, 2281, 2285, 2440, 2442, 2445, 2448, 2451, 2456, 2459, 2462, 2466, 2469, 2472, 2476, 2480, 2484, 2488, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3317, 3318, 3319, 3320, 3321, 3322, 3323, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4267, 4281, 4313, 4314, 4338, 4356, 4584, 4655) + +'(4 * x**2 + 2 * y**2 + 2 * x + 0 * y + 2 * x * y) % 8' (0, 306, 307, 308, 3252, 3253, 3254, 3255, 3256, 3455, 3457, 3460, 3463, 3466, 4267, 4268, 4281, 4282, 4285, 4315, 4357, 4598, 4605, 4634, 4676) + +'(4 * x**2 + 2 * y**2 + 3 * x + 6 * y + 0 * x * y) % 8' (0, 22, 25, 1628, 1629, 1630, 1631, 1632, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 1660, 1661, 1662, 1831, 1832, 1836, 1837, 1838, 1849, 1850, 1851, 1859, 1860, 1861, 1870, 1871, 1872, 1873, 2440, 2442, 2445, 2448, 2451, 2456, 2459, 2462, 2466, 2469, 2472, 2476, 2480, 2484, 2488, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4267, 4281, 4313, 4314, 4338, 4356, 4584, 4597, 4655, 4672) + +'(6 * x**2 + 2 * y**2 + 5 * x + 1 * y + 4 * x * y) % 8' (0, 42, 410, 510, 512, 613, 706, 713, 1019, 1112, 1119, 1222, 1288, 1315, 1425, 1628, 1831, 2034, 2237, 2330, 2337, 2440, 2506, 2533, 2846, 2912, 2939, 3049, 3078, 3115, 4282, 4357, 4379, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4634, 4676) + +'(6 * x**2 + 2 * y**2 + 5 * x + 5 * y + 2 * x * y) % 8' (0, 613, 706, 1222, 1315, 1425, 1518, 2034, 2127, 2237, 2330, 2846, 2939) + +'(0 * x**2 + 4 * y**2 + 5 * x + 5 * y + 4 * x * y) % 8' (0, 613, 706, 715, 816, 882, 918, 1222, 1315, 1324, 1425, 1454, 1527, 2034, 2100, 2136, 2237, 2266, 2303, 2330, 2339, 2846, 2939, 2948, 4319, 4361, 4604, 4683) + +'(0 * x**2 + 2 * y**2 + 3 * x + 7 * y + 0 * x * y) % 8' (0, 1628, 1657, 1683, 1730, 1831, 1860, 2440, 2469, 3049, 3078) + +'(0 * x**2 + 0 * y**2 + 3 * x + 1 * y + 0 * x * y) % 7' (0, 202, 230, 1222, 1238, 1278, 1324, 2034, 2043, 2087, 2136, 4275, 4319, 4361, 4635) + +'(1 * x**2 + 4 * y**2 + 2 * x + 5 * y + 0 * x * y) % 8' (0, 22, 30, 1628, 1636, 1717, 1730, 1745, 2237, 2245, 2255, 2262, 2292, 2299, 2326, 2339, 2354, 2388, 2401, 2440, 2448, 2458, 2465, 2495, 2502, 2529, 2542, 2557, 2591, 2604, 2643, 2651, 2661, 2668, 2698, 2705, 2732, 2745, 2760, 2794, 2807, 2846, 2854, 2864, 2871, 2901, 2908, 2935, 2948, 2963, 2997, 3010, 3049, 3057, 3067, 3074, 3104, 3111, 3138, 3151, 3166, 3200, 3213, 3455, 3463, 3508, 3521, 3536, 3658, 3683, 3711, 3758, 3819, 4064, 4089, 4117, 4164, 4225, 4319, 4361, 4589, 4621) + +'(2 * x**2 + 4 * y**2 + 1 * x + 2 * y + 4 * x * y) % 8' (0, 22, 150, 158, 202, 208, 306, 325, 1425, 1426, 1450, 1451, 1452, 1628, 1631, 1654, 1656, 1831, 1837, 1850, 1859, 2237, 2239, 2253, 2256, 2259, 2440, 2448, 2459, 2466, 3049, 3078, 3252, 3253, 3317, 3318, 3319, 3455, 3458, 3517, 3521, 3525, 4064, 4117, 4119, 4126, 4597, 4672) + +'(2 * x**2 + 0 * y**2 + 0 * x + 0 * y + 2 * x * y) % 8' (0, 3861, 3863, 3866, 3869, 3872, 4268, 4269, 4313, 4315, 4317, 4340, 4582, 4584, 4586, 4589, 4590, 4591, 4594, 4596, 4598, 4602, 4604, 4607, 4608, 4611, 4613, 4618, 4621, 4622, 4626, 4655, 4657, 4660, 4665, 4669, 4683) + +'(8 * x**2 + 5 * y**2 + 4 * x + 0 * y + 2 * x * y) % 9' (0, 254, 259, 306, 2034, 2643, 2846, 2851, 2861, 2871, 2881, 3252, 3305, 3455, 3460) + +'(2 * x**2 + 2 * y**2 + 3 * x + 1 * y + 6 * x * y) % 8' (0, 22, 25, 1019, 1081, 1112, 1628, 1631, 1653, 1657, 1661, 1683, 1831, 1837, 1849, 1860, 1872, 2440, 2448, 2456, 2469, 2484, 2533, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3455, 3458, 3517, 3521, 3525, 3555, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4584, 4655) + +'(6 * x**2 + 6 * y**2 + 7 * x + 2 * y + 2 * x * y) % 8' (0, 306, 307, 324, 3049, 3055, 3067, 3078, 3090, 3252, 3253, 3254, 3255, 3256, 3314, 3315, 3316, 3455, 3456, 3457, 3458, 3459, 3517, 3521, 3525, 4267, 4281) + +'(5 * x**2 + 5 * y**2 + 4 * x + 3 * y + 2 * x * y) % 8' (0, 98, 103, 150, 158, 410, 428, 1222, 1227, 1237, 1247, 1257, 2034, 2042, 2049, 2062, 2077, 3861, 3866, 3914, 3924, 3934) + +'(2 * x**2 + 4 * y**2 + 3 * x + 3 * y + 4 * x * y) % 8' (0, 410, 512, 1019, 1121, 1628, 1730, 1831, 1847, 1860, 1933) + +'(6 * x**2 + 0 * y**2 + 2 * x + 0 * y + 6 * x * y) % 8' (0, 4282, 4283, 4313, 4357, 4583, 4584, 4586, 4587, 4590, 4593, 4594, 4628, 4630, 4632, 4634, 4635, 4638, 4639, 4641, 4645, 4646, 4650, 4651, 4655, 4657, 4660, 4665, 4669, 4676) + +'(1 * x**2 + 6 * y**2 + 7 * x + 4 * y + 0 * x * y) % 8' (0, 3658, 3659, 3660, 3661, 3662, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 3861, 3863, 3866, 3869, 3872, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4597, 4672) + +'(4 * x**2 + 0 * y**2 + 2 * x + 4 * y + 0 * x * y) % 8' (0, 4267, 4268, 4269, 4270, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4313, 4314, 4315, 4316, 4317, 4318, 4338, 4339, 4340, 4341, 4356, 4357, 4358, 4359, 4360, 4583, 4587, 4590, 4593, 4598, 4601, 4604, 4607, 4609, 4630, 4635, 4638, 4646, 4650, 4654, 4657, 4659, 4674, 4683, 4685) + +'(6 * x**2 + 2 * y**2 + 2 * x + 6 * y + 6 * x * y) % 8' (0, 42, 4267, 4268, 4281, 4282, 4285, 4315, 4357, 4379, 4381, 4384, 4394, 4397, 4400, 4404, 4414, 4431, 4434, 4437, 4441, 4451, 4481, 4530, 4543, 4583, 4586, 4630, 4634, 4641, 4665, 4676) + +'(0 * x**2 + 0 * y**2 + 0 * x + 4 * y + 0 * x * y) % 7' (0, 38, 44, 46, 48, 51, 54, 57, 61, 64, 67, 71, 74, 77, 81, 85, 89, 93, 358, 360, 363, 366, 369, 374, 377, 380, 384, 387, 390, 394, 398, 402, 406, 613, 615, 618, 621, 624, 628, 631, 634, 638, 641, 644, 648, 652, 656, 660, 665, 668, 671, 675, 678, 681, 685, 689, 693, 697, 702, 705, 708, 712, 715, 718, 722, 726, 730, 734, 739, 743, 747, 751, 756, 760, 764, 768, 773, 777, 781, 785, 790, 795, 800, 805, 810, 816, 818, 821, 824, 827, 831, 834, 837, 841, 844, 847, 851, 855, 859, 863, 868, 871, 874, 878, 881, 884, 888, 892, 896, 900, 905, 908, 911, 915, 918, 921, 925, 929, 933, 937, 942, 946, 950, 954, 959, 963, 967, 971, 976, 980, 984, 988, 993, 998, 1003, 1008, 1013, 1425, 1427, 1430, 1433, 1436, 1440, 1443, 1446, 1450, 1453, 1456, 1460, 1464, 1468, 1472, 1477, 1480, 1483, 1487, 1490, 1493, 1497, 1501, 1505, 1509, 1514, 1517, 1520, 1524, 1527, 1530, 1534, 1538, 1542, 1546, 1551, 1555, 1559, 1563, 1568, 1572, 1576, 1580, 1585, 1589, 1593, 1597, 1602, 1607, 1612, 1617, 1622, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 3914, 3917, 3920, 3924, 3927, 3930, 3934, 3938, 3942, 3946, 3951, 3954, 3957, 3961, 3964, 3967, 3971, 3975, 3979, 3983, 3988, 3992, 3996, 4000, 4005, 4009, 4013, 4017, 4022, 4026, 4030, 4034, 4039, 4044, 4049, 4054, 4059, 4064, 4066, 4069, 4072, 4075, 4079, 4082, 4085, 4089, 4092, 4095, 4099, 4103, 4107, 4111, 4117, 4120, 4123, 4127, 4130, 4133, 4137, 4141, 4145, 4149, 4154, 4157, 4160, 4164, 4167, 4170, 4174, 4178, 4182, 4186, 4191, 4195, 4199, 4203, 4208, 4212, 4216, 4220, 4225, 4229, 4233, 4237, 4242, 4247, 4252, 4257, 4262, 4268, 4271, 4274, 4277, 4283, 4286, 4290, 4295, 4299, 4303, 4306, 4309, 4315, 4319, 4322, 4326, 4329, 4333, 4339, 4347, 4350, 4353, 4359, 4361, 4366, 4373, 4377, 4583, 4586, 4589, 4592, 4598, 4601, 4605, 4610, 4614, 4618, 4621, 4624, 4630, 4634, 4637, 4641, 4644, 4648, 4654, 4662, 4665, 4668, 4674, 4676, 4681, 4688, 4692) + +'(0 * x**2 + 0 * y**2 + 1 * x + 5 * y + 0 * x * y) % 8' (0, 613, 642, 706, 1222, 1251, 1315, 1322, 1324, 1425, 1454, 1525, 2034, 2063, 2136, 2237, 2266, 2330, 2643, 2672, 2743, 2846, 2875, 2939, 4289, 4368, 4597, 4672) + +'(0 * x**2 + 0 * y**2 + 3 * x + 1 * y + 0 * x * y) % 5' (0, 98, 104, 126, 150, 166, 178, 2237, 2243, 2253, 2290, 2339, 3049, 3055, 3067, 3078, 3090, 3105, 3111, 3151, 3200, 4292, 4319, 4361, 4587, 4646, 4657) + +'(1 * x**2 + 1 * y**2 + 2 * x + 4 * y + 3 * x * y) % 5' (0, 2, 7, 22, 46, 98, 150, 166, 202, 254, 259, 306, 325, 358, 374, 410, 613, 615, 816, 832, 1019, 1222, 1227, 1425, 1478, 1481, 1628, 1681, 1831, 1884, 2034, 2049, 2124, 2237, 2440, 2643, 2658, 2698, 2846, 2851, 2861, 2871, 2881, 3049, 3054, 3064, 3067, 3252, 3318, 3455, 3511, 3521, 3658, 3674, 3714, 3721, 3861, 3914, 4064, 4069, 4117, 4379, 4469) + +'(4 * x**2 + 6 * y**2 + 7 * x + 2 * y + 6 * x * y) % 8' (0, 2, 7, 8, 22, 25, 46, 47, 48, 49, 50, 98, 99, 100, 101, 102, 150, 151, 159, 202, 204, 211, 254, 257, 260, 262, 306, 307, 325, 358, 361, 374, 376, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1425, 1426, 1427, 1428, 1429, 1453, 1454, 1455, 1628, 1629, 1630, 1631, 1632, 1653, 1657, 1661, 1831, 1832, 1836, 1837, 1838, 1849, 1860, 1872, 2034, 2035, 2043, 2053, 2059, 2060, 2061, 2237, 2239, 2242, 2245, 2248, 2263, 2266, 2269, 2440, 2442, 2445, 2448, 2451, 2456, 2469, 2484, 2643, 2645, 2652, 2659, 2662, 2665, 2671, 2846, 2849, 2851, 2855, 2859, 2872, 2874, 3049, 3052, 3055, 3057, 3065, 3067, 3074, 3078, 3082, 3090, 3093, 3252, 3253, 3254, 3255, 3256, 3317, 3318, 3319, 3455, 3456, 3457, 3458, 3459, 3517, 3521, 3525, 3658, 3659, 3667, 3714, 3720, 3721, 3722, 3861, 3863, 3870, 3914, 3917, 3920, 3926, 4064, 4067, 4070, 4072, 4117, 4119, 4126, 4130, 4134, 4142, 4145, 4267, 4281, 4379, 4382, 4394, 4398, 4402, 4469, 4471, 4584, 4597, 4655, 4672) + +'(0 * x**2 + 0 * y**2 + 5 * x + 3 * y + 0 * x * y) % 7' (0, 2, 7, 13, 22, 28, 46, 52, 65, 98, 104, 114, 150, 169, 176, 202, 218, 220, 254, 272, 280, 306, 312, 325, 358, 364, 374, 410, 416, 429, 465, 476, 488, 613, 619, 629, 668, 679, 691, 706, 712, 745, 816, 835, 842, 872, 879, 1019, 1035, 1037, 1072, 1074, 1112, 1151, 1154, 1222, 1240, 1248, 1275, 1315, 1357, 1425, 1431, 1441, 1480, 1491, 1503, 1518, 1557, 1628, 1634, 1683, 1694, 1706, 1718, 1831, 1847, 1887, 1893, 1931, 1976, 2034, 2050, 2062, 2089, 2096, 2127, 2134, 2166, 2179, 2237, 2255, 2290, 2302, 2330, 2372, 2440, 2449, 2456, 2458, 2493, 2495, 2533, 2572, 2575, 2643, 2706, 2708, 2733, 2735, 2846, 2862, 2901, 2908, 2939, 2946, 2978, 2991, 3049, 3065, 3111, 3141, 3149, 3194, 3252, 3258, 3271, 3307, 3318, 3330, 3455, 3461, 3471, 3510, 3521, 3533, 3548, 3554, 3587, 3658, 3677, 3684, 3714, 3721, 3861, 3877, 3879, 3914, 3916, 3954, 3993, 3996, 4064, 4082, 4090, 4117, 4157, 4199, 4272, 4331, 4379, 4385, 4434, 4445, 4457, 4469, 4587, 4646, 4657) + +'(2 * x**2 + 4 * y**2 + 4 * x + 5 * y + 2 * x * y) % 8' (0, 2, 7, 15, 22, 27, 46, 54, 64, 71, 98, 103, 126, 150, 165, 178, 202, 207, 217, 227, 237, 254, 259, 269, 279, 289, 306, 314, 325, 332, 358, 363, 374, 410, 418, 428, 435, 465, 472, 499, 512, 527, 561, 574, 613, 618, 641, 678, 702, 712, 722, 816, 831, 844, 871, 908, 915, 946, 1019, 1024, 1034, 1044, 1054, 1074, 1121, 1183, 1222, 1227, 1237, 1247, 1257, 1287, 1324, 1369, 1425, 1433, 1477, 1490, 1505, 1517, 1524, 1628, 1633, 1646, 1680, 1690, 1700, 1730, 1779, 1831, 1839, 1846, 1883, 1920, 1933, 1948, 1957, 2034, 2049, 2062, 2086, 2123, 2136, 2160, 2202, 2237, 2242, 2252, 2262, 2272, 2289, 2299, 2309, 2326, 2336, 2346, 2363, 2380, 2397, 2414, 2440, 2445, 2455, 2465, 2475, 2492, 2502, 2512, 2529, 2539, 2549, 2566, 2583, 2600, 2617, 2643, 2648, 2658, 2668, 2678, 2695, 2705, 2715, 2732, 2742, 2752, 2769, 2786, 2803, 2820, 2846, 2851, 2861, 2871, 2881, 2898, 2908, 2918, 2935, 2945, 2955, 2972, 2989, 3006, 3023, 3049, 3054, 3064, 3074, 3084, 3101, 3111, 3121, 3138, 3148, 3158, 3175, 3192, 3209, 3226, 3252, 3260, 3270, 3277, 3305, 3318, 3333, 3345, 3352, 3387, 3413, 3455, 3460, 3483, 3511, 3521, 3532, 3545, 3658, 3673, 3686, 3714, 3721, 3758, 3802, 3861, 3866, 3876, 3886, 3896, 3914, 3961, 4022, 4064, 4069, 4079, 4089, 4099, 4117, 4154, 4191, 4274, 4306, 4319, 4361, 4379, 4384, 4398, 4408, 4419, 4444, 4469, 4586, 4665) + +'(0 * x**2 + 6 * y**2 + 4 * x + 4 * y + 2 * x * y) % 8' (0, 39, 3455, 3457, 3460, 3463, 3466, 3471, 3474, 3477, 3481, 3484, 3487, 3491, 3495, 3499, 3503, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 4267, 4269, 4281, 4283, 4287, 4320, 4340, 4583, 4589, 4605, 4610, 4621, 4630) + +'(0 * x**2 + 8 * y**2 + 1 * x + 5 * y + 1 * x * y) % 9' (0, 816, 845, 3252, 3861) + +'(8 * x**2 + 2 * y**2 + 6 * x + 4 * y + 5 * x * y) % 9' (0, 46, 48, 358, 613, 615, 618, 621, 624, 816, 1425, 3861, 3863, 4064, 4130) + +'(0 * x**2 + 0 * y**2 + 2 * x + 3 * y + 0 * x * y) % 5' (0, 39, 98, 106, 116, 410, 413, 428, 436, 472, 476, 480, 512, 561, 1425, 1428, 1453, 1487, 1491, 1495, 1514, 1518, 1522, 2034, 2037, 2040, 2099, 2123, 2127, 2131, 2134, 2145, 3049, 3055, 3067, 3078, 3090, 3105, 3138, 3149, 3160, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3748, 4269, 4320, 4340, 4589, 4621, 4657) + +'(4 * x**2 + 6 * y**2 + 7 * x + 1 * y + 6 * x * y) % 8' (0, 39, 1019, 1027, 1112, 1831, 1834, 1856, 1860, 1864, 2440, 2465, 2533, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 4269, 4340, 4589, 4621) + +'(6 * x**2 + 4 * y**2 + 5 * x + 1 * y + 6 * x * y) % 8' (0, 410, 512, 1019, 1085, 1121, 1831, 1897, 1933, 2643, 2709) + +'(7 * x**2 + 6 * y**2 + 0 * x + 3 * y + 4 * x * y) % 8' (0, 22, 1628, 1730, 2440, 2465, 2643, 2732, 2846, 2871, 2908, 2935, 3049, 3074, 3111, 3138, 3455, 3521, 3658, 3861, 3914, 4064, 4089, 4117, 4164, 4225) + +'(5 * x**2 + 1 * y**2 + 7 * x + 4 * y + 2 * x * y) % 8' (0, 150, 158, 202, 204, 1425, 1427, 1450, 1453, 1456, 2237, 2239, 2242, 2245, 2248, 3049, 3067, 3455, 3457, 3518, 3521, 3524) + +'(0 * x**2 + 3 * y**2 + 4 * x + 2 * y + 6 * x * y) % 9' (0, 1019, 1022, 1035, 1074, 1082, 1108, 1112, 1116, 1151, 2440, 2443, 2458, 2493, 2529, 2533, 2537, 2575, 4289, 4320, 4368, 4587, 4646) + +'(0 * x**2 + 0 * y**2 + 2 * x + 5 * y + 0 * x * y) % 7' (0, 39, 254, 263, 279, 2237, 2243, 2245, 2293, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 4269, 4340, 4589, 4621) + +'(0 * x**2 + 6 * y**2 + 0 * x + 8 * y + 3 * x * y) % 9' (0, 98, 103, 116, 126, 137, 150, 158, 165, 178, 193, 1222, 1227, 1237, 1247, 1257, 1277, 1287, 1298, 1314, 1324, 1335, 1352, 1369, 1386, 1404, 2034, 2042, 2049, 2062, 2077, 2086, 2099, 2114, 2123, 2136, 2151, 2160, 2181, 2202, 2226, 3861, 3866, 3876, 3886, 3896, 3914, 3924, 3934, 3951, 3961, 3971, 3988, 4005, 4022, 4039, 4319, 4361, 4586, 4605, 4614, 4644, 4665, 4688) + +'(0 * x**2 + 0 * y**2 + 4 * x + 2 * y + 0 * x * y) % 7' (0, 46, 65, 74, 150, 169, 176, 254, 263, 280, 4289, 4320, 4368, 4604, 4683) + +'(5 * x**2 + 5 * y**2 + 3 * x + 9 * y + 5 * x * y) % 10' (0, 7, 410, 1019, 1628, 1831, 2643, 3049, 3252, 3305, 3318, 3352, 3861, 3914, 3926, 3950, 3961, 4342, 4604, 4683) + +'(0 * x**2 + 0 * y**2 + 1 * x + 3 * y + 0 * x * y) % 5' (0, 150, 159, 166, 202, 211, 220, 410, 416, 428, 439, 451, 472, 500, 512, 561, 1222, 1251, 1275, 1277, 1284, 4272, 4292, 4331, 4597, 4657, 4672) + +'(4 * x**2 + 5 * y**2 + 5 * x + 6 * y + 4 * x * y) % 8' (0, 7, 10, 410, 413, 416, 418, 426, 428, 435, 439, 443, 451, 454, 613, 616, 619, 621, 629, 631, 638, 642, 646, 654, 657, 816, 819, 822, 824, 832, 834, 841, 845, 849, 857, 860, 1019, 1022, 1025, 1027, 1035, 1037, 1044, 1048, 1052, 1060, 1063, 1222, 1225, 1228, 1230, 1238, 1240, 1247, 1251, 1255, 1263, 1266, 1831, 1834, 1856, 1860, 1864, 3252, 3255, 3314, 3318, 3322, 3658, 3661, 3720, 3724, 3728, 3861, 3869, 3914, 3927, 3942, 4269, 4340, 4597, 4672) + +'(0 * x**2 + 0 * y**2 + 6 * x + 3 * y + 0 * x * y) % 7' (0, 22, 25, 1628, 1631, 1653, 1657, 1661, 1718, 1831, 1837, 1849, 1860, 1872, 1887, 2440, 2448, 2456, 2469, 2484, 2539, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3112, 3455, 3458, 3483, 3517, 3521, 3525, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4156, 4342, 4584, 4635, 4655) + +'(0 * x**2 + 0 * y**2 + 4 * x + 4 * y + 0 * x * y) % 7' (0, 2, 7, 22, 42, 46, 72, 74, 98, 117, 124, 150, 202, 221, 228, 254, 263, 273, 306, 325, 331, 358, 374, 386, 410, 436, 438, 503, 509, 613, 632, 639, 703, 715, 816, 882, 909, 916, 918, 1019, 1038, 1045, 1085, 1109, 1222, 1231, 1241, 1278, 1322, 1425, 1525, 1527, 1628, 1721, 1728, 1831, 1897, 1924, 2034, 2063, 2100, 2237, 2303, 2327, 2329, 2336, 2440, 2496, 2505, 2532, 2540, 2643, 2672, 2709, 2736, 2743, 2846, 2875, 2902, 2911, 2938, 3049, 3058, 3077, 3114, 3142, 3252, 3278, 3280, 3318, 3341, 3455, 3474, 3481, 3521, 3544, 3658, 3714, 3721, 3723, 3748, 3750, 3757, 3861, 3880, 3887, 3914, 3963, 4064, 4073, 4083, 4117, 4166, 4282, 4342, 4357, 4379, 4397, 4404, 4434, 4441, 4469, 4481, 4530, 4543, 4607, 4634, 4676) + +'(0 * x**2 + 0 * y**2 + 3 * x + 4 * y + 0 * x * y) % 5' (0, 7, 15, 410, 418, 429, 435, 465, 499, 512, 527, 574, 1019, 1025, 1044, 1074, 1085, 1097, 1109, 1121, 1183, 1628, 1637, 1646, 1681, 1690, 1721, 1730, 1763, 1779, 1831, 1839, 1857, 1884, 1897, 1912, 1920, 1933, 1948, 2643, 2649, 2659, 2671, 2698, 2709, 2721, 2736, 2775, 3049, 3055, 3067, 3078, 3090, 3102, 3142, 3148, 3184, 3252, 3260, 3271, 3277, 3305, 3318, 3333, 3352, 3413, 3861, 3867, 3886, 3914, 3926, 3950, 3961, 3972, 4022, 4274, 4306, 4342, 4590, 4604, 4683) + +'(0 * x**2 + 0 * y**2 + 7 * x + 5 * y + 0 * x * y) % 9' (0, 1019, 1022, 1035, 1074, 1108, 1112, 1116, 1151, 2440, 2443, 2458, 2493, 2505, 2529, 2533, 2537, 2575, 4289, 4368, 4587, 4646, 4657) + +'(4 * x**2 + 5 * y**2 + 0 * x + 3 * y + 2 * x * y) % 8' (0, 3252, 3277, 3305, 3352, 3413, 3658, 3663, 3673, 3683, 3693, 3711, 3721, 3731, 3748, 3758, 3768, 3785, 3802, 3819, 3836, 4605) + +'(5 * x**2 + 5 * y**2 + 8 * x + 7 * y + 0 * x * y) % 10' (0, 202, 208, 210, 410, 413, 428, 1425, 1428, 1451, 2034, 2037, 2040, 2062, 3049, 3055, 3067, 3078, 3090, 3658, 3661, 3664, 3723, 4269, 4340) + +'(0 * x**2 + 0 * y**2 + 3 * x + 2 * y + 0 * x * y) % 5' (0, 39, 202, 208, 210, 410, 413, 428, 472, 476, 480, 500, 512, 561, 1425, 1428, 1451, 1487, 1491, 1495, 1514, 1518, 1522, 2034, 2037, 2040, 2062, 2123, 2127, 2131, 2134, 2145, 3049, 3055, 3067, 3078, 3090, 3114, 3138, 3149, 3160, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3723, 4269, 4292, 4340, 4589, 4621, 4635) + +'(0 * x**2 + 0 * y**2 + 3 * x + 3 * y + 0 * x * y) % 5' (0, 2, 7, 22, 42, 46, 62, 64, 98, 116, 123, 150, 202, 205, 208, 254, 260, 270, 306, 325, 331, 358, 374, 386, 410, 426, 428, 466, 472, 510, 512, 555, 561, 613, 631, 638, 666, 678, 706, 713, 748, 774, 816, 869, 871, 878, 905, 1019, 1022, 1025, 1084, 1108, 1112, 1116, 1119, 1130, 1222, 1228, 1238, 1277, 1288, 1300, 1315, 1321, 1354, 1425, 1451, 1453, 1488, 1490, 1515, 1517, 1628, 1647, 1654, 1684, 1691, 1720, 1727, 1831, 1840, 1850, 1894, 1896, 1921, 1923, 2034, 2053, 2060, 2062, 2090, 2097, 2099, 2237, 2246, 2253, 2292, 2299, 2330, 2337, 2369, 2382, 2440, 2443, 2466, 2502, 2506, 2510, 2529, 2533, 2537, 2643, 2646, 2649, 2659, 2696, 2846, 2854, 2864, 2872, 2899, 2912, 2927, 2939, 2981, 3049, 3055, 3067, 3078, 3090, 3104, 3115, 3127, 3139, 3252, 3268, 3270, 3318, 3341, 3455, 3473, 3480, 3521, 3544, 3658, 3714, 3721, 3723, 3748, 3750, 3757, 3861, 3864, 3867, 3914, 3963, 4064, 4070, 4080, 4117, 4166, 4282, 4342, 4357, 4379, 4397, 4404, 4434, 4441, 4469, 4481, 4530, 4543, 4607, 4634, 4676) + +'(0 * x**2 + 0 * y**2 + 4 * x + 2 * y + 0 * x * y) % 5' (0, 2, 7, 22, 25, 46, 64, 72, 98, 101, 116, 124, 150, 159, 166, 202, 211, 228, 254, 257, 262, 306, 325, 334, 358, 361, 374, 410, 428, 436, 463, 472, 503, 512, 545, 561, 613, 616, 631, 639, 678, 703, 816, 825, 832, 871, 878, 909, 916, 948, 961, 1019, 1028, 1045, 1075, 1084, 1109, 1118, 1222, 1225, 1230, 1277, 1322, 1425, 1454, 1481, 1490, 1517, 1525, 1628, 1631, 1653, 1657, 1661, 1681, 1720, 1728, 1789, 1831, 1837, 1849, 1860, 1872, 1884, 1896, 1924, 1966, 2034, 2043, 2052, 2059, 2099, 2124, 2237, 2266, 2293, 2299, 2327, 2329, 2440, 2448, 2456, 2469, 2484, 2502, 2532, 2540, 2585, 2643, 2652, 2662, 2671, 2698, 2743, 2846, 2849, 2862, 2874, 2909, 2938, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3112, 3252, 3270, 3278, 3318, 3342, 3351, 3455, 3458, 3473, 3481, 3517, 3521, 3525, 3557, 3606, 3658, 3667, 3674, 3714, 3721, 3760, 3861, 3870, 3887, 3914, 3923, 3953, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4156, 4289, 4320, 4368, 4379, 4382, 4407, 4434, 4442, 4469, 4584, 4635, 4655) + +'(0 * x**2 + 0 * y**2 + 9 * x + 8 * y + 0 * x * y) % 10' (0, 22, 25, 410, 419, 428, 816, 832, 844, 1628, 1631, 1653, 1657, 1661, 1831, 1837, 1849, 1860, 1872, 2440, 2448, 2456, 2469, 2484, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3455, 3458, 3517, 3521, 3525, 4064, 4067, 4072, 4117, 4126, 4130, 4134, 4145, 4584, 4655) + +'(0 * x**2 + 6 * y**2 + 1 * x + 5 * y + 3 * x * y) % 9' (0, 816, 845, 869, 1019, 1048, 1074, 4597, 4657, 4672) + +'(0 * x**2 + 0 * y**2 + 4 * x + 3 * y + 0 * x * y) % 5' (0, 22, 25, 410, 419, 428, 463, 472, 503, 512, 545, 561, 816, 832, 844, 871, 878, 909, 916, 948, 961, 1628, 1631, 1653, 1657, 1661, 1681, 1693, 1728, 1789, 1831, 1837, 1849, 1860, 1872, 1884, 1924, 1930, 1966, 2440, 2448, 2456, 2469, 2484, 2496, 2502, 2540, 2585, 3049, 3052, 3057, 3065, 3074, 3078, 3082, 3093, 3141, 3455, 3458, 3473, 3517, 3521, 3525, 3545, 3557, 3606, 4064, 4067, 4072, 4090, 4117, 4126, 4130, 4134, 4145, 4275, 4289, 4368, 4584, 4607, 4655) + +'(2 * x**2 + 0 * y**2 + 0 * x + 4 * y + 2 * x * y) % 8' (0, 39, 3658, 3659, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 3861, 3863, 3866, 3869, 3872, 3877, 3880, 3883, 3887, 3890, 3893, 3897, 3901, 3905, 3909, 4268, 4269, 4313, 4315, 4317, 4340, 4586, 4589, 4598, 4618, 4621, 4635, 4665) + +'(0 * x**2 + 0 * y**2 + 2 * x + 1 * y + 0 * x * y) % 11' (0, 2846, 2865, 2902, 2948, 4319, 4361) + +'(0 * x**2 + 6 * y**2 + 1 * x + 7 * y + 0 * x * y) % 8' (0, 816, 845, 916, 1019, 1048, 1112, 1628, 1657, 1728, 1730, 2440, 2469, 2533, 2540, 4597, 4672) + +'(0 * x**2 + 0 * y**2 + 2 * x + 2 * y + 0 * x * y) % 5' (0, 42, 150, 410, 419, 426, 428, 472, 510, 512, 555, 561, 613, 622, 631, 638, 666, 706, 713, 748, 774, 1019, 1022, 1025, 1047, 1108, 1112, 1116, 1119, 1130, 1222, 1228, 1238, 1250, 1277, 1288, 1300, 1315, 1354, 2237, 2253, 2265, 2292, 2299, 2330, 2337, 2369, 2382, 2440, 2443, 2468, 2502, 2506, 2510, 2529, 2533, 2537, 2846, 2854, 2864, 2899, 2912, 2927, 2939, 2945, 2981, 3049, 3055, 3067, 3078, 3090, 3104, 3115, 3127, 3148, 4275, 4282, 4357, 4379, 4388, 4397, 4404, 4434, 4441, 4481, 4530, 4543, 4590, 4634, 4676) + +'(0 * x**2 + 0 * y**2 + 3 * x + 4 * y + 0 * x * y) % 7' (0, 39, 46, 49, 74, 2846, 2862, 2871, 2909, 2938, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3748, 4269, 4320, 4340, 4589, 4621, 4657) + +'(6 * x**2 + 4 * y**2 + 0 * x + 7 * y + 3 * x * y) % 9' (0, 3861, 3863, 3866, 3869, 3872, 3876, 3879, 3882, 3886, 3889, 3892, 3896, 3900, 3904, 3908, 4586, 4605, 4614, 4644, 4665, 4688) + +'(0 * x**2 + 0 * y**2 + 4 * x + 3 * y + 0 * x * y) % 7' (0, 39, 254, 263, 279, 613, 621, 632, 668, 676, 3658, 3661, 3664, 3676, 3683, 3687, 3691, 3699, 3723, 4269, 4292, 4340, 4589, 4621, 4635) + +'(0 * x**2 + 3 * y**2 + 8 * x + 0 * y + 6 * x * y) % 9' (0, 150, 151, 158, 159, 160, 202, 204, 208, 211, 214, 1425, 1426, 1427, 1428, 1429, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 2237, 2239, 2242, 2245, 2248, 2253, 2256, 2259, 2263, 2266, 2269, 2273, 2277, 2281, 2285, 3455, 3456, 3457, 3458, 3459, 3517, 3518, 3519, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 4267, 4281, 4313, 4314, 4338, 4356) + diff --git a/equational_theories/Generated/FinitePoly/src/implications.json b/equational_theories/Generated/FinitePoly/src/implications.json new file mode 100644 index 00000000..169dbee9 --- /dev/null +++ b/equational_theories/Generated/FinitePoly/src/implications.json @@ -0,0 +1,35279 @@ +{"unconditionals": ["Equation1"], + "nonimplications": + [{"rhs": "Equation3", "lhs": "Equation39"}, + {"rhs": "Equation3", "lhs": "Equation42"}, + {"rhs": "Equation3", "lhs": "Equation4512"}, + {"rhs": "Equation4", "lhs": "Equation39"}, + {"rhs": "Equation4", "lhs": "Equation40"}, + {"rhs": "Equation4", "lhs": "Equation43"}, + {"rhs": "Equation4", "lhs": "Equation4582"}, + {"rhs": "Equation5", "lhs": "Equation42"}, + {"rhs": "Equation5", "lhs": "Equation43"}, + {"rhs": "Equation5", "lhs": "Equation4513"}, + {"rhs": "Equation8", "lhs": "Equation3"}, + {"rhs": "Equation23", "lhs": "Equation3"}, + {"rhs": "Equation38", "lhs": "Equation23"}, + {"rhs": "Equation23", "lhs": "Equation39"}, + {"rhs": "Equation39", "lhs": "Equation8"}, + {"rhs": "Equation39", "lhs": "Equation23"}, + {"rhs": "Equation39", "lhs": "Equation40"}, + {"rhs": "Equation39", "lhs": "Equation168"}, + {"rhs": "Equation39", "lhs": "Equation4512"}, + {"rhs": "Equation39", "lhs": "Equation4513"}, + {"rhs": "Equation39", "lhs": "Equation4522"}, + {"rhs": "Equation39", "lhs": "Equation4564"}, + {"rhs": "Equation39", "lhs": "Equation4579"}, + {"rhs": "Equation39", "lhs": "Equation4582"}, + {"rhs": "Equation40", "lhs": "Equation3"}, + {"rhs": "Equation40", "lhs": "Equation39"}, + {"rhs": "Equation40", "lhs": "Equation42"}, + {"rhs": "Equation40", "lhs": "Equation43"}, + {"rhs": "Equation40", "lhs": "Equation4512"}, + {"rhs": "Equation42", "lhs": "Equation43"}, + {"rhs": "Equation42", "lhs": "Equation4512"}, + {"rhs": "Equation43", "lhs": "Equation3"}, + {"rhs": "Equation43", "lhs": "Equation3"}, + {"rhs": "Equation43", "lhs": "Equation42"}, + {"rhs": "Equation43", "lhs": "Equation387"}, + {"rhs": "Equation43", "lhs": "Equation4512"}, + {"rhs": "Equation46", "lhs": "Equation3"}, + {"rhs": "Equation46", "lhs": "Equation4"}, + {"rhs": "Equation168", "lhs": "Equation8"}, + {"rhs": "Equation168", "lhs": "Equation23"}, + {"rhs": "Equation168", "lhs": "Equation39"}, + {"rhs": "Equation387", "lhs": "Equation39"}, + {"rhs": "Equation387", "lhs": "Equation40"}, + {"rhs": "Equation387", "lhs": "Equation42"}, + {"rhs": "Equation387", "lhs": "Equation4512"}, + {"rhs": "Equation4512", "lhs": "Equation42"}, + {"rhs": "Equation4512", "lhs": "Equation4513"}, + {"rhs": "Equation4513", "lhs": "Equation4522"}, + {"rhs": "Equation4582", "lhs": "Equation39"}, + {"rhs": "Equation4582", "lhs": "Equation40"}, + {"rhs": "Equation4582", "lhs": "Equation42"}, + {"rhs": "Equation4582", "lhs": "Equation43"}], + "implications": + [{"rhs": "Equation3", "lhs": "Equation2"}, + {"rhs": "Equation4", "lhs": "Equation2"}, + {"rhs": "Equation5", "lhs": "Equation2"}, + {"rhs": "Equation6", "lhs": "Equation2"}, + {"rhs": "Equation7", "lhs": "Equation2"}, + {"rhs": "Equation8", "lhs": "Equation2"}, + {"rhs": "Equation23", "lhs": "Equation2"}, + {"rhs": "Equation38", "lhs": "Equation2"}, + {"rhs": "Equation39", "lhs": "Equation2"}, + {"rhs": "Equation40", "lhs": "Equation2"}, + {"rhs": "Equation41", "lhs": "Equation2"}, + {"rhs": "Equation42", "lhs": "Equation2"}, + {"rhs": "Equation43", "lhs": "Equation2"}, + {"rhs": "Equation46", "lhs": "Equation2"}, + {"rhs": "Equation168", "lhs": "Equation2"}, + {"rhs": "Equation387", "lhs": "Equation2"}, + {"rhs": "Equation4512", "lhs": "Equation2"}, + {"rhs": "Equation4513", "lhs": "Equation2"}, + {"rhs": "Equation4522", "lhs": "Equation2"}, + {"rhs": "Equation4582", "lhs": "Equation2"}, + {"rhs": "Equation8", "lhs": "Equation3"}, + {"rhs": "Equation23", "lhs": "Equation3"}, + {"rhs": "Equation8", "lhs": "Equation4"}, + {"rhs": "Equation23", "lhs": "Equation4"}, + {"rhs": "Equation42", "lhs": "Equation4"}, + {"rhs": "Equation4522", "lhs": "Equation4"}, + {"rhs": "Equation3", "lhs": "Equation5"}, + {"rhs": "Equation8", "lhs": "Equation5"}, + {"rhs": "Equation23", "lhs": "Equation5"}, + {"rhs": "Equation39", "lhs": "Equation5"}, + {"rhs": "Equation4512", "lhs": "Equation5"}, + {"rhs": "Equation2", "lhs": "Equation6"}, + {"rhs": "Equation3", "lhs": "Equation6"}, + {"rhs": "Equation2", "lhs": "Equation7"}, + {"rhs": "Equation3", "lhs": "Equation7"}, + {"rhs": "Equation41", "lhs": "Equation7"}, + {"rhs": "Equation14", "lhs": "Equation29"}, + {"rhs": "Equation42", "lhs": "Equation38"}, + {"rhs": "Equation45", "lhs": "Equation39"}, + {"rhs": "Equation39", "lhs": "Equation41"}, + {"rhs": "Equation40", "lhs": "Equation41"}, + {"rhs": "Equation46", "lhs": "Equation41"}, + {"rhs": "Equation38", "lhs": "Equation42"}, + {"rhs": "Equation39", "lhs": "Equation45"}, + {"rhs": "Equation39", "lhs": "Equation46"}, + {"rhs": "Equation40", "lhs": "Equation46"}, + {"rhs": "Equation41", "lhs": "Equation46"}, + {"rhs": "Equation42", "lhs": "Equation46"}, + {"rhs": "Equation387", "lhs": "Equation46"}, + {"rhs": "Equation4582", "lhs": "Equation46"}, + {"rhs": "Equation43", "lhs": "Equation387"}, + {"rhs": "Equation381", "lhs": "Equation3744"}, + {"rhs": "Equation3722", "lhs": "Equation3744"}, + {"rhs": "Equation4512", "lhs": "Equation4513"}, + {"rhs": "Equation4513", "lhs": "Equation4522"}, + {"rhs": "Equation4522", "lhs": "Equation4582"}, + {"rhs": "Equation4564", "lhs": "Equation4582"}, + {"rhs": "Equation4579", "lhs": "Equation4582"}, + {"rhs": "Equation97", "lhs": "Equation98"}, + {"rhs": "Equation149", "lhs": "Equation150"}, + {"rhs": "Equation201", "lhs": "Equation202"}, + {"rhs": "Equation253", "lhs": "Equation254"}, + {"rhs": "Equation305", "lhs": "Equation306"}, + {"rhs": "Equation357", "lhs": "Equation358"}, + {"rhs": "Equation409", "lhs": "Equation410"}, + {"rhs": "Equation461", "lhs": "Equation462"}, + {"rhs": "Equation498", "lhs": "Equation499"}, + {"rhs": "Equation535", "lhs": "Equation536"}, + {"rhs": "Equation552", "lhs": "Equation553"}, + {"rhs": "Equation569", "lhs": "Equation570"}, + {"rhs": "Equation586", "lhs": "Equation587"}, + {"rhs": "Equation591", "lhs": "Equation592"}, + {"rhs": "Equation596", "lhs": "Equation597"}, + {"rhs": "Equation601", "lhs": "Equation602"}, + {"rhs": "Equation606", "lhs": "Equation607"}, + {"rhs": "Equation603", "lhs": "Equation608"}, + {"rhs": "Equation604", "lhs": "Equation609"}, + {"rhs": "Equation605", "lhs": "Equation610"}, + {"rhs": "Equation606", "lhs": "Equation611"}, + {"rhs": "Equation606", "lhs": "Equation612"}, + {"rhs": "Equation664", "lhs": "Equation665"}, + {"rhs": "Equation701", "lhs": "Equation702"}, + {"rhs": "Equation738", "lhs": "Equation739"}, + {"rhs": "Equation755", "lhs": "Equation756"}, + {"rhs": "Equation772", "lhs": "Equation773"}, + {"rhs": "Equation789", "lhs": "Equation790"}, + {"rhs": "Equation794", "lhs": "Equation795"}, + {"rhs": "Equation799", "lhs": "Equation800"}, + {"rhs": "Equation804", "lhs": "Equation805"}, + {"rhs": "Equation809", "lhs": "Equation810"}, + {"rhs": "Equation806", "lhs": "Equation811"}, + {"rhs": "Equation807", "lhs": "Equation812"}, + {"rhs": "Equation808", "lhs": "Equation813"}, + {"rhs": "Equation809", "lhs": "Equation814"}, + {"rhs": "Equation809", "lhs": "Equation815"}, + {"rhs": "Equation867", "lhs": "Equation868"}, + {"rhs": "Equation904", "lhs": "Equation905"}, + {"rhs": "Equation941", "lhs": "Equation942"}, + {"rhs": "Equation958", "lhs": "Equation959"}, + {"rhs": "Equation975", "lhs": "Equation976"}, + {"rhs": "Equation992", "lhs": "Equation993"}, + {"rhs": "Equation997", "lhs": "Equation998"}, + {"rhs": "Equation1002", "lhs": "Equation1003"}, + {"rhs": "Equation1007", "lhs": "Equation1008"}, + {"rhs": "Equation1012", "lhs": "Equation1013"}, + {"rhs": "Equation1009", "lhs": "Equation1014"}, + {"rhs": "Equation1010", "lhs": "Equation1015"}, + {"rhs": "Equation1011", "lhs": "Equation1016"}, + {"rhs": "Equation1012", "lhs": "Equation1017"}, + {"rhs": "Equation1012", "lhs": "Equation1018"}, + {"rhs": "Equation1070", "lhs": "Equation1071"}, + {"rhs": "Equation1107", "lhs": "Equation1108"}, + {"rhs": "Equation1144", "lhs": "Equation1145"}, + {"rhs": "Equation1161", "lhs": "Equation1162"}, + {"rhs": "Equation1178", "lhs": "Equation1179"}, + {"rhs": "Equation1195", "lhs": "Equation1196"}, + {"rhs": "Equation1200", "lhs": "Equation1201"}, + {"rhs": "Equation1205", "lhs": "Equation1206"}, + {"rhs": "Equation1210", "lhs": "Equation1211"}, + {"rhs": "Equation1215", "lhs": "Equation1216"}, + {"rhs": "Equation1212", "lhs": "Equation1217"}, + {"rhs": "Equation1213", "lhs": "Equation1218"}, + {"rhs": "Equation1214", "lhs": "Equation1219"}, + {"rhs": "Equation1215", "lhs": "Equation1220"}, + {"rhs": "Equation1215", "lhs": "Equation1221"}, + {"rhs": "Equation1273", "lhs": "Equation1274"}, + {"rhs": "Equation1310", "lhs": "Equation1311"}, + {"rhs": "Equation1347", "lhs": "Equation1348"}, + {"rhs": "Equation1364", "lhs": "Equation1365"}, + {"rhs": "Equation1381", "lhs": "Equation1382"}, + {"rhs": "Equation1398", "lhs": "Equation1399"}, + {"rhs": "Equation1403", "lhs": "Equation1404"}, + {"rhs": "Equation1408", "lhs": "Equation1409"}, + {"rhs": "Equation1413", "lhs": "Equation1414"}, + {"rhs": "Equation1418", "lhs": "Equation1419"}, + {"rhs": "Equation1415", "lhs": "Equation1420"}, + {"rhs": "Equation1416", "lhs": "Equation1421"}, + {"rhs": "Equation1417", "lhs": "Equation1422"}, + {"rhs": "Equation1418", "lhs": "Equation1423"}, + {"rhs": "Equation1418", "lhs": "Equation1424"}, + {"rhs": "Equation1476", "lhs": "Equation1477"}, + {"rhs": "Equation1513", "lhs": "Equation1514"}, + {"rhs": "Equation1550", "lhs": "Equation1551"}, + {"rhs": "Equation1567", "lhs": "Equation1568"}, + {"rhs": "Equation1584", "lhs": "Equation1585"}, + {"rhs": "Equation1601", "lhs": "Equation1602"}, + {"rhs": "Equation1606", "lhs": "Equation1607"}, + {"rhs": "Equation1611", "lhs": "Equation1612"}, + {"rhs": "Equation1616", "lhs": "Equation1617"}, + {"rhs": "Equation1621", "lhs": "Equation1622"}, + {"rhs": "Equation1618", "lhs": "Equation1623"}, + {"rhs": "Equation1619", "lhs": "Equation1624"}, + {"rhs": "Equation1620", "lhs": "Equation1625"}, + {"rhs": "Equation1621", "lhs": "Equation1626"}, + {"rhs": "Equation1621", "lhs": "Equation1627"}, + {"rhs": "Equation1679", "lhs": "Equation1680"}, + {"rhs": "Equation1716", "lhs": "Equation1717"}, + {"rhs": "Equation1753", "lhs": "Equation1754"}, + {"rhs": "Equation1770", "lhs": "Equation1771"}, + {"rhs": "Equation1787", "lhs": "Equation1788"}, + {"rhs": "Equation1804", "lhs": "Equation1805"}, + {"rhs": "Equation1809", "lhs": "Equation1810"}, + {"rhs": "Equation1814", "lhs": "Equation1815"}, + {"rhs": "Equation1819", "lhs": "Equation1820"}, + {"rhs": "Equation1824", "lhs": "Equation1825"}, + {"rhs": "Equation1821", "lhs": "Equation1826"}, + {"rhs": "Equation1822", "lhs": "Equation1827"}, + {"rhs": "Equation1823", "lhs": "Equation1828"}, + {"rhs": "Equation1824", "lhs": "Equation1829"}, + {"rhs": "Equation1824", "lhs": "Equation1830"}, + {"rhs": "Equation1882", "lhs": "Equation1883"}, + {"rhs": "Equation1919", "lhs": "Equation1920"}, + {"rhs": "Equation1956", "lhs": "Equation1957"}, + {"rhs": "Equation1973", "lhs": "Equation1974"}, + {"rhs": "Equation1990", "lhs": "Equation1991"}, + {"rhs": "Equation2007", "lhs": "Equation2008"}, + {"rhs": "Equation2012", "lhs": "Equation2013"}, + {"rhs": "Equation2017", "lhs": "Equation2018"}, + {"rhs": "Equation2022", "lhs": "Equation2023"}, + {"rhs": "Equation2027", "lhs": "Equation2028"}, + {"rhs": "Equation2024", "lhs": "Equation2029"}, + {"rhs": "Equation2025", "lhs": "Equation2030"}, + {"rhs": "Equation2026", "lhs": "Equation2031"}, + {"rhs": "Equation2027", "lhs": "Equation2032"}, + {"rhs": "Equation2027", "lhs": "Equation2033"}, + {"rhs": "Equation2085", "lhs": "Equation2086"}, + {"rhs": "Equation2122", "lhs": "Equation2123"}, + {"rhs": "Equation2159", "lhs": "Equation2160"}, + {"rhs": "Equation2176", "lhs": "Equation2177"}, + {"rhs": "Equation2193", "lhs": "Equation2194"}, + {"rhs": "Equation2210", "lhs": "Equation2211"}, + {"rhs": "Equation2215", "lhs": "Equation2216"}, + {"rhs": "Equation2220", "lhs": "Equation2221"}, + {"rhs": "Equation2225", "lhs": "Equation2226"}, + {"rhs": "Equation2230", "lhs": "Equation2231"}, + {"rhs": "Equation2227", "lhs": "Equation2232"}, + {"rhs": "Equation2228", "lhs": "Equation2233"}, + {"rhs": "Equation2229", "lhs": "Equation2234"}, + {"rhs": "Equation2230", "lhs": "Equation2235"}, + {"rhs": "Equation2230", "lhs": "Equation2236"}, + {"rhs": "Equation2288", "lhs": "Equation2289"}, + {"rhs": "Equation2325", "lhs": "Equation2326"}, + {"rhs": "Equation2362", "lhs": "Equation2363"}, + {"rhs": "Equation2379", "lhs": "Equation2380"}, + {"rhs": "Equation2396", "lhs": "Equation2397"}, + {"rhs": "Equation2413", "lhs": "Equation2414"}, + {"rhs": "Equation2418", "lhs": "Equation2419"}, + {"rhs": "Equation2423", "lhs": "Equation2424"}, + {"rhs": "Equation2428", "lhs": "Equation2429"}, + {"rhs": "Equation2433", "lhs": "Equation2434"}, + {"rhs": "Equation2430", "lhs": "Equation2435"}, + {"rhs": "Equation2431", "lhs": "Equation2436"}, + {"rhs": "Equation2432", "lhs": "Equation2437"}, + {"rhs": "Equation2433", "lhs": "Equation2438"}, + {"rhs": "Equation2433", "lhs": "Equation2439"}, + {"rhs": "Equation2491", "lhs": "Equation2492"}, + {"rhs": "Equation2528", "lhs": "Equation2529"}, + {"rhs": "Equation2565", "lhs": "Equation2566"}, + {"rhs": "Equation2582", "lhs": "Equation2583"}, + {"rhs": "Equation2599", "lhs": "Equation2600"}, + {"rhs": "Equation2616", "lhs": "Equation2617"}, + {"rhs": "Equation2621", "lhs": "Equation2622"}, + {"rhs": "Equation2626", "lhs": "Equation2627"}, + {"rhs": "Equation2631", "lhs": "Equation2632"}, + {"rhs": "Equation2636", "lhs": "Equation2637"}, + {"rhs": "Equation2633", "lhs": "Equation2638"}, + {"rhs": "Equation2634", "lhs": "Equation2639"}, + {"rhs": "Equation2635", "lhs": "Equation2640"}, + {"rhs": "Equation2636", "lhs": "Equation2641"}, + {"rhs": "Equation2636", "lhs": "Equation2642"}, + {"rhs": "Equation2694", "lhs": "Equation2695"}, + {"rhs": "Equation2731", "lhs": "Equation2732"}, + {"rhs": "Equation2768", "lhs": "Equation2769"}, + {"rhs": "Equation2785", "lhs": "Equation2786"}, + {"rhs": "Equation2802", "lhs": "Equation2803"}, + {"rhs": "Equation2819", "lhs": "Equation2820"}, + {"rhs": "Equation2824", "lhs": "Equation2825"}, + {"rhs": "Equation2829", "lhs": "Equation2830"}, + {"rhs": "Equation2834", "lhs": "Equation2835"}, + {"rhs": "Equation2839", "lhs": "Equation2840"}, + {"rhs": "Equation2836", "lhs": "Equation2841"}, + {"rhs": "Equation2837", "lhs": "Equation2842"}, + {"rhs": "Equation2838", "lhs": "Equation2843"}, + {"rhs": "Equation2839", "lhs": "Equation2844"}, + {"rhs": "Equation2839", "lhs": "Equation2845"}, + {"rhs": "Equation2897", "lhs": "Equation2898"}, + {"rhs": "Equation2934", "lhs": "Equation2935"}, + {"rhs": "Equation2971", "lhs": "Equation2972"}, + {"rhs": "Equation2988", "lhs": "Equation2989"}, + {"rhs": "Equation3005", "lhs": "Equation3006"}, + {"rhs": "Equation3022", "lhs": "Equation3023"}, + {"rhs": "Equation3027", "lhs": "Equation3028"}, + {"rhs": "Equation3032", "lhs": "Equation3033"}, + {"rhs": "Equation3037", "lhs": "Equation3038"}, + {"rhs": "Equation3042", "lhs": "Equation3043"}, + {"rhs": "Equation3039", "lhs": "Equation3044"}, + {"rhs": "Equation3040", "lhs": "Equation3045"}, + {"rhs": "Equation3041", "lhs": "Equation3046"}, + {"rhs": "Equation3042", "lhs": "Equation3047"}, + {"rhs": "Equation3042", "lhs": "Equation3048"}, + {"rhs": "Equation3100", "lhs": "Equation3101"}, + {"rhs": "Equation3137", "lhs": "Equation3138"}, + {"rhs": "Equation3174", "lhs": "Equation3175"}, + {"rhs": "Equation3191", "lhs": "Equation3192"}, + {"rhs": "Equation3208", "lhs": "Equation3209"}, + {"rhs": "Equation3225", "lhs": "Equation3226"}, + {"rhs": "Equation3230", "lhs": "Equation3231"}, + {"rhs": "Equation3235", "lhs": "Equation3236"}, + {"rhs": "Equation3240", "lhs": "Equation3241"}, + {"rhs": "Equation3245", "lhs": "Equation3246"}, + {"rhs": "Equation3242", "lhs": "Equation3247"}, + {"rhs": "Equation3243", "lhs": "Equation3248"}, + {"rhs": "Equation3244", "lhs": "Equation3249"}, + {"rhs": "Equation3245", "lhs": "Equation3250"}, + {"rhs": "Equation3245", "lhs": "Equation3251"}, + {"rhs": "Equation3303", "lhs": "Equation3304"}, + {"rhs": "Equation3340", "lhs": "Equation3341"}, + {"rhs": "Equation3377", "lhs": 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"Equation3642"}, + {"rhs": "Equation3646", "lhs": "Equation3647"}, + {"rhs": "Equation3651", "lhs": "Equation3652"}, + {"rhs": "Equation3648", "lhs": "Equation3653"}, + {"rhs": "Equation3649", "lhs": "Equation3654"}, + {"rhs": "Equation3650", "lhs": "Equation3655"}, + {"rhs": "Equation3651", "lhs": "Equation3656"}, + {"rhs": "Equation3651", "lhs": "Equation3657"}, + {"rhs": "Equation3709", "lhs": "Equation3710"}, + {"rhs": "Equation3746", "lhs": "Equation3747"}, + {"rhs": "Equation3783", "lhs": "Equation3784"}, + {"rhs": "Equation3800", "lhs": "Equation3801"}, + {"rhs": "Equation3817", "lhs": "Equation3818"}, + {"rhs": "Equation3834", "lhs": "Equation3835"}, + {"rhs": "Equation3839", "lhs": "Equation3840"}, + {"rhs": "Equation3844", "lhs": "Equation3845"}, + {"rhs": "Equation3849", "lhs": "Equation3850"}, + {"rhs": "Equation3854", "lhs": "Equation3855"}, + {"rhs": "Equation3851", "lhs": "Equation3856"}, + {"rhs": "Equation3852", "lhs": "Equation3857"}, + {"rhs": "Equation3853", "lhs": "Equation3858"}, + {"rhs": "Equation3854", "lhs": "Equation3859"}, + {"rhs": "Equation3854", "lhs": "Equation3860"}, + {"rhs": "Equation3912", "lhs": "Equation3913"}, + {"rhs": "Equation3949", "lhs": "Equation3950"}, + {"rhs": "Equation3986", "lhs": "Equation3987"}, + {"rhs": "Equation4003", "lhs": "Equation4004"}, + {"rhs": "Equation4020", "lhs": "Equation4021"}, + {"rhs": "Equation4037", "lhs": "Equation4038"}, + {"rhs": "Equation4042", "lhs": "Equation4043"}, + {"rhs": "Equation4047", "lhs": "Equation4048"}, + {"rhs": "Equation4052", "lhs": "Equation4053"}, + {"rhs": "Equation4057", "lhs": "Equation4058"}, + {"rhs": "Equation4054", "lhs": "Equation4059"}, + {"rhs": "Equation4055", "lhs": "Equation4060"}, + {"rhs": "Equation4056", "lhs": "Equation4061"}, + {"rhs": "Equation4057", "lhs": "Equation4062"}, + {"rhs": "Equation4057", "lhs": "Equation4063"}, + {"rhs": "Equation4115", "lhs": "Equation4116"}, + {"rhs": "Equation4152", "lhs": "Equation4153"}, + {"rhs": "Equation4189", "lhs": "Equation4190"}, + {"rhs": "Equation4206", "lhs": "Equation4207"}, + {"rhs": "Equation4223", "lhs": "Equation4224"}, + {"rhs": "Equation4240", "lhs": "Equation4241"}, + {"rhs": "Equation4245", "lhs": "Equation4246"}, + {"rhs": "Equation4250", "lhs": "Equation4251"}, + {"rhs": "Equation4255", "lhs": "Equation4256"}, + {"rhs": "Equation4260", "lhs": "Equation4261"}, + {"rhs": "Equation4257", "lhs": "Equation4262"}, + {"rhs": "Equation4258", "lhs": "Equation4263"}, + {"rhs": "Equation4259", "lhs": "Equation4264"}, + {"rhs": "Equation4260", "lhs": "Equation4265"}, + {"rhs": "Equation4260", "lhs": "Equation4266"}, + {"rhs": "Equation4312", "lhs": "Equation4313"}, + {"rhs": "Equation4337", "lhs": "Equation4338"}, + {"rhs": "Equation4355", "lhs": "Equation4356"}, + {"rhs": "Equation4430", "lhs": "Equation4431"}, + {"rhs": "Equation4467", "lhs": "Equation4468"}, + {"rhs": "Equation4504", "lhs": "Equation4505"}, + {"rhs": "Equation4521", "lhs": "Equation4522"}, + {"rhs": "Equation4538", "lhs": "Equation4539"}, + {"rhs": "Equation4555", "lhs": "Equation4556"}, + {"rhs": "Equation4560", "lhs": "Equation4561"}, + {"rhs": "Equation4565", "lhs": "Equation4566"}, + {"rhs": "Equation4570", "lhs": "Equation4571"}, + {"rhs": "Equation4575", "lhs": "Equation4576"}, + {"rhs": "Equation4572", "lhs": "Equation4577"}, + {"rhs": "Equation4573", "lhs": "Equation4578"}, + {"rhs": "Equation4574", "lhs": "Equation4579"}, + {"rhs": "Equation4575", "lhs": "Equation4580"}, + {"rhs": "Equation4575", "lhs": "Equation4581"}, + {"rhs": "Equation4627", "lhs": "Equation4628"}, + {"rhs": "Equation4652", "lhs": "Equation4653"}, + {"rhs": "Equation4670", "lhs": "Equation4671"}, + {"rhs": "Equation607", "lhs": "Equation613"}, + {"rhs": "Equation810", "lhs": "Equation816"}, + {"rhs": "Equation1013", "lhs": "Equation1019"}, + {"rhs": "Equation1216", "lhs": "Equation1222"}, + {"rhs": "Equation1419", "lhs": "Equation1425"}, + {"rhs": "Equation1622", "lhs": "Equation1628"}, + {"rhs": "Equation1825", "lhs": "Equation1831"}, + {"rhs": "Equation2028", "lhs": "Equation2034"}, + {"rhs": "Equation2231", "lhs": "Equation2237"}, + {"rhs": "Equation2434", "lhs": "Equation2440"}, + {"rhs": "Equation2637", "lhs": "Equation2643"}, + {"rhs": "Equation2840", "lhs": "Equation2846"}, + {"rhs": "Equation3043", "lhs": "Equation3049"}, + {"rhs": "Equation3246", "lhs": "Equation3252"}, + {"rhs": "Equation3449", "lhs": "Equation3455"}, + {"rhs": "Equation3652", "lhs": "Equation3658"}, + {"rhs": "Equation3855", "lhs": "Equation3861"}, + {"rhs": "Equation4058", "lhs": "Equation4064"}, + {"rhs": "Equation4261", "lhs": "Equation4267"}, + {"rhs": "Equation4576", "lhs": "Equation4582"}, + {"rhs": "Equation553", "lhs": "Equation613"}, + {"rhs": "Equation756", "lhs": "Equation816"}, + {"rhs": "Equation959", "lhs": "Equation1019"}, + {"rhs": "Equation1162", "lhs": "Equation1222"}, + {"rhs": "Equation1365", "lhs": "Equation1425"}, + {"rhs": "Equation1568", "lhs": "Equation1628"}, + {"rhs": "Equation1771", "lhs": "Equation1831"}, + {"rhs": "Equation1974", "lhs": "Equation2034"}, + {"rhs": "Equation2177", "lhs": "Equation2237"}, + {"rhs": "Equation2380", "lhs": "Equation2440"}, + {"rhs": "Equation2583", "lhs": "Equation2643"}, + {"rhs": "Equation2786", "lhs": "Equation2846"}, + {"rhs": "Equation2989", "lhs": "Equation3049"}, + {"rhs": "Equation3192", "lhs": "Equation3252"}, + {"rhs": "Equation3395", "lhs": "Equation3455"}, + {"rhs": "Equation3598", "lhs": "Equation3658"}, + {"rhs": "Equation3801", "lhs": "Equation3861"}, + {"rhs": "Equation4004", "lhs": "Equation4064"}, + {"rhs": "Equation4207", "lhs": "Equation4267"}, + {"rhs": "Equation4361", "lhs": "Equation4379"}, + {"rhs": "Equation4522", "lhs": "Equation4582"}, + {"rhs": "Equation4676", "lhs": "Equation4694"}, + {"rhs": "Equation570", "lhs": "Equation613"}, + {"rhs": "Equation773", "lhs": "Equation816"}, + {"rhs": "Equation976", "lhs": "Equation1019"}, + {"rhs": "Equation1179", "lhs": "Equation1222"}, + {"rhs": "Equation1382", "lhs": "Equation1425"}, + {"rhs": "Equation1585", "lhs": "Equation1628"}, + {"rhs": "Equation1788", "lhs": "Equation1831"}, + {"rhs": "Equation1991", "lhs": "Equation2034"}, + {"rhs": "Equation2194", "lhs": "Equation2237"}, + {"rhs": "Equation2397", "lhs": "Equation2440"}, + {"rhs": "Equation2600", "lhs": "Equation2643"}, + {"rhs": "Equation2803", "lhs": "Equation2846"}, + {"rhs": "Equation3006", "lhs": "Equation3049"}, + {"rhs": "Equation3209", "lhs": "Equation3252"}, + {"rhs": "Equation3412", "lhs": "Equation3455"}, + {"rhs": "Equation3615", "lhs": "Equation3658"}, + {"rhs": "Equation3818", "lhs": "Equation3861"}, + {"rhs": "Equation4021", "lhs": "Equation4064"}, + {"rhs": "Equation4224", "lhs": "Equation4267"}, + {"rhs": "Equation4368", "lhs": "Equation4379"}, + {"rhs": "Equation4539", "lhs": "Equation4582"}, + {"rhs": "Equation4683", "lhs": "Equation4694"}, + {"rhs": "Equation587", "lhs": "Equation613"}, + {"rhs": "Equation790", "lhs": "Equation816"}, + {"rhs": "Equation993", "lhs": "Equation1019"}, + {"rhs": "Equation1196", "lhs": "Equation1222"}, + {"rhs": "Equation1399", "lhs": "Equation1425"}, + {"rhs": "Equation1602", "lhs": "Equation1628"}, + {"rhs": "Equation1805", "lhs": "Equation1831"}, + {"rhs": "Equation2008", "lhs": "Equation2034"}, + {"rhs": "Equation2211", "lhs": "Equation2237"}, + {"rhs": "Equation2414", "lhs": "Equation2440"}, + {"rhs": "Equation2617", "lhs": "Equation2643"}, + {"rhs": "Equation2820", "lhs": "Equation2846"}, + {"rhs": "Equation3023", "lhs": "Equation3049"}, + {"rhs": "Equation3226", "lhs": "Equation3252"}, + {"rhs": "Equation3429", "lhs": "Equation3455"}, + {"rhs": "Equation3632", "lhs": "Equation3658"}, + {"rhs": "Equation3835", "lhs": "Equation3861"}, + {"rhs": "Equation4038", "lhs": "Equation4064"}, + {"rhs": "Equation4241", "lhs": "Equation4267"}, + {"rhs": "Equation4373", "lhs": "Equation4379"}, + {"rhs": "Equation4556", "lhs": "Equation4582"}, + {"rhs": "Equation4688", "lhs": "Equation4694"}, + {"rhs": "Equation462", "lhs": 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{"rhs": "Equation859", "lhs": "Equation868"}, + {"rhs": "Equation896", "lhs": "Equation905"}, + {"rhs": "Equation933", "lhs": "Equation942"}, + {"rhs": "Equation950", "lhs": "Equation959"}, + {"rhs": "Equation967", "lhs": "Equation976"}, + {"rhs": "Equation984", "lhs": "Equation993"}, + {"rhs": "Equation963", "lhs": "Equation998"}, + {"rhs": "Equation967", "lhs": "Equation1003"}, + {"rhs": "Equation971", "lhs": "Equation1008"}, + {"rhs": "Equation967", "lhs": "Equation1013"}, + {"rhs": "Equation972", "lhs": "Equation1014"}, + {"rhs": "Equation973", "lhs": "Equation1015"}, + {"rhs": "Equation974", "lhs": "Equation1016"}, + {"rhs": "Equation973", "lhs": "Equation1017"}, + {"rhs": "Equation975", "lhs": "Equation1018"}, + {"rhs": "Equation1062", "lhs": "Equation1071"}, + {"rhs": "Equation1099", "lhs": "Equation1108"}, + {"rhs": "Equation1136", "lhs": "Equation1145"}, + {"rhs": "Equation1153", "lhs": "Equation1162"}, + {"rhs": "Equation1170", "lhs": "Equation1179"}, + {"rhs": "Equation1187", "lhs": "Equation1196"}, + {"rhs": "Equation1166", "lhs": "Equation1201"}, + {"rhs": "Equation1170", "lhs": "Equation1206"}, + {"rhs": "Equation1174", "lhs": "Equation1211"}, + {"rhs": "Equation1170", "lhs": "Equation1216"}, + {"rhs": "Equation1175", "lhs": "Equation1217"}, + {"rhs": "Equation1176", "lhs": "Equation1218"}, + {"rhs": "Equation1177", "lhs": "Equation1219"}, + {"rhs": "Equation1176", "lhs": "Equation1220"}, + {"rhs": "Equation1178", "lhs": "Equation1221"}, + {"rhs": "Equation1265", "lhs": "Equation1274"}, + {"rhs": "Equation1302", "lhs": "Equation1311"}, + {"rhs": "Equation1339", "lhs": "Equation1348"}, + {"rhs": "Equation1356", "lhs": "Equation1365"}, + {"rhs": "Equation1373", "lhs": "Equation1382"}, + {"rhs": "Equation1390", "lhs": "Equation1399"}, + {"rhs": "Equation1369", "lhs": "Equation1404"}, + {"rhs": "Equation1373", "lhs": "Equation1409"}, + {"rhs": "Equation1377", "lhs": "Equation1414"}, + {"rhs": "Equation1373", "lhs": "Equation1419"}, + {"rhs": "Equation1378", "lhs": "Equation1420"}, + {"rhs": "Equation1379", "lhs": "Equation1421"}, + {"rhs": "Equation1380", "lhs": "Equation1422"}, + {"rhs": "Equation1379", "lhs": "Equation1423"}, + {"rhs": "Equation1381", "lhs": "Equation1424"}, + {"rhs": "Equation1468", "lhs": "Equation1477"}, + {"rhs": "Equation1505", "lhs": "Equation1514"}, + {"rhs": "Equation1542", "lhs": "Equation1551"}, + {"rhs": "Equation1559", "lhs": "Equation1568"}, + {"rhs": "Equation1576", "lhs": "Equation1585"}, + {"rhs": "Equation1593", "lhs": "Equation1602"}, + {"rhs": "Equation1572", "lhs": "Equation1607"}, + {"rhs": "Equation1576", "lhs": "Equation1612"}, + {"rhs": "Equation1580", "lhs": "Equation1617"}, + {"rhs": "Equation1576", "lhs": "Equation1622"}, + {"rhs": "Equation1581", "lhs": "Equation1623"}, + {"rhs": "Equation1582", "lhs": "Equation1624"}, + {"rhs": "Equation1583", "lhs": "Equation1625"}, + {"rhs": "Equation1582", "lhs": "Equation1626"}, + {"rhs": "Equation1584", "lhs": "Equation1627"}, + {"rhs": 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"lhs": "Equation868"}, + {"rhs": "Equation900", "lhs": "Equation905"}, + {"rhs": "Equation937", "lhs": "Equation942"}, + {"rhs": "Equation954", "lhs": "Equation959"}, + {"rhs": "Equation971", "lhs": "Equation976"}, + {"rhs": "Equation988", "lhs": "Equation993"}, + {"rhs": "Equation980", "lhs": "Equation998"}, + {"rhs": "Equation984", "lhs": "Equation1003"}, + {"rhs": "Equation988", "lhs": "Equation1008"}, + {"rhs": "Equation988", "lhs": "Equation1013"}, + {"rhs": "Equation989", "lhs": "Equation1014"}, + {"rhs": "Equation990", "lhs": "Equation1015"}, + {"rhs": "Equation991", "lhs": "Equation1016"}, + {"rhs": "Equation991", "lhs": "Equation1017"}, + {"rhs": "Equation992", "lhs": "Equation1018"}, + {"rhs": "Equation1066", "lhs": "Equation1071"}, + {"rhs": "Equation1103", "lhs": "Equation1108"}, + {"rhs": "Equation1140", "lhs": "Equation1145"}, + {"rhs": "Equation1157", "lhs": "Equation1162"}, + {"rhs": "Equation1174", "lhs": "Equation1179"}, + {"rhs": "Equation1191", "lhs": 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"Equation4099", "lhs": "Equation4116"}, + {"rhs": "Equation4136", "lhs": "Equation4153"}, + {"rhs": "Equation4173", "lhs": "Equation4190"}, + {"rhs": "Equation4163", "lhs": "Equation4207"}, + {"rhs": "Equation4173", "lhs": "Equation4224"}, + {"rhs": "Equation4173", "lhs": "Equation4241"}, + {"rhs": "Equation4177", "lhs": "Equation4246"}, + {"rhs": "Equation4181", "lhs": "Equation4251"}, + {"rhs": "Equation4181", "lhs": "Equation4256"}, + {"rhs": "Equation4185", "lhs": "Equation4261"}, + {"rhs": "Equation4186", "lhs": "Equation4262"}, + {"rhs": "Equation4187", "lhs": "Equation4263"}, + {"rhs": "Equation4187", "lhs": "Equation4264"}, + {"rhs": "Equation4188", "lhs": "Equation4265"}, + {"rhs": "Equation4189", "lhs": "Equation4266"}, + {"rhs": "Equation4298", "lhs": "Equation4313"}, + {"rhs": "Equation4326", "lhs": "Equation4338"}, + {"rhs": "Equation4347", "lhs": "Equation4356"}, + {"rhs": "Equation4342", "lhs": "Equation4361"}, + {"rhs": "Equation4347", "lhs": "Equation4368"}, + {"rhs": "Equation4347", "lhs": "Equation4373"}, + {"rhs": "Equation4352", "lhs": "Equation4375"}, + {"rhs": "Equation4352", "lhs": "Equation4377"}, + {"rhs": "Equation4354", "lhs": "Equation4378"}, + {"rhs": "Equation4414", "lhs": "Equation4431"}, + {"rhs": "Equation4451", "lhs": "Equation4468"}, + {"rhs": "Equation4488", "lhs": "Equation4505"}, + {"rhs": "Equation4478", "lhs": "Equation4522"}, + {"rhs": "Equation4488", "lhs": "Equation4539"}, + {"rhs": "Equation4488", "lhs": "Equation4556"}, + {"rhs": "Equation4492", "lhs": "Equation4561"}, + {"rhs": "Equation4496", "lhs": "Equation4566"}, + {"rhs": "Equation4496", "lhs": "Equation4571"}, + {"rhs": "Equation4500", "lhs": "Equation4576"}, + {"rhs": "Equation4501", "lhs": "Equation4577"}, + {"rhs": "Equation4502", "lhs": "Equation4578"}, + {"rhs": "Equation4502", "lhs": "Equation4579"}, + {"rhs": "Equation4503", "lhs": "Equation4580"}, + {"rhs": "Equation4504", "lhs": "Equation4581"}, + {"rhs": "Equation4613", "lhs": "Equation4628"}, + {"rhs": "Equation4641", "lhs": "Equation4653"}, + {"rhs": "Equation4662", "lhs": "Equation4671"}, + {"rhs": "Equation4657", "lhs": "Equation4676"}, + {"rhs": "Equation4662", "lhs": "Equation4683"}, + {"rhs": "Equation4662", "lhs": "Equation4688"}, + {"rhs": "Equation4667", "lhs": "Equation4690"}, + {"rhs": "Equation4667", "lhs": "Equation4692"}, + {"rhs": "Equation4669", "lhs": "Equation4693"}, + {"rhs": "Equation94", "lhs": "Equation98"}, + {"rhs": "Equation146", "lhs": "Equation150"}, + {"rhs": "Equation198", "lhs": "Equation202"}, + {"rhs": "Equation250", "lhs": "Equation254"}, + {"rhs": "Equation302", "lhs": "Equation306"}, + {"rhs": "Equation354", "lhs": "Equation358"}, + {"rhs": "Equation406", "lhs": "Equation410"}, + {"rhs": "Equation458", "lhs": "Equation462"}, + {"rhs": "Equation495", "lhs": "Equation499"}, + {"rhs": "Equation532", "lhs": "Equation536"}, + {"rhs": "Equation549", "lhs": "Equation553"}, + {"rhs": "Equation566", "lhs": "Equation570"}, + {"rhs": "Equation583", "lhs": "Equation587"}, + {"rhs": "Equation588", "lhs": "Equation592"}, + {"rhs": "Equation593", "lhs": "Equation597"}, + {"rhs": "Equation598", "lhs": "Equation602"}, + {"rhs": "Equation603", "lhs": "Equation607"}, + {"rhs": "Equation588", "lhs": "Equation608"}, + {"rhs": "Equation589", "lhs": "Equation609"}, + {"rhs": "Equation590", "lhs": "Equation610"}, + {"rhs": "Equation591", "lhs": "Equation611"}, + {"rhs": "Equation588", "lhs": "Equation612"}, + {"rhs": "Equation661", "lhs": "Equation665"}, + {"rhs": "Equation698", "lhs": "Equation702"}, + {"rhs": "Equation735", "lhs": "Equation739"}, + {"rhs": "Equation752", "lhs": "Equation756"}, + {"rhs": "Equation769", "lhs": "Equation773"}, + {"rhs": "Equation786", "lhs": "Equation790"}, + {"rhs": "Equation791", "lhs": "Equation795"}, + {"rhs": "Equation796", "lhs": "Equation800"}, + {"rhs": "Equation801", "lhs": "Equation805"}, + {"rhs": "Equation806", "lhs": "Equation810"}, + {"rhs": "Equation791", "lhs": "Equation811"}, + {"rhs": "Equation792", "lhs": "Equation812"}, + {"rhs": "Equation793", "lhs": "Equation813"}, + {"rhs": "Equation794", "lhs": "Equation814"}, + {"rhs": "Equation791", "lhs": "Equation815"}, + {"rhs": "Equation864", "lhs": "Equation868"}, + {"rhs": "Equation901", "lhs": "Equation905"}, + {"rhs": "Equation938", "lhs": "Equation942"}, + {"rhs": "Equation955", "lhs": "Equation959"}, + {"rhs": "Equation972", "lhs": "Equation976"}, + {"rhs": "Equation989", "lhs": "Equation993"}, + {"rhs": "Equation994", "lhs": "Equation998"}, + {"rhs": "Equation999", "lhs": "Equation1003"}, + {"rhs": "Equation1004", "lhs": "Equation1008"}, + {"rhs": "Equation1009", "lhs": "Equation1013"}, + {"rhs": "Equation994", "lhs": "Equation1014"}, + {"rhs": "Equation995", "lhs": "Equation1015"}, + {"rhs": "Equation996", "lhs": "Equation1016"}, + {"rhs": "Equation997", "lhs": "Equation1017"}, + {"rhs": "Equation994", "lhs": "Equation1018"}, + {"rhs": "Equation1067", "lhs": "Equation1071"}, + {"rhs": "Equation1104", "lhs": "Equation1108"}, + {"rhs": "Equation1141", "lhs": "Equation1145"}, + {"rhs": "Equation1158", "lhs": "Equation1162"}, + {"rhs": "Equation1175", "lhs": "Equation1179"}, + {"rhs": "Equation1192", "lhs": "Equation1196"}, + {"rhs": "Equation1197", "lhs": "Equation1201"}, + {"rhs": "Equation1202", "lhs": "Equation1206"}, + {"rhs": "Equation1207", "lhs": "Equation1211"}, + {"rhs": "Equation1212", "lhs": "Equation1216"}, + {"rhs": "Equation1197", "lhs": "Equation1217"}, + {"rhs": "Equation1198", "lhs": "Equation1218"}, + {"rhs": "Equation1199", "lhs": "Equation1219"}, + {"rhs": "Equation1200", "lhs": "Equation1220"}, + {"rhs": "Equation1197", "lhs": "Equation1221"}, + {"rhs": "Equation1270", "lhs": "Equation1274"}, + {"rhs": "Equation1307", "lhs": "Equation1311"}, + {"rhs": "Equation1344", "lhs": "Equation1348"}, + {"rhs": "Equation1361", "lhs": "Equation1365"}, + {"rhs": "Equation1378", "lhs": "Equation1382"}, + {"rhs": "Equation1395", "lhs": "Equation1399"}, + {"rhs": "Equation1400", "lhs": "Equation1404"}, + {"rhs": "Equation1405", "lhs": "Equation1409"}, + {"rhs": "Equation1410", "lhs": "Equation1414"}, + {"rhs": "Equation1415", "lhs": "Equation1419"}, + {"rhs": "Equation1400", "lhs": "Equation1420"}, + {"rhs": "Equation1401", "lhs": "Equation1421"}, + {"rhs": "Equation1402", "lhs": "Equation1422"}, + {"rhs": "Equation1403", "lhs": "Equation1423"}, + {"rhs": "Equation1400", "lhs": "Equation1424"}, + {"rhs": "Equation1473", "lhs": "Equation1477"}, + {"rhs": "Equation1510", "lhs": "Equation1514"}, + {"rhs": "Equation1547", "lhs": "Equation1551"}, + {"rhs": "Equation1564", "lhs": "Equation1568"}, + {"rhs": "Equation1581", "lhs": "Equation1585"}, + {"rhs": "Equation1598", "lhs": "Equation1602"}, + {"rhs": "Equation1603", "lhs": "Equation1607"}, + {"rhs": "Equation1608", "lhs": "Equation1612"}, + {"rhs": "Equation1613", "lhs": "Equation1617"}, + {"rhs": "Equation1618", "lhs": "Equation1622"}, + {"rhs": "Equation1603", "lhs": "Equation1623"}, + {"rhs": "Equation1604", "lhs": "Equation1624"}, + {"rhs": "Equation1605", "lhs": "Equation1625"}, + {"rhs": "Equation1606", "lhs": "Equation1626"}, + {"rhs": "Equation1603", "lhs": "Equation1627"}, + {"rhs": "Equation1676", "lhs": "Equation1680"}, + {"rhs": "Equation1713", "lhs": "Equation1717"}, + {"rhs": "Equation1750", "lhs": "Equation1754"}, + {"rhs": "Equation1767", "lhs": "Equation1771"}, + {"rhs": "Equation1784", "lhs": "Equation1788"}, + {"rhs": "Equation1801", "lhs": "Equation1805"}, + {"rhs": "Equation1806", "lhs": "Equation1810"}, + {"rhs": "Equation1811", "lhs": "Equation1815"}, + {"rhs": "Equation1816", "lhs": "Equation1820"}, + {"rhs": "Equation1821", "lhs": "Equation1825"}, + {"rhs": "Equation1806", "lhs": "Equation1826"}, + {"rhs": "Equation1807", "lhs": "Equation1827"}, + {"rhs": "Equation1808", "lhs": "Equation1828"}, + {"rhs": "Equation1809", "lhs": "Equation1829"}, + {"rhs": "Equation1806", "lhs": "Equation1830"}, + {"rhs": "Equation1879", "lhs": "Equation1883"}, + {"rhs": "Equation1916", "lhs": "Equation1920"}, + {"rhs": "Equation1953", "lhs": "Equation1957"}, + {"rhs": "Equation1970", "lhs": "Equation1974"}, + {"rhs": "Equation1987", "lhs": "Equation1991"}, + {"rhs": "Equation2004", "lhs": "Equation2008"}, + {"rhs": "Equation2009", "lhs": "Equation2013"}, + {"rhs": "Equation2014", "lhs": "Equation2018"}, + {"rhs": "Equation2019", "lhs": "Equation2023"}, + {"rhs": "Equation2024", "lhs": "Equation2028"}, + {"rhs": "Equation2009", "lhs": "Equation2029"}, + {"rhs": "Equation2010", "lhs": "Equation2030"}, + {"rhs": "Equation2011", "lhs": "Equation2031"}, + {"rhs": "Equation2012", "lhs": "Equation2032"}, + {"rhs": "Equation2009", "lhs": "Equation2033"}, + {"rhs": "Equation2082", "lhs": "Equation2086"}, + {"rhs": "Equation2119", "lhs": "Equation2123"}, + {"rhs": "Equation2156", "lhs": "Equation2160"}, + {"rhs": "Equation2173", "lhs": "Equation2177"}, + {"rhs": "Equation2190", "lhs": "Equation2194"}, + {"rhs": "Equation2207", "lhs": "Equation2211"}, + {"rhs": "Equation2212", "lhs": "Equation2216"}, + {"rhs": "Equation2217", "lhs": "Equation2221"}, + {"rhs": "Equation2222", "lhs": "Equation2226"}, + {"rhs": "Equation2227", "lhs": "Equation2231"}, + {"rhs": "Equation2212", "lhs": "Equation2232"}, + {"rhs": "Equation2213", "lhs": "Equation2233"}, + {"rhs": "Equation2214", "lhs": "Equation2234"}, + {"rhs": "Equation2215", "lhs": "Equation2235"}, + {"rhs": "Equation2212", "lhs": "Equation2236"}, + {"rhs": "Equation2285", "lhs": "Equation2289"}, + {"rhs": "Equation2322", "lhs": "Equation2326"}, + {"rhs": "Equation2359", "lhs": "Equation2363"}, + {"rhs": "Equation2376", "lhs": "Equation2380"}, + {"rhs": "Equation2393", "lhs": "Equation2397"}, + {"rhs": "Equation2410", "lhs": "Equation2414"}, + {"rhs": "Equation2415", "lhs": "Equation2419"}, + {"rhs": "Equation2420", "lhs": "Equation2424"}, + {"rhs": "Equation2425", "lhs": "Equation2429"}, + {"rhs": "Equation2430", "lhs": "Equation2434"}, + {"rhs": "Equation2415", "lhs": "Equation2435"}, + {"rhs": "Equation2416", "lhs": "Equation2436"}, + {"rhs": "Equation2417", "lhs": "Equation2437"}, + {"rhs": "Equation2418", "lhs": "Equation2438"}, + {"rhs": "Equation2415", "lhs": "Equation2439"}, + {"rhs": "Equation2488", "lhs": "Equation2492"}, + {"rhs": "Equation2525", "lhs": "Equation2529"}, + {"rhs": "Equation2562", "lhs": "Equation2566"}, + {"rhs": "Equation2579", "lhs": "Equation2583"}, + {"rhs": "Equation2596", "lhs": "Equation2600"}, + {"rhs": "Equation2613", "lhs": "Equation2617"}, + {"rhs": "Equation2618", "lhs": "Equation2622"}, + {"rhs": "Equation2623", "lhs": "Equation2627"}, + {"rhs": "Equation2628", "lhs": "Equation2632"}, + {"rhs": "Equation2633", "lhs": "Equation2637"}, + {"rhs": "Equation2618", "lhs": "Equation2638"}, + {"rhs": "Equation2619", "lhs": "Equation2639"}, + {"rhs": "Equation2620", "lhs": "Equation2640"}, + {"rhs": "Equation2621", "lhs": "Equation2641"}, + {"rhs": "Equation2618", "lhs": "Equation2642"}, + {"rhs": "Equation2691", "lhs": "Equation2695"}, + {"rhs": "Equation2728", "lhs": "Equation2732"}, + {"rhs": "Equation2765", "lhs": "Equation2769"}, + {"rhs": "Equation2782", "lhs": "Equation2786"}, + {"rhs": "Equation2799", "lhs": "Equation2803"}, + {"rhs": "Equation2816", "lhs": "Equation2820"}, + {"rhs": "Equation2821", "lhs": "Equation2825"}, + {"rhs": "Equation2826", "lhs": "Equation2830"}, + {"rhs": "Equation2831", "lhs": "Equation2835"}, + {"rhs": "Equation2836", "lhs": "Equation2840"}, + {"rhs": "Equation2821", "lhs": "Equation2841"}, + {"rhs": "Equation2822", "lhs": "Equation2842"}, + {"rhs": "Equation2823", "lhs": "Equation2843"}, + {"rhs": "Equation2824", "lhs": "Equation2844"}, + {"rhs": "Equation2821", "lhs": "Equation2845"}, + {"rhs": "Equation2894", "lhs": "Equation2898"}, + {"rhs": "Equation2931", "lhs": "Equation2935"}, + {"rhs": "Equation2968", "lhs": "Equation2972"}, + {"rhs": "Equation2985", "lhs": "Equation2989"}, + {"rhs": "Equation3002", "lhs": "Equation3006"}, + {"rhs": "Equation3019", "lhs": "Equation3023"}, + {"rhs": "Equation3024", "lhs": "Equation3028"}, + {"rhs": "Equation3029", "lhs": "Equation3033"}, + {"rhs": "Equation3034", "lhs": "Equation3038"}, + {"rhs": "Equation3039", "lhs": "Equation3043"}, + {"rhs": "Equation3024", "lhs": "Equation3044"}, + {"rhs": "Equation3025", "lhs": "Equation3045"}, + {"rhs": "Equation3026", "lhs": "Equation3046"}, + {"rhs": "Equation3027", "lhs": "Equation3047"}, + {"rhs": "Equation3024", "lhs": "Equation3048"}, + {"rhs": "Equation3097", "lhs": "Equation3101"}, + {"rhs": "Equation3134", "lhs": "Equation3138"}, + {"rhs": "Equation3171", "lhs": "Equation3175"}, + {"rhs": "Equation3188", "lhs": "Equation3192"}, + {"rhs": "Equation3205", "lhs": "Equation3209"}, + {"rhs": "Equation3222", "lhs": "Equation3226"}, + {"rhs": "Equation3227", "lhs": "Equation3231"}, + {"rhs": "Equation3232", "lhs": "Equation3236"}, + {"rhs": "Equation3237", "lhs": "Equation3241"}, + {"rhs": "Equation3242", "lhs": "Equation3246"}, + {"rhs": "Equation3227", "lhs": "Equation3247"}, + {"rhs": "Equation3228", "lhs": "Equation3248"}, + {"rhs": "Equation3229", "lhs": "Equation3249"}, + {"rhs": "Equation3230", "lhs": "Equation3250"}, + {"rhs": "Equation3227", "lhs": "Equation3251"}, + {"rhs": "Equation3300", "lhs": "Equation3304"}, + {"rhs": "Equation3337", "lhs": "Equation3341"}, + {"rhs": "Equation3374", "lhs": "Equation3378"}, + {"rhs": "Equation3391", "lhs": "Equation3395"}, + {"rhs": "Equation3408", "lhs": "Equation3412"}, + {"rhs": "Equation3425", "lhs": "Equation3429"}, + {"rhs": "Equation3430", "lhs": "Equation3434"}, + {"rhs": "Equation3435", "lhs": "Equation3439"}, + {"rhs": "Equation3440", "lhs": "Equation3444"}, + {"rhs": "Equation3445", "lhs": "Equation3449"}, + {"rhs": "Equation3430", "lhs": "Equation3450"}, + {"rhs": "Equation3431", "lhs": "Equation3451"}, + {"rhs": "Equation3432", "lhs": "Equation3452"}, + {"rhs": "Equation3433", "lhs": "Equation3453"}, + {"rhs": "Equation3430", "lhs": "Equation3454"}, + {"rhs": "Equation3503", "lhs": "Equation3507"}, + {"rhs": "Equation3540", "lhs": "Equation3544"}, + {"rhs": "Equation3577", "lhs": "Equation3581"}, + {"rhs": "Equation3594", "lhs": "Equation3598"}, + {"rhs": "Equation3611", "lhs": "Equation3615"}, + {"rhs": "Equation3628", "lhs": "Equation3632"}, + {"rhs": "Equation3633", "lhs": "Equation3637"}, + {"rhs": "Equation3638", "lhs": "Equation3642"}, + {"rhs": "Equation3643", "lhs": "Equation3647"}, + {"rhs": "Equation3648", "lhs": "Equation3652"}, + {"rhs": "Equation3633", "lhs": "Equation3653"}, + {"rhs": "Equation3634", "lhs": "Equation3654"}, + {"rhs": "Equation3635", "lhs": "Equation3655"}, + {"rhs": "Equation3636", "lhs": "Equation3656"}, + {"rhs": "Equation3633", "lhs": "Equation3657"}, + {"rhs": "Equation3706", "lhs": "Equation3710"}, + {"rhs": "Equation3743", "lhs": "Equation3747"}, + {"rhs": "Equation3780", "lhs": "Equation3784"}, + {"rhs": "Equation3797", "lhs": "Equation3801"}, + {"rhs": "Equation3814", "lhs": "Equation3818"}, + {"rhs": "Equation3831", "lhs": "Equation3835"}, + {"rhs": "Equation3836", "lhs": "Equation3840"}, + {"rhs": "Equation3841", "lhs": "Equation3845"}, + {"rhs": "Equation3846", "lhs": "Equation3850"}, + {"rhs": "Equation3851", "lhs": "Equation3855"}, + {"rhs": "Equation3836", "lhs": "Equation3856"}, + {"rhs": "Equation3837", "lhs": "Equation3857"}, + {"rhs": "Equation3838", "lhs": "Equation3858"}, + {"rhs": "Equation3839", "lhs": "Equation3859"}, + {"rhs": "Equation3836", "lhs": "Equation3860"}, + {"rhs": "Equation3909", "lhs": "Equation3913"}, + {"rhs": "Equation3946", "lhs": "Equation3950"}, + {"rhs": "Equation3983", "lhs": "Equation3987"}, + {"rhs": "Equation4000", "lhs": "Equation4004"}, + {"rhs": "Equation4017", "lhs": "Equation4021"}, + {"rhs": "Equation4034", "lhs": "Equation4038"}, + {"rhs": "Equation4039", "lhs": "Equation4043"}, + {"rhs": "Equation4044", "lhs": "Equation4048"}, + {"rhs": "Equation4049", "lhs": "Equation4053"}, + {"rhs": "Equation4054", "lhs": "Equation4058"}, + {"rhs": "Equation4039", "lhs": "Equation4059"}, + {"rhs": "Equation4040", "lhs": "Equation4060"}, + {"rhs": "Equation4041", "lhs": "Equation4061"}, + {"rhs": "Equation4042", "lhs": "Equation4062"}, + {"rhs": "Equation4039", "lhs": "Equation4063"}, + {"rhs": "Equation4112", "lhs": "Equation4116"}, + {"rhs": "Equation4149", "lhs": "Equation4153"}, + {"rhs": "Equation4186", "lhs": "Equation4190"}, + {"rhs": "Equation4203", "lhs": "Equation4207"}, + {"rhs": "Equation4220", "lhs": "Equation4224"}, + {"rhs": "Equation4237", "lhs": "Equation4241"}, + {"rhs": "Equation4242", "lhs": "Equation4246"}, + {"rhs": "Equation4247", "lhs": "Equation4251"}, + {"rhs": "Equation4252", "lhs": "Equation4256"}, + {"rhs": "Equation4257", "lhs": "Equation4261"}, + {"rhs": "Equation4242", "lhs": "Equation4262"}, + {"rhs": "Equation4243", "lhs": "Equation4263"}, + {"rhs": "Equation4244", "lhs": "Equation4264"}, + {"rhs": "Equation4245", "lhs": "Equation4265"}, + {"rhs": "Equation4242", "lhs": "Equation4266"}, + {"rhs": "Equation4309", "lhs": "Equation4313"}, + {"rhs": "Equation4334", "lhs": "Equation4338"}, + {"rhs": "Equation4353", "lhs": "Equation4356"}, + {"rhs": "Equation4366", "lhs": "Equation4368"}, + {"rhs": "Equation4371", "lhs": "Equation4373"}, + {"rhs": "Equation4427", "lhs": "Equation4431"}, + {"rhs": "Equation4464", "lhs": "Equation4468"}, + {"rhs": "Equation4501", "lhs": "Equation4505"}, + {"rhs": "Equation4518", "lhs": "Equation4522"}, + {"rhs": "Equation4535", "lhs": "Equation4539"}, + {"rhs": "Equation4552", "lhs": "Equation4556"}, + {"rhs": "Equation4557", "lhs": "Equation4561"}, + {"rhs": "Equation4562", "lhs": "Equation4566"}, + {"rhs": "Equation4567", "lhs": "Equation4571"}, + {"rhs": "Equation4572", "lhs": "Equation4576"}, + {"rhs": "Equation4557", "lhs": "Equation4577"}, + {"rhs": "Equation4558", "lhs": "Equation4578"}, + {"rhs": "Equation4559", "lhs": "Equation4579"}, + {"rhs": "Equation4560", "lhs": "Equation4580"}, + {"rhs": "Equation4557", "lhs": "Equation4581"}, + {"rhs": "Equation4624", "lhs": "Equation4628"}, + {"rhs": "Equation4649", "lhs": "Equation4653"}, + {"rhs": "Equation4668", "lhs": "Equation4671"}, + {"rhs": "Equation4681", "lhs": "Equation4683"}, + {"rhs": "Equation4686", "lhs": "Equation4688"}, + {"rhs": "Equation592", "lhs": "Equation613"}, + {"rhs": "Equation795", "lhs": "Equation816"}, + {"rhs": "Equation998", "lhs": "Equation1019"}, + {"rhs": "Equation1201", "lhs": "Equation1222"}, + {"rhs": "Equation1404", "lhs": "Equation1425"}, + {"rhs": "Equation1607", "lhs": "Equation1628"}, + {"rhs": "Equation1810", "lhs": "Equation1831"}, + {"rhs": "Equation2013", "lhs": "Equation2034"}, + {"rhs": "Equation2216", "lhs": "Equation2237"}, + {"rhs": "Equation2419", "lhs": "Equation2440"}, + {"rhs": "Equation2622", "lhs": "Equation2643"}, + {"rhs": "Equation2825", "lhs": "Equation2846"}, + {"rhs": "Equation3028", "lhs": "Equation3049"}, + {"rhs": "Equation3231", "lhs": "Equation3252"}, + {"rhs": "Equation3434", "lhs": "Equation3455"}, + {"rhs": "Equation3637", "lhs": "Equation3658"}, + {"rhs": "Equation3840", "lhs": "Equation3861"}, + 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{"rhs": "Equation940", "lhs": "Equation942"}, + {"rhs": "Equation957", "lhs": "Equation959"}, + {"rhs": "Equation974", "lhs": "Equation976"}, + {"rhs": "Equation991", "lhs": "Equation993"}, + {"rhs": "Equation996", "lhs": "Equation998"}, + {"rhs": "Equation1001", "lhs": "Equation1003"}, + {"rhs": "Equation1006", "lhs": "Equation1008"}, + {"rhs": "Equation1011", "lhs": "Equation1013"}, + {"rhs": "Equation1004", "lhs": "Equation1014"}, + {"rhs": "Equation1005", "lhs": "Equation1015"}, + {"rhs": "Equation1006", "lhs": "Equation1016"}, + {"rhs": "Equation1007", "lhs": "Equation1017"}, + {"rhs": "Equation1006", "lhs": "Equation1018"}, + {"rhs": "Equation1069", "lhs": "Equation1071"}, + {"rhs": "Equation1106", "lhs": "Equation1108"}, + {"rhs": "Equation1143", "lhs": "Equation1145"}, + {"rhs": "Equation1160", "lhs": "Equation1162"}, + {"rhs": "Equation1177", "lhs": "Equation1179"}, + {"rhs": "Equation1194", "lhs": "Equation1196"}, + {"rhs": "Equation1199", "lhs": "Equation1201"}, + {"rhs": 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"Equation610", "lhs": "Equation613"}, + {"rhs": "Equation813", "lhs": "Equation816"}, + {"rhs": "Equation1016", "lhs": "Equation1019"}, + {"rhs": "Equation1219", "lhs": "Equation1222"}, + {"rhs": "Equation1422", "lhs": "Equation1425"}, + {"rhs": "Equation1625", "lhs": "Equation1628"}, + {"rhs": "Equation1828", "lhs": "Equation1831"}, + {"rhs": "Equation2031", "lhs": "Equation2034"}, + {"rhs": "Equation2234", "lhs": "Equation2237"}, + {"rhs": "Equation2437", "lhs": "Equation2440"}, + {"rhs": "Equation2640", "lhs": "Equation2643"}, + {"rhs": "Equation2843", "lhs": "Equation2846"}, + {"rhs": "Equation3046", "lhs": "Equation3049"}, + {"rhs": "Equation3249", "lhs": "Equation3252"}, + {"rhs": "Equation3452", "lhs": "Equation3455"}, + {"rhs": "Equation3655", "lhs": "Equation3658"}, + {"rhs": "Equation3858", "lhs": "Equation3861"}, + {"rhs": "Equation4061", "lhs": "Equation4064"}, + {"rhs": "Equation4264", "lhs": "Equation4267"}, + {"rhs": "Equation4378", "lhs": "Equation4379"}, + {"rhs": "Equation4579", "lhs": "Equation4582"}, + {"rhs": "Equation4693", "lhs": "Equation4694"}, + {"rhs": "Equation19", "lhs": "Equation22"}, + {"rhs": "Equation34", "lhs": "Equation37"}, + {"rhs": "Equation58", "lhs": "Equation61"}, + {"rhs": "Equation68", "lhs": "Equation71"}, + {"rhs": "Equation78", "lhs": "Equation81"}, + {"rhs": "Equation82", "lhs": "Equation85"}, + {"rhs": "Equation86", "lhs": "Equation89"}, + {"rhs": "Equation90", "lhs": "Equation93"}, + {"rhs": "Equation82", "lhs": "Equation94"}, + {"rhs": "Equation83", "lhs": "Equation95"}, + {"rhs": "Equation84", "lhs": "Equation96"}, + {"rhs": "Equation82", "lhs": "Equation97"}, + {"rhs": "Equation110", "lhs": "Equation113"}, + {"rhs": "Equation120", "lhs": "Equation123"}, + {"rhs": "Equation130", "lhs": "Equation133"}, + {"rhs": "Equation134", "lhs": "Equation137"}, + {"rhs": "Equation138", "lhs": "Equation141"}, + {"rhs": "Equation142", "lhs": "Equation145"}, + {"rhs": "Equation134", "lhs": "Equation146"}, + {"rhs": "Equation135", "lhs": "Equation147"}, + {"rhs": "Equation136", "lhs": "Equation148"}, + {"rhs": "Equation134", "lhs": "Equation149"}, + {"rhs": "Equation162", "lhs": "Equation165"}, + {"rhs": "Equation172", "lhs": "Equation175"}, + {"rhs": "Equation182", "lhs": "Equation185"}, + {"rhs": "Equation186", "lhs": "Equation189"}, + {"rhs": "Equation190", "lhs": "Equation193"}, + {"rhs": "Equation194", "lhs": "Equation197"}, + {"rhs": "Equation186", "lhs": "Equation198"}, + {"rhs": "Equation187", "lhs": "Equation199"}, + {"rhs": "Equation188", "lhs": "Equation200"}, + {"rhs": "Equation186", "lhs": "Equation201"}, + {"rhs": "Equation214", "lhs": "Equation217"}, + {"rhs": "Equation224", "lhs": "Equation227"}, + {"rhs": "Equation234", "lhs": "Equation237"}, + {"rhs": "Equation238", "lhs": "Equation241"}, + {"rhs": "Equation242", "lhs": "Equation245"}, + {"rhs": "Equation246", "lhs": "Equation249"}, + {"rhs": "Equation238", "lhs": "Equation250"}, + {"rhs": "Equation239", "lhs": "Equation251"}, + {"rhs": "Equation240", "lhs": "Equation252"}, + {"rhs": "Equation238", "lhs": "Equation253"}, + {"rhs": "Equation266", "lhs": "Equation269"}, + {"rhs": "Equation276", "lhs": "Equation279"}, + {"rhs": "Equation286", "lhs": "Equation289"}, + {"rhs": "Equation290", "lhs": "Equation293"}, + {"rhs": "Equation294", "lhs": "Equation297"}, + {"rhs": "Equation298", "lhs": "Equation301"}, + {"rhs": "Equation290", "lhs": "Equation302"}, + {"rhs": "Equation291", "lhs": "Equation303"}, + {"rhs": "Equation292", "lhs": "Equation304"}, + {"rhs": "Equation290", "lhs": "Equation305"}, + {"rhs": "Equation318", "lhs": "Equation321"}, + {"rhs": "Equation328", "lhs": "Equation331"}, + {"rhs": "Equation338", "lhs": "Equation341"}, + {"rhs": "Equation342", "lhs": "Equation345"}, + {"rhs": "Equation346", "lhs": "Equation349"}, + {"rhs": "Equation350", "lhs": "Equation353"}, + {"rhs": "Equation342", "lhs": "Equation354"}, + {"rhs": "Equation343", "lhs": "Equation355"}, + {"rhs": "Equation344", "lhs": "Equation356"}, + {"rhs": "Equation342", "lhs": "Equation357"}, + {"rhs": "Equation370", "lhs": "Equation373"}, + {"rhs": "Equation380", "lhs": "Equation383"}, + {"rhs": "Equation390", "lhs": "Equation393"}, + {"rhs": "Equation394", "lhs": "Equation397"}, + {"rhs": "Equation398", "lhs": "Equation401"}, + {"rhs": "Equation402", "lhs": "Equation405"}, + {"rhs": "Equation394", "lhs": "Equation406"}, + {"rhs": "Equation395", "lhs": "Equation407"}, + {"rhs": "Equation396", "lhs": "Equation408"}, + {"rhs": "Equation394", "lhs": "Equation409"}, + {"rhs": "Equation422", "lhs": "Equation425"}, + {"rhs": "Equation432", "lhs": "Equation435"}, + {"rhs": "Equation442", "lhs": "Equation445"}, + {"rhs": "Equation446", "lhs": "Equation449"}, + {"rhs": "Equation450", "lhs": "Equation453"}, + {"rhs": "Equation454", "lhs": "Equation457"}, + {"rhs": "Equation446", "lhs": "Equation458"}, + {"rhs": "Equation447", "lhs": "Equation459"}, + {"rhs": "Equation448", "lhs": "Equation460"}, + {"rhs": "Equation446", "lhs": "Equation461"}, + {"rhs": "Equation469", "lhs": "Equation472"}, + {"rhs": "Equation479", "lhs": "Equation482"}, + {"rhs": "Equation483", "lhs": "Equation486"}, + {"rhs": "Equation487", "lhs": "Equation490"}, + {"rhs": "Equation491", "lhs": "Equation494"}, + {"rhs": "Equation483", "lhs": "Equation495"}, + {"rhs": "Equation484", "lhs": "Equation496"}, + {"rhs": "Equation485", "lhs": "Equation497"}, + {"rhs": "Equation483", "lhs": "Equation498"}, + {"rhs": "Equation506", "lhs": "Equation509"}, + {"rhs": "Equation516", "lhs": "Equation519"}, + {"rhs": "Equation520", "lhs": "Equation523"}, + {"rhs": "Equation524", "lhs": "Equation527"}, + {"rhs": "Equation528", "lhs": "Equation531"}, + {"rhs": "Equation520", "lhs": "Equation532"}, + {"rhs": "Equation521", "lhs": "Equation533"}, + {"rhs": "Equation522", "lhs": "Equation534"}, + {"rhs": "Equation520", "lhs": "Equation535"}, + {"rhs": "Equation537", "lhs": "Equation540"}, + {"rhs": "Equation541", "lhs": "Equation544"}, + {"rhs": "Equation545", "lhs": "Equation548"}, + {"rhs": "Equation537", "lhs": "Equation549"}, + {"rhs": "Equation538", "lhs": "Equation550"}, + {"rhs": "Equation539", "lhs": "Equation551"}, + {"rhs": "Equation537", "lhs": "Equation552"}, + {"rhs": "Equation554", "lhs": "Equation557"}, + {"rhs": "Equation558", "lhs": "Equation561"}, + {"rhs": "Equation562", "lhs": "Equation565"}, + {"rhs": "Equation554", "lhs": "Equation566"}, + {"rhs": "Equation555", "lhs": "Equation567"}, + {"rhs": "Equation556", "lhs": "Equation568"}, + {"rhs": "Equation554", "lhs": "Equation569"}, + {"rhs": "Equation571", "lhs": "Equation574"}, + {"rhs": "Equation575", "lhs": "Equation578"}, + {"rhs": "Equation579", "lhs": "Equation582"}, + {"rhs": "Equation571", "lhs": "Equation583"}, + {"rhs": "Equation572", "lhs": "Equation584"}, + {"rhs": "Equation573", "lhs": "Equation585"}, + {"rhs": "Equation571", "lhs": "Equation586"}, + {"rhs": "Equation537", "lhs": "Equation588"}, + {"rhs": "Equation538", "lhs": "Equation589"}, + {"rhs": "Equation539", "lhs": "Equation590"}, + {"rhs": "Equation537", "lhs": "Equation591"}, + {"rhs": "Equation541", "lhs": "Equation593"}, + {"rhs": "Equation542", "lhs": "Equation594"}, + {"rhs": "Equation543", "lhs": "Equation595"}, + {"rhs": "Equation541", "lhs": "Equation596"}, + {"rhs": "Equation545", "lhs": "Equation598"}, + {"rhs": "Equation546", "lhs": "Equation599"}, + {"rhs": "Equation547", "lhs": "Equation600"}, + {"rhs": "Equation545", "lhs": "Equation601"}, + {"rhs": "Equation537", "lhs": "Equation603"}, + {"rhs": "Equation538", "lhs": "Equation604"}, + {"rhs": "Equation539", "lhs": "Equation605"}, + {"rhs": "Equation537", "lhs": "Equation606"}, + {"rhs": "Equation625", "lhs": "Equation628"}, + {"rhs": "Equation635", "lhs": "Equation638"}, + {"rhs": "Equation645", "lhs": "Equation648"}, + {"rhs": "Equation649", "lhs": "Equation652"}, + {"rhs": "Equation653", "lhs": "Equation656"}, + {"rhs": "Equation657", "lhs": "Equation660"}, + {"rhs": "Equation649", "lhs": "Equation661"}, + {"rhs": "Equation650", "lhs": "Equation662"}, + {"rhs": "Equation651", "lhs": "Equation663"}, + {"rhs": "Equation649", "lhs": "Equation664"}, + {"rhs": "Equation672", "lhs": "Equation675"}, + {"rhs": "Equation682", "lhs": "Equation685"}, + {"rhs": "Equation686", "lhs": "Equation689"}, + {"rhs": "Equation690", "lhs": "Equation693"}, + {"rhs": "Equation694", "lhs": "Equation697"}, + {"rhs": "Equation686", "lhs": "Equation698"}, + {"rhs": "Equation687", "lhs": "Equation699"}, + {"rhs": "Equation688", "lhs": "Equation700"}, + {"rhs": "Equation686", "lhs": "Equation701"}, + {"rhs": "Equation709", "lhs": "Equation712"}, + {"rhs": "Equation719", "lhs": "Equation722"}, + {"rhs": "Equation723", "lhs": "Equation726"}, + {"rhs": "Equation727", "lhs": "Equation730"}, + {"rhs": "Equation731", "lhs": "Equation734"}, + {"rhs": "Equation723", "lhs": "Equation735"}, + {"rhs": "Equation724", "lhs": "Equation736"}, + {"rhs": "Equation725", "lhs": "Equation737"}, + {"rhs": "Equation723", "lhs": "Equation738"}, + {"rhs": "Equation740", "lhs": "Equation743"}, + {"rhs": "Equation744", "lhs": "Equation747"}, + {"rhs": "Equation748", "lhs": "Equation751"}, + {"rhs": "Equation740", "lhs": "Equation752"}, + {"rhs": "Equation741", "lhs": "Equation753"}, + {"rhs": "Equation742", "lhs": "Equation754"}, + {"rhs": "Equation740", "lhs": "Equation755"}, + {"rhs": "Equation757", "lhs": "Equation760"}, + {"rhs": "Equation761", "lhs": "Equation764"}, + {"rhs": "Equation765", "lhs": "Equation768"}, + {"rhs": "Equation757", "lhs": "Equation769"}, + {"rhs": "Equation758", "lhs": "Equation770"}, + {"rhs": "Equation759", "lhs": "Equation771"}, + {"rhs": "Equation757", "lhs": "Equation772"}, + {"rhs": "Equation774", "lhs": "Equation777"}, + {"rhs": "Equation778", "lhs": "Equation781"}, + {"rhs": "Equation782", "lhs": "Equation785"}, + {"rhs": "Equation774", "lhs": "Equation786"}, + {"rhs": "Equation775", "lhs": "Equation787"}, + {"rhs": "Equation776", "lhs": "Equation788"}, + {"rhs": "Equation774", "lhs": "Equation789"}, + {"rhs": "Equation740", "lhs": "Equation791"}, + {"rhs": "Equation741", "lhs": "Equation792"}, + {"rhs": "Equation742", "lhs": "Equation793"}, + {"rhs": "Equation740", "lhs": "Equation794"}, + {"rhs": "Equation744", "lhs": "Equation796"}, + {"rhs": "Equation745", "lhs": "Equation797"}, + {"rhs": "Equation746", "lhs": "Equation798"}, + {"rhs": "Equation744", "lhs": "Equation799"}, + {"rhs": "Equation748", "lhs": "Equation801"}, + {"rhs": "Equation749", "lhs": "Equation802"}, + {"rhs": "Equation750", "lhs": "Equation803"}, + {"rhs": "Equation748", "lhs": "Equation804"}, + {"rhs": "Equation740", "lhs": "Equation806"}, + {"rhs": "Equation741", "lhs": "Equation807"}, + {"rhs": "Equation742", "lhs": "Equation808"}, + {"rhs": "Equation740", "lhs": "Equation809"}, + {"rhs": "Equation828", "lhs": "Equation831"}, + {"rhs": "Equation838", "lhs": "Equation841"}, + {"rhs": "Equation848", "lhs": "Equation851"}, + {"rhs": "Equation852", "lhs": "Equation855"}, + {"rhs": "Equation856", "lhs": "Equation859"}, + {"rhs": "Equation860", "lhs": "Equation863"}, + {"rhs": "Equation852", "lhs": "Equation864"}, + {"rhs": "Equation853", "lhs": "Equation865"}, + {"rhs": "Equation854", "lhs": "Equation866"}, + {"rhs": "Equation852", "lhs": "Equation867"}, + {"rhs": "Equation875", "lhs": "Equation878"}, + {"rhs": "Equation885", "lhs": "Equation888"}, + {"rhs": "Equation889", "lhs": "Equation892"}, + {"rhs": "Equation893", "lhs": "Equation896"}, + {"rhs": "Equation897", "lhs": "Equation900"}, + {"rhs": "Equation889", "lhs": "Equation901"}, + {"rhs": "Equation890", "lhs": "Equation902"}, + {"rhs": "Equation891", "lhs": "Equation903"}, + {"rhs": "Equation889", "lhs": "Equation904"}, + {"rhs": "Equation912", "lhs": "Equation915"}, + {"rhs": "Equation922", "lhs": "Equation925"}, + {"rhs": "Equation926", "lhs": "Equation929"}, + {"rhs": "Equation930", "lhs": "Equation933"}, + {"rhs": "Equation934", "lhs": "Equation937"}, + {"rhs": "Equation926", "lhs": "Equation938"}, + {"rhs": "Equation927", "lhs": "Equation939"}, + {"rhs": "Equation928", "lhs": "Equation940"}, + {"rhs": "Equation926", "lhs": "Equation941"}, + {"rhs": "Equation943", "lhs": "Equation946"}, + {"rhs": "Equation947", "lhs": "Equation950"}, + {"rhs": "Equation951", "lhs": "Equation954"}, + {"rhs": "Equation943", "lhs": "Equation955"}, + {"rhs": "Equation944", "lhs": "Equation956"}, + {"rhs": "Equation945", "lhs": "Equation957"}, + {"rhs": "Equation943", "lhs": "Equation958"}, + {"rhs": "Equation960", "lhs": "Equation963"}, + {"rhs": "Equation964", "lhs": "Equation967"}, + {"rhs": "Equation968", "lhs": "Equation971"}, + {"rhs": "Equation960", "lhs": "Equation972"}, + {"rhs": "Equation961", "lhs": "Equation973"}, + {"rhs": "Equation962", "lhs": "Equation974"}, + {"rhs": "Equation960", "lhs": "Equation975"}, + {"rhs": "Equation977", "lhs": "Equation980"}, + {"rhs": "Equation981", "lhs": "Equation984"}, + {"rhs": "Equation985", "lhs": "Equation988"}, + {"rhs": "Equation977", "lhs": "Equation989"}, + {"rhs": "Equation978", "lhs": "Equation990"}, + {"rhs": "Equation979", "lhs": "Equation991"}, + {"rhs": "Equation977", "lhs": "Equation992"}, + {"rhs": "Equation943", "lhs": "Equation994"}, + {"rhs": "Equation944", "lhs": "Equation995"}, + {"rhs": "Equation945", "lhs": "Equation996"}, + {"rhs": "Equation943", "lhs": "Equation997"}, + {"rhs": "Equation947", "lhs": "Equation999"}, + {"rhs": "Equation948", "lhs": "Equation1000"}, + {"rhs": "Equation949", "lhs": "Equation1001"}, + {"rhs": "Equation947", "lhs": "Equation1002"}, + {"rhs": "Equation951", "lhs": "Equation1004"}, + {"rhs": "Equation952", "lhs": "Equation1005"}, + {"rhs": "Equation953", "lhs": "Equation1006"}, + {"rhs": "Equation951", "lhs": "Equation1007"}, + {"rhs": "Equation943", "lhs": "Equation1009"}, + {"rhs": "Equation944", "lhs": "Equation1010"}, + {"rhs": "Equation945", "lhs": "Equation1011"}, + {"rhs": "Equation943", "lhs": "Equation1012"}, + {"rhs": "Equation1031", "lhs": "Equation1034"}, + {"rhs": "Equation1041", "lhs": "Equation1044"}, + {"rhs": "Equation1051", "lhs": "Equation1054"}, + {"rhs": "Equation1055", "lhs": "Equation1058"}, + {"rhs": "Equation1059", "lhs": "Equation1062"}, + {"rhs": "Equation1063", "lhs": "Equation1066"}, + {"rhs": "Equation1055", "lhs": "Equation1067"}, + {"rhs": "Equation1056", "lhs": "Equation1068"}, + {"rhs": "Equation1057", "lhs": "Equation1069"}, + {"rhs": "Equation1055", "lhs": "Equation1070"}, + {"rhs": "Equation1078", "lhs": "Equation1081"}, + {"rhs": "Equation1088", "lhs": "Equation1091"}, + {"rhs": "Equation1092", "lhs": "Equation1095"}, + {"rhs": "Equation1096", "lhs": "Equation1099"}, + {"rhs": "Equation1100", "lhs": "Equation1103"}, + {"rhs": "Equation1092", "lhs": "Equation1104"}, + {"rhs": "Equation1093", "lhs": "Equation1105"}, + {"rhs": "Equation1094", "lhs": "Equation1106"}, + {"rhs": "Equation1092", "lhs": "Equation1107"}, + {"rhs": "Equation1115", "lhs": "Equation1118"}, + {"rhs": "Equation1125", "lhs": "Equation1128"}, + {"rhs": "Equation1129", "lhs": "Equation1132"}, + {"rhs": "Equation1133", "lhs": "Equation1136"}, + {"rhs": "Equation1137", "lhs": "Equation1140"}, + {"rhs": "Equation1129", "lhs": "Equation1141"}, + {"rhs": "Equation1130", "lhs": "Equation1142"}, + {"rhs": "Equation1131", "lhs": "Equation1143"}, + {"rhs": "Equation1129", "lhs": "Equation1144"}, + {"rhs": "Equation1146", "lhs": "Equation1149"}, + {"rhs": "Equation1150", "lhs": "Equation1153"}, + {"rhs": "Equation1154", "lhs": "Equation1157"}, + {"rhs": "Equation1146", "lhs": "Equation1158"}, + {"rhs": "Equation1147", "lhs": "Equation1159"}, + {"rhs": "Equation1148", "lhs": "Equation1160"}, + {"rhs": "Equation1146", "lhs": "Equation1161"}, + {"rhs": "Equation1163", "lhs": "Equation1166"}, + {"rhs": "Equation1167", "lhs": "Equation1170"}, + {"rhs": "Equation1171", "lhs": "Equation1174"}, + {"rhs": "Equation1163", "lhs": "Equation1175"}, + {"rhs": "Equation1164", "lhs": "Equation1176"}, + {"rhs": "Equation1165", "lhs": "Equation1177"}, + {"rhs": "Equation1163", "lhs": "Equation1178"}, + {"rhs": "Equation1180", "lhs": "Equation1183"}, + {"rhs": "Equation1184", "lhs": "Equation1187"}, + {"rhs": "Equation1188", "lhs": "Equation1191"}, + {"rhs": "Equation1180", "lhs": "Equation1192"}, + {"rhs": "Equation1181", "lhs": "Equation1193"}, + {"rhs": "Equation1182", "lhs": "Equation1194"}, + {"rhs": "Equation1180", "lhs": "Equation1195"}, + {"rhs": "Equation1146", "lhs": "Equation1197"}, + {"rhs": "Equation1147", "lhs": "Equation1198"}, + {"rhs": "Equation1148", "lhs": "Equation1199"}, + {"rhs": "Equation1146", "lhs": "Equation1200"}, + {"rhs": "Equation1150", "lhs": "Equation1202"}, + {"rhs": "Equation1151", "lhs": "Equation1203"}, + {"rhs": "Equation1152", "lhs": "Equation1204"}, + {"rhs": "Equation1150", "lhs": "Equation1205"}, + {"rhs": "Equation1154", "lhs": "Equation1207"}, + {"rhs": "Equation1155", "lhs": "Equation1208"}, + {"rhs": "Equation1156", "lhs": "Equation1209"}, + {"rhs": "Equation1154", "lhs": "Equation1210"}, + {"rhs": "Equation1146", "lhs": "Equation1212"}, + {"rhs": "Equation1147", "lhs": "Equation1213"}, + {"rhs": "Equation1148", "lhs": "Equation1214"}, + {"rhs": "Equation1146", "lhs": "Equation1215"}, + {"rhs": "Equation1234", "lhs": "Equation1237"}, + {"rhs": "Equation1244", "lhs": "Equation1247"}, + {"rhs": "Equation1254", "lhs": "Equation1257"}, + {"rhs": "Equation1258", "lhs": "Equation1261"}, + {"rhs": "Equation1262", "lhs": "Equation1265"}, + {"rhs": "Equation1266", "lhs": "Equation1269"}, + {"rhs": "Equation1258", "lhs": "Equation1270"}, + {"rhs": "Equation1259", "lhs": "Equation1271"}, + {"rhs": "Equation1260", "lhs": "Equation1272"}, + {"rhs": "Equation1258", "lhs": "Equation1273"}, + {"rhs": "Equation1281", "lhs": "Equation1284"}, + {"rhs": "Equation1291", "lhs": "Equation1294"}, + {"rhs": "Equation1295", "lhs": "Equation1298"}, + {"rhs": "Equation1299", "lhs": "Equation1302"}, + {"rhs": "Equation1303", "lhs": "Equation1306"}, + {"rhs": "Equation1295", "lhs": "Equation1307"}, + {"rhs": "Equation1296", "lhs": "Equation1308"}, + {"rhs": "Equation1297", "lhs": "Equation1309"}, + {"rhs": "Equation1295", "lhs": "Equation1310"}, + {"rhs": "Equation1318", "lhs": "Equation1321"}, + {"rhs": "Equation1328", "lhs": "Equation1331"}, + {"rhs": "Equation1332", "lhs": "Equation1335"}, + {"rhs": "Equation1336", "lhs": "Equation1339"}, + {"rhs": "Equation1340", "lhs": "Equation1343"}, + {"rhs": "Equation1332", "lhs": "Equation1344"}, + {"rhs": "Equation1333", "lhs": "Equation1345"}, + {"rhs": "Equation1334", "lhs": "Equation1346"}, + {"rhs": "Equation1332", "lhs": "Equation1347"}, + {"rhs": "Equation1349", "lhs": "Equation1352"}, + {"rhs": "Equation1353", "lhs": "Equation1356"}, + {"rhs": "Equation1357", "lhs": "Equation1360"}, + {"rhs": "Equation1349", "lhs": "Equation1361"}, + {"rhs": "Equation1350", "lhs": "Equation1362"}, + {"rhs": "Equation1351", "lhs": "Equation1363"}, + {"rhs": "Equation1349", "lhs": "Equation1364"}, + {"rhs": "Equation1366", "lhs": "Equation1369"}, + {"rhs": "Equation1370", "lhs": "Equation1373"}, + {"rhs": "Equation1374", "lhs": "Equation1377"}, + {"rhs": "Equation1366", "lhs": "Equation1378"}, + {"rhs": "Equation1367", "lhs": "Equation1379"}, + {"rhs": "Equation1368", "lhs": "Equation1380"}, + {"rhs": "Equation1366", "lhs": "Equation1381"}, + {"rhs": "Equation1383", "lhs": "Equation1386"}, + {"rhs": "Equation1387", "lhs": "Equation1390"}, + {"rhs": "Equation1391", "lhs": "Equation1394"}, + {"rhs": "Equation1383", "lhs": "Equation1395"}, + {"rhs": "Equation1384", "lhs": "Equation1396"}, + {"rhs": "Equation1385", "lhs": "Equation1397"}, + {"rhs": "Equation1383", "lhs": "Equation1398"}, + {"rhs": "Equation1349", "lhs": "Equation1400"}, + {"rhs": "Equation1350", "lhs": "Equation1401"}, + {"rhs": "Equation1351", "lhs": "Equation1402"}, + {"rhs": "Equation1349", "lhs": "Equation1403"}, + {"rhs": "Equation1353", "lhs": "Equation1405"}, + {"rhs": "Equation1354", "lhs": "Equation1406"}, + {"rhs": "Equation1355", "lhs": "Equation1407"}, + {"rhs": "Equation1353", "lhs": "Equation1408"}, + {"rhs": "Equation1357", "lhs": "Equation1410"}, + {"rhs": "Equation1358", "lhs": "Equation1411"}, + {"rhs": "Equation1359", "lhs": "Equation1412"}, + {"rhs": "Equation1357", "lhs": "Equation1413"}, + {"rhs": "Equation1349", "lhs": "Equation1415"}, + {"rhs": "Equation1350", "lhs": "Equation1416"}, + {"rhs": "Equation1351", "lhs": "Equation1417"}, + {"rhs": "Equation1349", "lhs": "Equation1418"}, + {"rhs": "Equation1437", "lhs": "Equation1440"}, + {"rhs": "Equation1447", "lhs": "Equation1450"}, + {"rhs": "Equation1457", "lhs": "Equation1460"}, + {"rhs": "Equation1461", "lhs": "Equation1464"}, + {"rhs": "Equation1465", "lhs": "Equation1468"}, + {"rhs": "Equation1469", "lhs": "Equation1472"}, + {"rhs": "Equation1461", "lhs": "Equation1473"}, + {"rhs": "Equation1462", "lhs": "Equation1474"}, + {"rhs": "Equation1463", "lhs": "Equation1475"}, + {"rhs": "Equation1461", "lhs": "Equation1476"}, + {"rhs": "Equation1484", "lhs": "Equation1487"}, + {"rhs": "Equation1494", "lhs": "Equation1497"}, + {"rhs": "Equation1498", "lhs": "Equation1501"}, + {"rhs": "Equation1502", "lhs": "Equation1505"}, + {"rhs": "Equation1506", "lhs": "Equation1509"}, + {"rhs": "Equation1498", "lhs": "Equation1510"}, + {"rhs": "Equation1499", "lhs": "Equation1511"}, + {"rhs": "Equation1500", "lhs": "Equation1512"}, + {"rhs": "Equation1498", "lhs": "Equation1513"}, + {"rhs": "Equation1521", "lhs": "Equation1524"}, + {"rhs": "Equation1531", "lhs": "Equation1534"}, + {"rhs": "Equation1535", "lhs": "Equation1538"}, + {"rhs": "Equation1539", "lhs": "Equation1542"}, + {"rhs": "Equation1543", "lhs": "Equation1546"}, + {"rhs": "Equation1535", "lhs": "Equation1547"}, + {"rhs": "Equation1536", "lhs": "Equation1548"}, + {"rhs": "Equation1537", "lhs": "Equation1549"}, + {"rhs": "Equation1535", "lhs": "Equation1550"}, + {"rhs": "Equation1552", "lhs": "Equation1555"}, + {"rhs": "Equation1556", "lhs": "Equation1559"}, + {"rhs": "Equation1560", "lhs": "Equation1563"}, + {"rhs": "Equation1552", "lhs": "Equation1564"}, + {"rhs": "Equation1553", "lhs": "Equation1565"}, + {"rhs": "Equation1554", "lhs": "Equation1566"}, + {"rhs": "Equation1552", "lhs": "Equation1567"}, + {"rhs": "Equation1569", "lhs": "Equation1572"}, + {"rhs": "Equation1573", "lhs": "Equation1576"}, + {"rhs": "Equation1577", "lhs": "Equation1580"}, + {"rhs": "Equation1569", "lhs": "Equation1581"}, + {"rhs": "Equation1570", "lhs": "Equation1582"}, + {"rhs": "Equation1571", "lhs": "Equation1583"}, + {"rhs": "Equation1569", "lhs": "Equation1584"}, + {"rhs": "Equation1586", "lhs": "Equation1589"}, + {"rhs": "Equation1590", "lhs": "Equation1593"}, + {"rhs": "Equation1594", "lhs": "Equation1597"}, + {"rhs": "Equation1586", "lhs": "Equation1598"}, + {"rhs": "Equation1587", "lhs": "Equation1599"}, + {"rhs": "Equation1588", "lhs": "Equation1600"}, + {"rhs": "Equation1586", "lhs": "Equation1601"}, + {"rhs": "Equation1552", "lhs": "Equation1603"}, + {"rhs": "Equation1553", "lhs": "Equation1604"}, + {"rhs": "Equation1554", "lhs": "Equation1605"}, + {"rhs": "Equation1552", "lhs": "Equation1606"}, + {"rhs": "Equation1556", "lhs": "Equation1608"}, + {"rhs": "Equation1557", "lhs": "Equation1609"}, + {"rhs": "Equation1558", "lhs": "Equation1610"}, + {"rhs": "Equation1556", "lhs": "Equation1611"}, + {"rhs": "Equation1560", "lhs": "Equation1613"}, + {"rhs": "Equation1561", "lhs": "Equation1614"}, + {"rhs": "Equation1562", "lhs": "Equation1615"}, + {"rhs": "Equation1560", "lhs": "Equation1616"}, + {"rhs": "Equation1552", "lhs": "Equation1618"}, + {"rhs": "Equation1553", "lhs": "Equation1619"}, + {"rhs": "Equation1554", "lhs": "Equation1620"}, + {"rhs": "Equation1552", "lhs": "Equation1621"}, + {"rhs": "Equation1640", "lhs": "Equation1643"}, + {"rhs": "Equation1650", "lhs": "Equation1653"}, + {"rhs": "Equation1660", "lhs": "Equation1663"}, + {"rhs": "Equation1664", "lhs": "Equation1667"}, + {"rhs": "Equation1668", "lhs": "Equation1671"}, + {"rhs": "Equation1672", "lhs": "Equation1675"}, + {"rhs": "Equation1664", "lhs": "Equation1676"}, + {"rhs": "Equation1665", "lhs": "Equation1677"}, + {"rhs": "Equation1666", "lhs": "Equation1678"}, + {"rhs": "Equation1664", "lhs": "Equation1679"}, + {"rhs": "Equation1687", "lhs": "Equation1690"}, + {"rhs": "Equation1697", "lhs": "Equation1700"}, + {"rhs": "Equation1701", "lhs": "Equation1704"}, + {"rhs": "Equation1705", "lhs": "Equation1708"}, + {"rhs": "Equation1709", "lhs": "Equation1712"}, + {"rhs": "Equation1701", "lhs": "Equation1713"}, + {"rhs": "Equation1702", "lhs": "Equation1714"}, + {"rhs": "Equation1703", "lhs": "Equation1715"}, + {"rhs": "Equation1701", "lhs": "Equation1716"}, + {"rhs": "Equation1724", "lhs": "Equation1727"}, + {"rhs": "Equation1734", "lhs": "Equation1737"}, + {"rhs": "Equation1738", "lhs": "Equation1741"}, + {"rhs": "Equation1742", "lhs": "Equation1745"}, + {"rhs": "Equation1746", "lhs": "Equation1749"}, + {"rhs": "Equation1738", "lhs": "Equation1750"}, + {"rhs": "Equation1739", "lhs": "Equation1751"}, + {"rhs": "Equation1740", "lhs": "Equation1752"}, + {"rhs": "Equation1738", "lhs": "Equation1753"}, + {"rhs": "Equation1755", "lhs": "Equation1758"}, + {"rhs": "Equation1759", "lhs": "Equation1762"}, + {"rhs": "Equation1763", "lhs": "Equation1766"}, + {"rhs": "Equation1755", "lhs": "Equation1767"}, + {"rhs": "Equation1756", "lhs": "Equation1768"}, + {"rhs": "Equation1757", "lhs": "Equation1769"}, + {"rhs": "Equation1755", "lhs": "Equation1770"}, + {"rhs": "Equation1772", "lhs": "Equation1775"}, + {"rhs": "Equation1776", "lhs": "Equation1779"}, + {"rhs": "Equation1780", "lhs": "Equation1783"}, + {"rhs": "Equation1772", "lhs": "Equation1784"}, + {"rhs": "Equation1773", "lhs": "Equation1785"}, + {"rhs": "Equation1774", "lhs": "Equation1786"}, + {"rhs": "Equation1772", "lhs": "Equation1787"}, + {"rhs": "Equation1789", "lhs": "Equation1792"}, + {"rhs": "Equation1793", "lhs": "Equation1796"}, + {"rhs": "Equation1797", "lhs": "Equation1800"}, + {"rhs": "Equation1789", "lhs": "Equation1801"}, + {"rhs": "Equation1790", "lhs": "Equation1802"}, + {"rhs": "Equation1791", "lhs": "Equation1803"}, + {"rhs": "Equation1789", "lhs": "Equation1804"}, + {"rhs": "Equation1755", "lhs": "Equation1806"}, + {"rhs": "Equation1756", "lhs": "Equation1807"}, + {"rhs": "Equation1757", "lhs": "Equation1808"}, + {"rhs": "Equation1755", "lhs": "Equation1809"}, + {"rhs": "Equation1759", "lhs": "Equation1811"}, + {"rhs": "Equation1760", "lhs": "Equation1812"}, + {"rhs": "Equation1761", "lhs": "Equation1813"}, + {"rhs": "Equation1759", "lhs": "Equation1814"}, + {"rhs": "Equation1763", "lhs": "Equation1816"}, + {"rhs": "Equation1764", "lhs": "Equation1817"}, + {"rhs": "Equation1765", "lhs": "Equation1818"}, + {"rhs": "Equation1763", "lhs": "Equation1819"}, + {"rhs": "Equation1755", "lhs": "Equation1821"}, + {"rhs": "Equation1756", "lhs": "Equation1822"}, + {"rhs": "Equation1757", "lhs": "Equation1823"}, + {"rhs": "Equation1755", "lhs": "Equation1824"}, + {"rhs": "Equation1843", "lhs": "Equation1846"}, + {"rhs": "Equation1853", "lhs": "Equation1856"}, + {"rhs": "Equation1863", "lhs": "Equation1866"}, + {"rhs": "Equation1867", "lhs": "Equation1870"}, + {"rhs": "Equation1871", "lhs": "Equation1874"}, + {"rhs": "Equation1875", "lhs": "Equation1878"}, + {"rhs": "Equation1867", "lhs": "Equation1879"}, + {"rhs": "Equation1868", "lhs": "Equation1880"}, + {"rhs": "Equation1869", "lhs": "Equation1881"}, + {"rhs": "Equation1867", "lhs": "Equation1882"}, + {"rhs": "Equation1890", "lhs": "Equation1893"}, + {"rhs": "Equation1900", "lhs": "Equation1903"}, + {"rhs": "Equation1904", "lhs": "Equation1907"}, + {"rhs": "Equation1908", "lhs": "Equation1911"}, + {"rhs": "Equation1912", "lhs": "Equation1915"}, + {"rhs": "Equation1904", "lhs": "Equation1916"}, + {"rhs": "Equation1905", "lhs": "Equation1917"}, + {"rhs": "Equation1906", "lhs": "Equation1918"}, + {"rhs": "Equation1904", "lhs": "Equation1919"}, + {"rhs": "Equation1927", "lhs": "Equation1930"}, + {"rhs": "Equation1937", "lhs": "Equation1940"}, + {"rhs": "Equation1941", "lhs": "Equation1944"}, + {"rhs": "Equation1945", "lhs": "Equation1948"}, + {"rhs": "Equation1949", "lhs": "Equation1952"}, + {"rhs": "Equation1941", "lhs": "Equation1953"}, + {"rhs": "Equation1942", "lhs": "Equation1954"}, + {"rhs": "Equation1943", "lhs": "Equation1955"}, + {"rhs": "Equation1941", "lhs": "Equation1956"}, + {"rhs": "Equation1958", "lhs": "Equation1961"}, + {"rhs": "Equation1962", "lhs": "Equation1965"}, + {"rhs": "Equation1966", "lhs": "Equation1969"}, + {"rhs": "Equation1958", "lhs": "Equation1970"}, + {"rhs": "Equation1959", "lhs": "Equation1971"}, + {"rhs": "Equation1960", "lhs": "Equation1972"}, + {"rhs": "Equation1958", "lhs": "Equation1973"}, + {"rhs": "Equation1975", "lhs": "Equation1978"}, + {"rhs": "Equation1979", "lhs": "Equation1982"}, + {"rhs": "Equation1983", "lhs": "Equation1986"}, + {"rhs": "Equation1975", "lhs": "Equation1987"}, + {"rhs": "Equation1976", "lhs": "Equation1988"}, + {"rhs": "Equation1977", "lhs": "Equation1989"}, + {"rhs": "Equation1975", "lhs": "Equation1990"}, + {"rhs": "Equation1992", "lhs": "Equation1995"}, + {"rhs": "Equation1996", "lhs": "Equation1999"}, + {"rhs": "Equation2000", "lhs": "Equation2003"}, + {"rhs": "Equation1992", "lhs": "Equation2004"}, + {"rhs": "Equation1993", "lhs": "Equation2005"}, + {"rhs": "Equation1994", "lhs": "Equation2006"}, + {"rhs": "Equation1992", "lhs": "Equation2007"}, + {"rhs": "Equation1958", "lhs": "Equation2009"}, + {"rhs": "Equation1959", "lhs": "Equation2010"}, + {"rhs": "Equation1960", "lhs": "Equation2011"}, + {"rhs": "Equation1958", "lhs": "Equation2012"}, + {"rhs": "Equation1962", "lhs": "Equation2014"}, + {"rhs": "Equation1963", "lhs": "Equation2015"}, + {"rhs": "Equation1964", "lhs": "Equation2016"}, + {"rhs": "Equation1962", "lhs": "Equation2017"}, + {"rhs": "Equation1966", "lhs": "Equation2019"}, + {"rhs": "Equation1967", "lhs": "Equation2020"}, + {"rhs": "Equation1968", "lhs": "Equation2021"}, + {"rhs": "Equation1966", "lhs": "Equation2022"}, + {"rhs": "Equation1958", "lhs": "Equation2024"}, + {"rhs": "Equation1959", "lhs": "Equation2025"}, + {"rhs": "Equation1960", "lhs": "Equation2026"}, + {"rhs": "Equation1958", "lhs": "Equation2027"}, + {"rhs": "Equation2046", "lhs": "Equation2049"}, + {"rhs": "Equation2056", "lhs": "Equation2059"}, + {"rhs": "Equation2066", "lhs": "Equation2069"}, + {"rhs": "Equation2070", "lhs": "Equation2073"}, + {"rhs": "Equation2074", "lhs": "Equation2077"}, + {"rhs": "Equation2078", "lhs": "Equation2081"}, + {"rhs": "Equation2070", "lhs": "Equation2082"}, + {"rhs": "Equation2071", "lhs": "Equation2083"}, + {"rhs": "Equation2072", "lhs": "Equation2084"}, + {"rhs": "Equation2070", "lhs": "Equation2085"}, + {"rhs": "Equation2093", "lhs": "Equation2096"}, + {"rhs": "Equation2103", "lhs": "Equation2106"}, + {"rhs": "Equation2107", "lhs": "Equation2110"}, + {"rhs": "Equation2111", "lhs": "Equation2114"}, + {"rhs": "Equation2115", "lhs": "Equation2118"}, + {"rhs": "Equation2107", "lhs": "Equation2119"}, + {"rhs": "Equation2108", "lhs": "Equation2120"}, + {"rhs": "Equation2109", "lhs": "Equation2121"}, + {"rhs": "Equation2107", "lhs": "Equation2122"}, + {"rhs": "Equation2130", "lhs": "Equation2133"}, + {"rhs": "Equation2140", "lhs": "Equation2143"}, + {"rhs": "Equation2144", "lhs": "Equation2147"}, + {"rhs": "Equation2148", "lhs": "Equation2151"}, + {"rhs": "Equation2152", "lhs": "Equation2155"}, + {"rhs": "Equation2144", "lhs": "Equation2156"}, + {"rhs": "Equation2145", "lhs": "Equation2157"}, + {"rhs": "Equation2146", "lhs": "Equation2158"}, + {"rhs": "Equation2144", "lhs": "Equation2159"}, + {"rhs": "Equation2161", "lhs": "Equation2164"}, + {"rhs": "Equation2165", "lhs": "Equation2168"}, + {"rhs": "Equation2169", "lhs": "Equation2172"}, + {"rhs": "Equation2161", "lhs": "Equation2173"}, + {"rhs": "Equation2162", "lhs": "Equation2174"}, + {"rhs": "Equation2163", "lhs": "Equation2175"}, + {"rhs": "Equation2161", "lhs": "Equation2176"}, + {"rhs": "Equation2178", "lhs": "Equation2181"}, + {"rhs": "Equation2182", "lhs": "Equation2185"}, + {"rhs": "Equation2186", "lhs": "Equation2189"}, + {"rhs": "Equation2178", "lhs": "Equation2190"}, + {"rhs": "Equation2179", "lhs": "Equation2191"}, + {"rhs": "Equation2180", "lhs": "Equation2192"}, + {"rhs": "Equation2178", "lhs": "Equation2193"}, + {"rhs": "Equation2195", "lhs": "Equation2198"}, + {"rhs": "Equation2199", "lhs": "Equation2202"}, + {"rhs": "Equation2203", "lhs": "Equation2206"}, + {"rhs": "Equation2195", "lhs": "Equation2207"}, + {"rhs": "Equation2196", "lhs": "Equation2208"}, + {"rhs": "Equation2197", "lhs": "Equation2209"}, + {"rhs": "Equation2195", "lhs": "Equation2210"}, + {"rhs": "Equation2161", "lhs": "Equation2212"}, + {"rhs": "Equation2162", "lhs": "Equation2213"}, + {"rhs": "Equation2163", "lhs": "Equation2214"}, + {"rhs": "Equation2161", "lhs": "Equation2215"}, + {"rhs": "Equation2165", "lhs": "Equation2217"}, + {"rhs": "Equation2166", "lhs": "Equation2218"}, + {"rhs": "Equation2167", "lhs": "Equation2219"}, + {"rhs": "Equation2165", "lhs": "Equation2220"}, + {"rhs": "Equation2169", "lhs": "Equation2222"}, + {"rhs": "Equation2170", "lhs": "Equation2223"}, + {"rhs": "Equation2171", "lhs": "Equation2224"}, + {"rhs": "Equation2169", "lhs": "Equation2225"}, + {"rhs": "Equation2161", "lhs": "Equation2227"}, + {"rhs": "Equation2162", "lhs": "Equation2228"}, + {"rhs": "Equation2163", "lhs": "Equation2229"}, + {"rhs": "Equation2161", "lhs": "Equation2230"}, + {"rhs": "Equation2249", "lhs": "Equation2252"}, + {"rhs": "Equation2259", "lhs": "Equation2262"}, + {"rhs": "Equation2269", "lhs": "Equation2272"}, + {"rhs": "Equation2273", "lhs": "Equation2276"}, + {"rhs": "Equation2277", "lhs": "Equation2280"}, + {"rhs": "Equation2281", "lhs": "Equation2284"}, + {"rhs": "Equation2273", "lhs": "Equation2285"}, + {"rhs": "Equation2274", "lhs": "Equation2286"}, + {"rhs": "Equation2275", "lhs": "Equation2287"}, + {"rhs": "Equation2273", "lhs": "Equation2288"}, + {"rhs": "Equation2296", "lhs": "Equation2299"}, + {"rhs": "Equation2306", "lhs": "Equation2309"}, + {"rhs": "Equation2310", "lhs": "Equation2313"}, + {"rhs": "Equation2314", "lhs": "Equation2317"}, + {"rhs": "Equation2318", "lhs": "Equation2321"}, + {"rhs": "Equation2310", "lhs": "Equation2322"}, + {"rhs": "Equation2311", "lhs": "Equation2323"}, + {"rhs": "Equation2312", "lhs": "Equation2324"}, + {"rhs": "Equation2310", "lhs": "Equation2325"}, + {"rhs": "Equation2333", "lhs": "Equation2336"}, + {"rhs": "Equation2343", "lhs": "Equation2346"}, + {"rhs": "Equation2347", "lhs": "Equation2350"}, + {"rhs": "Equation2351", "lhs": "Equation2354"}, + {"rhs": "Equation2355", "lhs": "Equation2358"}, + {"rhs": "Equation2347", "lhs": "Equation2359"}, + {"rhs": "Equation2348", "lhs": "Equation2360"}, + {"rhs": "Equation2349", "lhs": "Equation2361"}, + {"rhs": "Equation2347", "lhs": "Equation2362"}, + {"rhs": "Equation2364", "lhs": "Equation2367"}, + {"rhs": "Equation2368", "lhs": "Equation2371"}, + {"rhs": "Equation2372", "lhs": "Equation2375"}, + {"rhs": "Equation2364", "lhs": "Equation2376"}, + {"rhs": "Equation2365", "lhs": "Equation2377"}, + {"rhs": "Equation2366", "lhs": "Equation2378"}, + {"rhs": "Equation2364", "lhs": "Equation2379"}, + {"rhs": "Equation2381", "lhs": "Equation2384"}, + {"rhs": "Equation2385", "lhs": "Equation2388"}, + {"rhs": "Equation2389", "lhs": "Equation2392"}, + {"rhs": "Equation2381", "lhs": "Equation2393"}, + {"rhs": "Equation2382", "lhs": "Equation2394"}, + {"rhs": "Equation2383", "lhs": "Equation2395"}, + {"rhs": "Equation2381", "lhs": "Equation2396"}, + {"rhs": "Equation2398", "lhs": "Equation2401"}, + {"rhs": "Equation2402", "lhs": "Equation2405"}, + {"rhs": "Equation2406", "lhs": "Equation2409"}, + {"rhs": "Equation2398", "lhs": "Equation2410"}, + {"rhs": "Equation2399", "lhs": "Equation2411"}, + {"rhs": "Equation2400", "lhs": "Equation2412"}, + {"rhs": "Equation2398", "lhs": "Equation2413"}, + {"rhs": "Equation2364", "lhs": "Equation2415"}, + {"rhs": "Equation2365", "lhs": "Equation2416"}, + {"rhs": "Equation2366", "lhs": "Equation2417"}, + {"rhs": "Equation2364", "lhs": "Equation2418"}, + {"rhs": "Equation2368", "lhs": "Equation2420"}, + {"rhs": "Equation2369", "lhs": "Equation2421"}, + {"rhs": "Equation2370", "lhs": "Equation2422"}, + {"rhs": "Equation2368", "lhs": "Equation2423"}, + {"rhs": "Equation2372", "lhs": "Equation2425"}, + {"rhs": "Equation2373", "lhs": "Equation2426"}, + {"rhs": "Equation2374", "lhs": "Equation2427"}, + {"rhs": "Equation2372", "lhs": "Equation2428"}, + {"rhs": "Equation2364", "lhs": "Equation2430"}, + {"rhs": "Equation2365", "lhs": "Equation2431"}, + {"rhs": "Equation2366", "lhs": "Equation2432"}, + {"rhs": "Equation2364", "lhs": "Equation2433"}, + {"rhs": "Equation2452", "lhs": "Equation2455"}, + {"rhs": "Equation2462", "lhs": "Equation2465"}, + {"rhs": "Equation2472", "lhs": "Equation2475"}, + {"rhs": "Equation2476", "lhs": "Equation2479"}, + {"rhs": "Equation2480", "lhs": "Equation2483"}, + {"rhs": "Equation2484", "lhs": "Equation2487"}, + {"rhs": "Equation2476", "lhs": "Equation2488"}, + {"rhs": "Equation2477", "lhs": "Equation2489"}, + {"rhs": "Equation2478", "lhs": "Equation2490"}, + {"rhs": "Equation2476", "lhs": "Equation2491"}, + {"rhs": "Equation2499", "lhs": "Equation2502"}, + {"rhs": "Equation2509", "lhs": "Equation2512"}, + {"rhs": "Equation2513", "lhs": "Equation2516"}, + {"rhs": "Equation2517", "lhs": "Equation2520"}, + {"rhs": "Equation2521", "lhs": "Equation2524"}, + {"rhs": "Equation2513", "lhs": "Equation2525"}, + {"rhs": "Equation2514", "lhs": "Equation2526"}, + {"rhs": "Equation2515", "lhs": "Equation2527"}, + {"rhs": "Equation2513", "lhs": "Equation2528"}, + {"rhs": "Equation2536", "lhs": "Equation2539"}, + {"rhs": "Equation2546", "lhs": "Equation2549"}, + {"rhs": "Equation2550", "lhs": "Equation2553"}, + {"rhs": "Equation2554", "lhs": "Equation2557"}, + {"rhs": "Equation2558", "lhs": "Equation2561"}, + {"rhs": "Equation2550", "lhs": "Equation2562"}, + {"rhs": "Equation2551", "lhs": "Equation2563"}, + {"rhs": "Equation2552", "lhs": "Equation2564"}, + {"rhs": "Equation2550", "lhs": "Equation2565"}, + {"rhs": "Equation2567", "lhs": "Equation2570"}, + {"rhs": "Equation2571", "lhs": "Equation2574"}, + {"rhs": "Equation2575", "lhs": "Equation2578"}, + {"rhs": "Equation2567", "lhs": "Equation2579"}, + {"rhs": "Equation2568", "lhs": "Equation2580"}, + {"rhs": "Equation2569", "lhs": "Equation2581"}, + {"rhs": "Equation2567", "lhs": "Equation2582"}, + {"rhs": "Equation2584", "lhs": "Equation2587"}, + {"rhs": "Equation2588", "lhs": "Equation2591"}, + {"rhs": "Equation2592", "lhs": "Equation2595"}, + {"rhs": "Equation2584", "lhs": "Equation2596"}, + {"rhs": "Equation2585", "lhs": "Equation2597"}, + {"rhs": "Equation2586", "lhs": "Equation2598"}, + {"rhs": "Equation2584", "lhs": "Equation2599"}, + {"rhs": "Equation2601", "lhs": "Equation2604"}, + {"rhs": "Equation2605", "lhs": "Equation2608"}, + {"rhs": "Equation2609", "lhs": "Equation2612"}, + {"rhs": "Equation2601", "lhs": "Equation2613"}, + {"rhs": "Equation2602", "lhs": "Equation2614"}, + {"rhs": "Equation2603", "lhs": "Equation2615"}, + {"rhs": "Equation2601", "lhs": "Equation2616"}, + {"rhs": "Equation2567", "lhs": "Equation2618"}, + {"rhs": "Equation2568", "lhs": "Equation2619"}, + {"rhs": "Equation2569", "lhs": "Equation2620"}, + {"rhs": "Equation2567", "lhs": "Equation2621"}, + {"rhs": "Equation2571", "lhs": "Equation2623"}, + {"rhs": "Equation2572", "lhs": "Equation2624"}, + {"rhs": "Equation2573", "lhs": "Equation2625"}, + {"rhs": "Equation2571", "lhs": "Equation2626"}, + {"rhs": "Equation2575", "lhs": "Equation2628"}, + {"rhs": "Equation2576", "lhs": "Equation2629"}, + {"rhs": "Equation2577", "lhs": "Equation2630"}, + {"rhs": "Equation2575", "lhs": "Equation2631"}, + {"rhs": "Equation2567", "lhs": "Equation2633"}, + {"rhs": "Equation2568", "lhs": "Equation2634"}, + {"rhs": "Equation2569", "lhs": "Equation2635"}, + {"rhs": "Equation2567", "lhs": "Equation2636"}, + {"rhs": "Equation2655", "lhs": "Equation2658"}, + {"rhs": "Equation2665", "lhs": "Equation2668"}, + {"rhs": "Equation2675", "lhs": "Equation2678"}, + {"rhs": "Equation2679", "lhs": "Equation2682"}, + {"rhs": "Equation2683", "lhs": "Equation2686"}, + {"rhs": "Equation2687", "lhs": "Equation2690"}, + {"rhs": "Equation2679", "lhs": "Equation2691"}, + {"rhs": "Equation2680", "lhs": "Equation2692"}, + {"rhs": "Equation2681", "lhs": "Equation2693"}, + {"rhs": "Equation2679", "lhs": "Equation2694"}, + {"rhs": "Equation2702", "lhs": "Equation2705"}, + {"rhs": "Equation2712", "lhs": "Equation2715"}, + {"rhs": "Equation2716", "lhs": "Equation2719"}, + {"rhs": "Equation2720", "lhs": "Equation2723"}, + {"rhs": "Equation2724", "lhs": "Equation2727"}, + {"rhs": "Equation2716", "lhs": "Equation2728"}, + {"rhs": "Equation2717", "lhs": "Equation2729"}, + {"rhs": "Equation2718", "lhs": "Equation2730"}, + {"rhs": "Equation2716", "lhs": "Equation2731"}, + {"rhs": "Equation2739", "lhs": "Equation2742"}, + {"rhs": "Equation2749", "lhs": "Equation2752"}, + {"rhs": "Equation2753", "lhs": "Equation2756"}, + {"rhs": "Equation2757", "lhs": "Equation2760"}, + {"rhs": "Equation2761", "lhs": "Equation2764"}, + {"rhs": "Equation2753", "lhs": "Equation2765"}, + {"rhs": "Equation2754", "lhs": "Equation2766"}, + {"rhs": "Equation2755", "lhs": "Equation2767"}, + {"rhs": "Equation2753", "lhs": "Equation2768"}, + {"rhs": "Equation2770", "lhs": "Equation2773"}, + {"rhs": "Equation2774", "lhs": "Equation2777"}, + {"rhs": "Equation2778", "lhs": "Equation2781"}, + {"rhs": "Equation2770", "lhs": "Equation2782"}, + {"rhs": "Equation2771", "lhs": "Equation2783"}, + {"rhs": "Equation2772", "lhs": "Equation2784"}, + {"rhs": "Equation2770", "lhs": "Equation2785"}, + {"rhs": "Equation2787", "lhs": "Equation2790"}, + {"rhs": "Equation2791", "lhs": "Equation2794"}, + {"rhs": "Equation2795", "lhs": "Equation2798"}, + {"rhs": "Equation2787", "lhs": "Equation2799"}, + {"rhs": "Equation2788", "lhs": "Equation2800"}, + {"rhs": "Equation2789", "lhs": "Equation2801"}, + {"rhs": "Equation2787", "lhs": "Equation2802"}, + {"rhs": "Equation2804", "lhs": "Equation2807"}, + {"rhs": "Equation2808", "lhs": "Equation2811"}, + {"rhs": "Equation2812", "lhs": "Equation2815"}, + {"rhs": "Equation2804", "lhs": "Equation2816"}, + {"rhs": "Equation2805", "lhs": "Equation2817"}, + {"rhs": "Equation2806", "lhs": "Equation2818"}, + {"rhs": "Equation2804", "lhs": "Equation2819"}, + {"rhs": "Equation2770", "lhs": "Equation2821"}, + {"rhs": "Equation2771", "lhs": "Equation2822"}, + {"rhs": "Equation2772", "lhs": "Equation2823"}, + {"rhs": "Equation2770", "lhs": "Equation2824"}, + {"rhs": "Equation2774", "lhs": "Equation2826"}, + {"rhs": "Equation2775", "lhs": "Equation2827"}, + {"rhs": "Equation2776", "lhs": "Equation2828"}, + {"rhs": "Equation2774", "lhs": "Equation2829"}, + {"rhs": "Equation2778", "lhs": "Equation2831"}, + {"rhs": "Equation2779", "lhs": "Equation2832"}, + {"rhs": "Equation2780", "lhs": "Equation2833"}, + {"rhs": "Equation2778", "lhs": "Equation2834"}, + {"rhs": "Equation2770", "lhs": "Equation2836"}, + {"rhs": "Equation2771", "lhs": "Equation2837"}, + {"rhs": "Equation2772", "lhs": "Equation2838"}, + {"rhs": "Equation2770", "lhs": "Equation2839"}, + {"rhs": "Equation2858", "lhs": "Equation2861"}, + {"rhs": "Equation2868", "lhs": "Equation2871"}, + {"rhs": "Equation2878", "lhs": "Equation2881"}, + {"rhs": "Equation2882", "lhs": "Equation2885"}, + {"rhs": "Equation2886", "lhs": "Equation2889"}, + {"rhs": "Equation2890", "lhs": "Equation2893"}, + {"rhs": "Equation2882", "lhs": "Equation2894"}, + {"rhs": "Equation2883", "lhs": "Equation2895"}, + {"rhs": "Equation2884", "lhs": "Equation2896"}, + {"rhs": "Equation2882", "lhs": "Equation2897"}, + {"rhs": "Equation2905", "lhs": "Equation2908"}, + {"rhs": "Equation2915", "lhs": "Equation2918"}, + {"rhs": "Equation2919", "lhs": "Equation2922"}, + {"rhs": "Equation2923", "lhs": "Equation2926"}, + {"rhs": "Equation2927", "lhs": "Equation2930"}, + {"rhs": "Equation2919", "lhs": "Equation2931"}, + {"rhs": "Equation2920", "lhs": "Equation2932"}, + {"rhs": "Equation2921", "lhs": "Equation2933"}, + {"rhs": "Equation2919", "lhs": "Equation2934"}, + {"rhs": "Equation2942", "lhs": "Equation2945"}, + {"rhs": "Equation2952", "lhs": "Equation2955"}, + {"rhs": "Equation2956", "lhs": "Equation2959"}, + {"rhs": "Equation2960", "lhs": "Equation2963"}, + {"rhs": "Equation2964", "lhs": "Equation2967"}, + {"rhs": "Equation2956", "lhs": "Equation2968"}, + {"rhs": "Equation2957", "lhs": "Equation2969"}, + {"rhs": "Equation2958", "lhs": "Equation2970"}, + {"rhs": "Equation2956", "lhs": "Equation2971"}, + {"rhs": "Equation2973", "lhs": "Equation2976"}, + {"rhs": "Equation2977", "lhs": "Equation2980"}, + {"rhs": "Equation2981", "lhs": "Equation2984"}, + {"rhs": "Equation2973", "lhs": "Equation2985"}, + {"rhs": "Equation2974", "lhs": "Equation2986"}, + {"rhs": "Equation2975", "lhs": "Equation2987"}, + {"rhs": "Equation2973", "lhs": "Equation2988"}, + {"rhs": "Equation2990", "lhs": "Equation2993"}, + {"rhs": "Equation2994", "lhs": "Equation2997"}, + {"rhs": "Equation2998", "lhs": "Equation3001"}, + {"rhs": "Equation2990", "lhs": "Equation3002"}, + {"rhs": "Equation2991", "lhs": "Equation3003"}, + {"rhs": "Equation2992", "lhs": "Equation3004"}, + {"rhs": "Equation2990", "lhs": "Equation3005"}, + {"rhs": "Equation3007", "lhs": "Equation3010"}, + {"rhs": "Equation3011", "lhs": "Equation3014"}, + {"rhs": "Equation3015", "lhs": "Equation3018"}, + {"rhs": "Equation3007", "lhs": "Equation3019"}, + {"rhs": "Equation3008", "lhs": "Equation3020"}, + {"rhs": "Equation3009", "lhs": "Equation3021"}, + {"rhs": "Equation3007", "lhs": "Equation3022"}, + {"rhs": "Equation2973", "lhs": "Equation3024"}, + {"rhs": "Equation2974", "lhs": "Equation3025"}, + {"rhs": "Equation2975", "lhs": "Equation3026"}, + {"rhs": "Equation2973", "lhs": "Equation3027"}, + {"rhs": "Equation2977", "lhs": "Equation3029"}, + {"rhs": "Equation2978", "lhs": "Equation3030"}, + {"rhs": "Equation2979", "lhs": "Equation3031"}, + {"rhs": "Equation2977", "lhs": "Equation3032"}, + {"rhs": "Equation2981", "lhs": "Equation3034"}, + {"rhs": "Equation2982", "lhs": "Equation3035"}, + {"rhs": "Equation2983", "lhs": "Equation3036"}, + {"rhs": "Equation2981", "lhs": "Equation3037"}, + {"rhs": "Equation2973", "lhs": "Equation3039"}, + {"rhs": "Equation2974", "lhs": "Equation3040"}, + {"rhs": "Equation2975", "lhs": "Equation3041"}, + {"rhs": "Equation2973", "lhs": "Equation3042"}, + {"rhs": "Equation3061", "lhs": "Equation3064"}, + {"rhs": "Equation3071", "lhs": "Equation3074"}, + {"rhs": "Equation3081", "lhs": "Equation3084"}, + {"rhs": "Equation3085", "lhs": "Equation3088"}, + {"rhs": "Equation3089", "lhs": "Equation3092"}, + {"rhs": "Equation3093", "lhs": "Equation3096"}, + {"rhs": "Equation3085", "lhs": "Equation3097"}, + {"rhs": "Equation3086", "lhs": "Equation3098"}, + {"rhs": "Equation3087", "lhs": "Equation3099"}, + {"rhs": "Equation3085", "lhs": "Equation3100"}, + {"rhs": "Equation3108", "lhs": "Equation3111"}, + {"rhs": "Equation3118", "lhs": "Equation3121"}, + {"rhs": "Equation3122", "lhs": "Equation3125"}, + {"rhs": "Equation3126", "lhs": "Equation3129"}, + {"rhs": "Equation3130", "lhs": "Equation3133"}, + {"rhs": "Equation3122", "lhs": "Equation3134"}, + {"rhs": "Equation3123", "lhs": "Equation3135"}, + {"rhs": "Equation3124", "lhs": "Equation3136"}, + {"rhs": "Equation3122", "lhs": "Equation3137"}, + {"rhs": "Equation3145", "lhs": "Equation3148"}, + {"rhs": "Equation3155", "lhs": "Equation3158"}, + {"rhs": "Equation3159", "lhs": "Equation3162"}, + {"rhs": "Equation3163", "lhs": "Equation3166"}, + {"rhs": "Equation3167", "lhs": "Equation3170"}, + {"rhs": "Equation3159", "lhs": "Equation3171"}, + {"rhs": "Equation3160", "lhs": "Equation3172"}, + {"rhs": "Equation3161", "lhs": "Equation3173"}, + {"rhs": "Equation3159", "lhs": "Equation3174"}, + {"rhs": "Equation3176", "lhs": "Equation3179"}, + {"rhs": "Equation3180", "lhs": "Equation3183"}, + {"rhs": "Equation3184", "lhs": "Equation3187"}, + {"rhs": "Equation3176", "lhs": "Equation3188"}, + {"rhs": "Equation3177", "lhs": "Equation3189"}, + {"rhs": "Equation3178", "lhs": "Equation3190"}, + {"rhs": "Equation3176", "lhs": "Equation3191"}, + {"rhs": "Equation3193", "lhs": "Equation3196"}, + {"rhs": "Equation3197", "lhs": "Equation3200"}, + {"rhs": "Equation3201", "lhs": "Equation3204"}, + {"rhs": "Equation3193", "lhs": "Equation3205"}, + {"rhs": "Equation3194", "lhs": "Equation3206"}, + {"rhs": "Equation3195", "lhs": "Equation3207"}, + {"rhs": "Equation3193", "lhs": "Equation3208"}, + {"rhs": "Equation3210", "lhs": "Equation3213"}, + {"rhs": "Equation3214", "lhs": "Equation3217"}, + {"rhs": "Equation3218", "lhs": "Equation3221"}, + {"rhs": "Equation3210", "lhs": "Equation3222"}, + {"rhs": "Equation3211", "lhs": "Equation3223"}, + {"rhs": "Equation3212", "lhs": "Equation3224"}, + {"rhs": "Equation3210", "lhs": "Equation3225"}, + {"rhs": "Equation3176", "lhs": "Equation3227"}, + {"rhs": "Equation3177", "lhs": "Equation3228"}, + {"rhs": "Equation3178", "lhs": "Equation3229"}, + {"rhs": "Equation3176", "lhs": "Equation3230"}, + {"rhs": "Equation3180", "lhs": "Equation3232"}, + {"rhs": "Equation3181", "lhs": "Equation3233"}, + {"rhs": "Equation3182", "lhs": "Equation3234"}, + {"rhs": "Equation3180", "lhs": "Equation3235"}, + {"rhs": "Equation3184", "lhs": "Equation3237"}, + {"rhs": "Equation3185", "lhs": "Equation3238"}, + {"rhs": "Equation3186", "lhs": "Equation3239"}, + {"rhs": "Equation3184", "lhs": "Equation3240"}, + {"rhs": "Equation3176", "lhs": "Equation3242"}, + {"rhs": "Equation3177", "lhs": "Equation3243"}, + {"rhs": "Equation3178", "lhs": "Equation3244"}, + {"rhs": "Equation3176", "lhs": "Equation3245"}, + {"rhs": "Equation3264", "lhs": "Equation3267"}, + {"rhs": "Equation3274", "lhs": "Equation3277"}, + {"rhs": "Equation3284", "lhs": "Equation3287"}, + {"rhs": "Equation3288", "lhs": "Equation3291"}, + {"rhs": "Equation3292", "lhs": "Equation3295"}, + {"rhs": "Equation3296", "lhs": "Equation3299"}, + {"rhs": "Equation3288", "lhs": "Equation3300"}, + {"rhs": "Equation3289", "lhs": "Equation3301"}, + {"rhs": "Equation3290", "lhs": "Equation3302"}, + {"rhs": "Equation3288", "lhs": "Equation3303"}, + {"rhs": "Equation3311", "lhs": "Equation3314"}, + {"rhs": "Equation3321", "lhs": "Equation3324"}, + {"rhs": "Equation3325", "lhs": "Equation3328"}, + {"rhs": "Equation3329", "lhs": "Equation3332"}, + {"rhs": "Equation3333", "lhs": "Equation3336"}, + {"rhs": "Equation3325", "lhs": "Equation3337"}, + {"rhs": "Equation3326", "lhs": "Equation3338"}, + {"rhs": "Equation3327", "lhs": "Equation3339"}, + {"rhs": "Equation3325", "lhs": "Equation3340"}, + {"rhs": "Equation3348", "lhs": "Equation3351"}, + {"rhs": "Equation3358", "lhs": "Equation3361"}, + {"rhs": "Equation3362", "lhs": "Equation3365"}, + {"rhs": "Equation3366", "lhs": "Equation3369"}, + {"rhs": "Equation3370", "lhs": "Equation3373"}, + {"rhs": "Equation3362", "lhs": "Equation3374"}, + {"rhs": "Equation3363", "lhs": "Equation3375"}, + {"rhs": "Equation3364", "lhs": "Equation3376"}, + {"rhs": "Equation3362", "lhs": "Equation3377"}, + {"rhs": "Equation3379", "lhs": "Equation3382"}, + {"rhs": "Equation3383", "lhs": "Equation3386"}, + {"rhs": "Equation3387", "lhs": "Equation3390"}, + {"rhs": "Equation3379", "lhs": "Equation3391"}, + {"rhs": "Equation3380", "lhs": "Equation3392"}, + {"rhs": "Equation3381", "lhs": "Equation3393"}, + {"rhs": "Equation3379", "lhs": "Equation3394"}, + {"rhs": "Equation3396", "lhs": "Equation3399"}, + {"rhs": "Equation3400", "lhs": "Equation3403"}, + {"rhs": "Equation3404", "lhs": "Equation3407"}, + {"rhs": "Equation3396", "lhs": "Equation3408"}, + {"rhs": "Equation3397", "lhs": "Equation3409"}, + {"rhs": "Equation3398", "lhs": "Equation3410"}, + {"rhs": "Equation3396", "lhs": "Equation3411"}, + {"rhs": "Equation3413", "lhs": "Equation3416"}, + {"rhs": "Equation3417", "lhs": "Equation3420"}, + {"rhs": "Equation3421", "lhs": "Equation3424"}, + {"rhs": "Equation3413", "lhs": "Equation3425"}, + {"rhs": "Equation3414", "lhs": "Equation3426"}, + {"rhs": "Equation3415", "lhs": "Equation3427"}, + {"rhs": "Equation3413", "lhs": "Equation3428"}, + {"rhs": "Equation3379", "lhs": "Equation3430"}, + {"rhs": "Equation3380", "lhs": "Equation3431"}, + {"rhs": "Equation3381", "lhs": "Equation3432"}, + {"rhs": "Equation3379", "lhs": "Equation3433"}, + {"rhs": "Equation3383", "lhs": "Equation3435"}, + {"rhs": "Equation3384", "lhs": "Equation3436"}, + {"rhs": "Equation3385", "lhs": "Equation3437"}, + {"rhs": "Equation3383", "lhs": "Equation3438"}, + {"rhs": "Equation3387", "lhs": "Equation3440"}, + {"rhs": "Equation3388", "lhs": "Equation3441"}, + {"rhs": "Equation3389", "lhs": "Equation3442"}, + {"rhs": "Equation3387", "lhs": "Equation3443"}, + {"rhs": "Equation3379", "lhs": "Equation3445"}, + {"rhs": "Equation3380", "lhs": "Equation3446"}, + {"rhs": "Equation3381", "lhs": "Equation3447"}, + {"rhs": "Equation3379", "lhs": "Equation3448"}, + {"rhs": "Equation3467", "lhs": "Equation3470"}, + {"rhs": "Equation3477", "lhs": "Equation3480"}, + {"rhs": "Equation3487", "lhs": "Equation3490"}, + {"rhs": "Equation3491", "lhs": "Equation3494"}, + {"rhs": "Equation3495", "lhs": "Equation3498"}, + {"rhs": "Equation3499", "lhs": "Equation3502"}, + {"rhs": "Equation3491", "lhs": "Equation3503"}, + {"rhs": "Equation3492", "lhs": "Equation3504"}, + {"rhs": "Equation3493", "lhs": "Equation3505"}, + {"rhs": "Equation3491", "lhs": "Equation3506"}, + {"rhs": "Equation3514", "lhs": "Equation3517"}, + {"rhs": "Equation3524", "lhs": "Equation3527"}, + {"rhs": "Equation3528", "lhs": "Equation3531"}, + {"rhs": "Equation3532", "lhs": "Equation3535"}, + {"rhs": "Equation3536", "lhs": "Equation3539"}, + {"rhs": "Equation3528", "lhs": "Equation3540"}, + {"rhs": "Equation3529", "lhs": "Equation3541"}, + {"rhs": "Equation3530", "lhs": "Equation3542"}, + {"rhs": "Equation3528", "lhs": "Equation3543"}, + {"rhs": "Equation3551", "lhs": "Equation3554"}, + {"rhs": "Equation3561", "lhs": "Equation3564"}, + {"rhs": "Equation3565", "lhs": "Equation3568"}, + {"rhs": "Equation3569", "lhs": "Equation3572"}, + {"rhs": "Equation3573", "lhs": "Equation3576"}, + {"rhs": "Equation3565", "lhs": "Equation3577"}, + {"rhs": "Equation3566", "lhs": "Equation3578"}, + {"rhs": "Equation3567", "lhs": "Equation3579"}, + {"rhs": "Equation3565", "lhs": "Equation3580"}, + {"rhs": "Equation3582", "lhs": "Equation3585"}, + {"rhs": "Equation3586", "lhs": "Equation3589"}, + {"rhs": "Equation3590", "lhs": "Equation3593"}, + {"rhs": "Equation3582", "lhs": "Equation3594"}, + {"rhs": "Equation3583", "lhs": "Equation3595"}, + {"rhs": "Equation3584", "lhs": "Equation3596"}, + {"rhs": "Equation3582", "lhs": "Equation3597"}, + {"rhs": "Equation3599", "lhs": "Equation3602"}, + {"rhs": "Equation3603", "lhs": "Equation3606"}, + {"rhs": "Equation3607", "lhs": "Equation3610"}, + {"rhs": "Equation3599", "lhs": "Equation3611"}, + {"rhs": "Equation3600", "lhs": "Equation3612"}, + {"rhs": "Equation3601", "lhs": "Equation3613"}, + {"rhs": "Equation3599", "lhs": "Equation3614"}, + {"rhs": "Equation3616", "lhs": "Equation3619"}, + {"rhs": "Equation3620", "lhs": "Equation3623"}, + {"rhs": "Equation3624", "lhs": "Equation3627"}, + {"rhs": "Equation3616", "lhs": "Equation3628"}, + {"rhs": "Equation3617", "lhs": "Equation3629"}, + {"rhs": "Equation3618", "lhs": "Equation3630"}, + {"rhs": "Equation3616", "lhs": "Equation3631"}, + {"rhs": "Equation3582", "lhs": "Equation3633"}, + {"rhs": "Equation3583", "lhs": "Equation3634"}, + {"rhs": "Equation3584", "lhs": "Equation3635"}, + {"rhs": "Equation3582", "lhs": "Equation3636"}, + {"rhs": "Equation3586", "lhs": "Equation3638"}, + {"rhs": "Equation3587", "lhs": "Equation3639"}, + {"rhs": "Equation3588", "lhs": "Equation3640"}, + {"rhs": "Equation3586", "lhs": "Equation3641"}, + {"rhs": "Equation3590", "lhs": "Equation3643"}, + {"rhs": "Equation3591", "lhs": "Equation3644"}, + {"rhs": "Equation3592", "lhs": "Equation3645"}, + {"rhs": "Equation3590", "lhs": "Equation3646"}, + {"rhs": "Equation3582", "lhs": "Equation3648"}, + {"rhs": "Equation3583", "lhs": "Equation3649"}, + {"rhs": "Equation3584", "lhs": "Equation3650"}, + {"rhs": "Equation3582", "lhs": "Equation3651"}, + {"rhs": "Equation3670", "lhs": "Equation3673"}, + {"rhs": "Equation3680", "lhs": "Equation3683"}, + {"rhs": "Equation3690", "lhs": "Equation3693"}, + {"rhs": "Equation3694", "lhs": "Equation3697"}, + {"rhs": "Equation3698", "lhs": "Equation3701"}, + {"rhs": "Equation3702", "lhs": "Equation3705"}, + {"rhs": "Equation3694", "lhs": "Equation3706"}, + {"rhs": "Equation3695", "lhs": "Equation3707"}, + {"rhs": "Equation3696", "lhs": "Equation3708"}, + {"rhs": "Equation3694", "lhs": "Equation3709"}, + {"rhs": "Equation3717", "lhs": "Equation3720"}, + {"rhs": "Equation3727", "lhs": "Equation3730"}, + {"rhs": "Equation3731", "lhs": "Equation3734"}, + {"rhs": "Equation3735", "lhs": "Equation3738"}, + {"rhs": "Equation3739", "lhs": "Equation3742"}, + {"rhs": "Equation3731", "lhs": "Equation3743"}, + {"rhs": "Equation3732", "lhs": "Equation3744"}, + {"rhs": "Equation3733", "lhs": "Equation3745"}, + {"rhs": "Equation3731", "lhs": "Equation3746"}, + {"rhs": "Equation3754", "lhs": "Equation3757"}, + {"rhs": "Equation3764", "lhs": "Equation3767"}, + {"rhs": "Equation3768", "lhs": "Equation3771"}, + {"rhs": "Equation3772", "lhs": "Equation3775"}, + {"rhs": "Equation3776", "lhs": "Equation3779"}, + {"rhs": "Equation3768", "lhs": "Equation3780"}, + {"rhs": "Equation3769", "lhs": "Equation3781"}, + {"rhs": "Equation3770", "lhs": "Equation3782"}, + {"rhs": "Equation3768", "lhs": "Equation3783"}, + {"rhs": "Equation3785", "lhs": "Equation3788"}, + {"rhs": "Equation3789", "lhs": "Equation3792"}, + {"rhs": "Equation3793", "lhs": "Equation3796"}, + {"rhs": "Equation3785", "lhs": "Equation3797"}, + {"rhs": "Equation3786", "lhs": "Equation3798"}, + {"rhs": "Equation3787", "lhs": "Equation3799"}, + {"rhs": "Equation3785", "lhs": "Equation3800"}, + {"rhs": "Equation3802", "lhs": "Equation3805"}, + {"rhs": "Equation3806", "lhs": "Equation3809"}, + {"rhs": "Equation3810", "lhs": "Equation3813"}, + {"rhs": "Equation3802", "lhs": "Equation3814"}, + {"rhs": "Equation3803", "lhs": "Equation3815"}, + {"rhs": "Equation3804", "lhs": "Equation3816"}, + {"rhs": "Equation3802", "lhs": "Equation3817"}, + {"rhs": "Equation3819", "lhs": "Equation3822"}, + {"rhs": "Equation3823", "lhs": "Equation3826"}, + {"rhs": "Equation3827", "lhs": "Equation3830"}, + {"rhs": "Equation3819", "lhs": "Equation3831"}, + {"rhs": "Equation3820", "lhs": "Equation3832"}, + {"rhs": "Equation3821", "lhs": "Equation3833"}, + {"rhs": "Equation3819", "lhs": "Equation3834"}, + {"rhs": "Equation3785", "lhs": "Equation3836"}, + {"rhs": "Equation3786", "lhs": "Equation3837"}, + {"rhs": "Equation3787", "lhs": "Equation3838"}, + {"rhs": "Equation3785", "lhs": "Equation3839"}, + {"rhs": "Equation3789", "lhs": "Equation3841"}, + {"rhs": "Equation3790", "lhs": "Equation3842"}, + {"rhs": "Equation3791", "lhs": "Equation3843"}, + {"rhs": "Equation3789", "lhs": "Equation3844"}, + {"rhs": "Equation3793", "lhs": "Equation3846"}, + {"rhs": "Equation3794", "lhs": "Equation3847"}, + {"rhs": "Equation3795", "lhs": "Equation3848"}, + {"rhs": "Equation3793", "lhs": "Equation3849"}, + {"rhs": "Equation3785", "lhs": "Equation3851"}, + {"rhs": "Equation3786", "lhs": "Equation3852"}, + {"rhs": "Equation3787", "lhs": "Equation3853"}, + {"rhs": "Equation3785", "lhs": "Equation3854"}, + {"rhs": "Equation3873", "lhs": "Equation3876"}, + {"rhs": "Equation3883", "lhs": "Equation3886"}, + {"rhs": "Equation3893", "lhs": "Equation3896"}, + {"rhs": "Equation3897", "lhs": "Equation3900"}, + {"rhs": "Equation3901", "lhs": "Equation3904"}, + {"rhs": "Equation3905", "lhs": "Equation3908"}, + {"rhs": "Equation3897", "lhs": "Equation3909"}, + {"rhs": "Equation3898", "lhs": "Equation3910"}, + {"rhs": "Equation3899", "lhs": "Equation3911"}, + {"rhs": "Equation3897", "lhs": "Equation3912"}, + {"rhs": "Equation3920", "lhs": "Equation3923"}, + {"rhs": "Equation3930", "lhs": "Equation3933"}, + {"rhs": "Equation3934", "lhs": "Equation3937"}, + {"rhs": "Equation3938", "lhs": "Equation3941"}, + {"rhs": "Equation3942", "lhs": "Equation3945"}, + {"rhs": "Equation3934", "lhs": "Equation3946"}, + {"rhs": "Equation3935", "lhs": "Equation3947"}, + {"rhs": "Equation3936", "lhs": "Equation3948"}, + {"rhs": "Equation3934", "lhs": "Equation3949"}, + {"rhs": "Equation3957", "lhs": "Equation3960"}, + {"rhs": "Equation3967", "lhs": "Equation3970"}, + {"rhs": "Equation3971", "lhs": "Equation3974"}, + {"rhs": "Equation3975", "lhs": "Equation3978"}, + {"rhs": "Equation3979", "lhs": "Equation3982"}, + {"rhs": "Equation3971", "lhs": "Equation3983"}, + {"rhs": "Equation3972", "lhs": "Equation3984"}, + {"rhs": "Equation3973", "lhs": "Equation3985"}, + {"rhs": "Equation3971", "lhs": "Equation3986"}, + {"rhs": "Equation3988", "lhs": "Equation3991"}, + {"rhs": "Equation3992", "lhs": "Equation3995"}, + {"rhs": "Equation3996", "lhs": "Equation3999"}, + {"rhs": "Equation3988", "lhs": "Equation4000"}, + {"rhs": "Equation3989", "lhs": "Equation4001"}, + {"rhs": "Equation3990", "lhs": "Equation4002"}, + {"rhs": "Equation3988", "lhs": "Equation4003"}, + {"rhs": "Equation4005", "lhs": "Equation4008"}, + {"rhs": "Equation4009", "lhs": "Equation4012"}, + {"rhs": "Equation4013", "lhs": "Equation4016"}, + {"rhs": "Equation4005", "lhs": "Equation4017"}, + {"rhs": "Equation4006", "lhs": "Equation4018"}, + {"rhs": "Equation4007", "lhs": "Equation4019"}, + {"rhs": "Equation4005", "lhs": "Equation4020"}, + {"rhs": "Equation4022", "lhs": "Equation4025"}, + {"rhs": "Equation4026", "lhs": "Equation4029"}, + {"rhs": "Equation4030", "lhs": "Equation4033"}, + {"rhs": "Equation4022", "lhs": "Equation4034"}, + {"rhs": "Equation4023", "lhs": "Equation4035"}, + {"rhs": "Equation4024", "lhs": "Equation4036"}, + {"rhs": "Equation4022", "lhs": "Equation4037"}, + {"rhs": "Equation3988", "lhs": "Equation4039"}, + {"rhs": "Equation3989", "lhs": "Equation4040"}, + {"rhs": "Equation3990", "lhs": "Equation4041"}, + {"rhs": "Equation3988", "lhs": "Equation4042"}, + {"rhs": "Equation3992", "lhs": "Equation4044"}, + {"rhs": "Equation3993", "lhs": "Equation4045"}, + {"rhs": "Equation3994", "lhs": "Equation4046"}, + {"rhs": "Equation3992", "lhs": "Equation4047"}, + {"rhs": "Equation3996", "lhs": "Equation4049"}, + {"rhs": "Equation3997", "lhs": "Equation4050"}, + {"rhs": "Equation3998", "lhs": "Equation4051"}, + {"rhs": "Equation3996", "lhs": "Equation4052"}, + {"rhs": "Equation3988", "lhs": "Equation4054"}, + {"rhs": "Equation3989", "lhs": "Equation4055"}, + {"rhs": "Equation3990", "lhs": "Equation4056"}, + {"rhs": "Equation3988", "lhs": "Equation4057"}, + {"rhs": "Equation4076", "lhs": "Equation4079"}, + {"rhs": "Equation4086", "lhs": "Equation4089"}, + {"rhs": "Equation4096", "lhs": "Equation4099"}, + {"rhs": "Equation4100", "lhs": "Equation4103"}, + {"rhs": "Equation4104", "lhs": "Equation4107"}, + {"rhs": "Equation4108", "lhs": "Equation4111"}, + {"rhs": "Equation4100", "lhs": "Equation4112"}, + {"rhs": "Equation4101", "lhs": "Equation4113"}, + {"rhs": "Equation4102", "lhs": "Equation4114"}, + {"rhs": "Equation4100", "lhs": "Equation4115"}, + {"rhs": "Equation4123", "lhs": "Equation4126"}, + {"rhs": "Equation4133", "lhs": "Equation4136"}, + {"rhs": "Equation4137", "lhs": "Equation4140"}, + {"rhs": "Equation4141", "lhs": "Equation4144"}, + {"rhs": "Equation4145", "lhs": "Equation4148"}, + {"rhs": "Equation4137", "lhs": "Equation4149"}, + {"rhs": "Equation4138", "lhs": "Equation4150"}, + {"rhs": "Equation4139", "lhs": "Equation4151"}, + {"rhs": "Equation4137", "lhs": "Equation4152"}, + {"rhs": "Equation4160", "lhs": "Equation4163"}, + {"rhs": "Equation4170", "lhs": "Equation4173"}, + {"rhs": "Equation4174", "lhs": "Equation4177"}, + {"rhs": "Equation4178", "lhs": "Equation4181"}, + {"rhs": "Equation4182", "lhs": "Equation4185"}, + {"rhs": "Equation4174", "lhs": "Equation4186"}, + {"rhs": "Equation4175", "lhs": "Equation4187"}, + {"rhs": "Equation4176", "lhs": "Equation4188"}, + {"rhs": "Equation4174", "lhs": "Equation4189"}, + {"rhs": "Equation4191", "lhs": "Equation4194"}, + {"rhs": "Equation4195", "lhs": "Equation4198"}, + {"rhs": "Equation4199", "lhs": "Equation4202"}, + {"rhs": "Equation4191", "lhs": "Equation4203"}, + {"rhs": "Equation4192", "lhs": "Equation4204"}, + {"rhs": "Equation4193", "lhs": "Equation4205"}, + {"rhs": "Equation4191", "lhs": "Equation4206"}, + {"rhs": "Equation4208", "lhs": "Equation4211"}, + {"rhs": "Equation4212", "lhs": "Equation4215"}, + {"rhs": "Equation4216", "lhs": "Equation4219"}, + {"rhs": "Equation4208", "lhs": "Equation4220"}, + {"rhs": "Equation4209", "lhs": "Equation4221"}, + {"rhs": "Equation4210", "lhs": "Equation4222"}, + {"rhs": "Equation4208", "lhs": "Equation4223"}, + {"rhs": "Equation4225", "lhs": "Equation4228"}, + {"rhs": "Equation4229", "lhs": "Equation4232"}, + {"rhs": "Equation4233", "lhs": "Equation4236"}, + {"rhs": "Equation4225", "lhs": "Equation4237"}, + {"rhs": "Equation4226", "lhs": "Equation4238"}, + {"rhs": "Equation4227", "lhs": "Equation4239"}, + {"rhs": "Equation4225", "lhs": "Equation4240"}, + {"rhs": "Equation4191", "lhs": "Equation4242"}, + {"rhs": "Equation4192", "lhs": "Equation4243"}, + {"rhs": "Equation4193", "lhs": "Equation4244"}, + {"rhs": "Equation4191", "lhs": "Equation4245"}, + {"rhs": "Equation4195", "lhs": "Equation4247"}, + {"rhs": "Equation4196", "lhs": "Equation4248"}, + {"rhs": "Equation4197", "lhs": "Equation4249"}, + {"rhs": "Equation4195", "lhs": "Equation4250"}, + {"rhs": "Equation4199", "lhs": "Equation4252"}, + {"rhs": "Equation4200", "lhs": "Equation4253"}, + {"rhs": "Equation4201", "lhs": "Equation4254"}, + {"rhs": "Equation4199", "lhs": "Equation4255"}, + {"rhs": "Equation4191", "lhs": "Equation4257"}, + {"rhs": "Equation4192", "lhs": "Equation4258"}, + {"rhs": "Equation4193", "lhs": "Equation4259"}, + {"rhs": "Equation4191", "lhs": "Equation4260"}, + {"rhs": "Equation4278", "lhs": "Equation4281"}, + {"rhs": "Equation4286", "lhs": "Equation4289"}, + {"rhs": "Equation4295", "lhs": "Equation4298"}, + {"rhs": "Equation4299", "lhs": "Equation4302"}, + {"rhs": "Equation4303", "lhs": "Equation4306"}, + {"rhs": "Equation4299", "lhs": "Equation4309"}, + {"rhs": "Equation4300", "lhs": "Equation4310"}, + {"rhs": "Equation4301", "lhs": "Equation4311"}, + {"rhs": "Equation4299", "lhs": "Equation4312"}, + {"rhs": "Equation4316", "lhs": "Equation4319"}, + {"rhs": "Equation4323", "lhs": "Equation4326"}, + {"rhs": "Equation4327", "lhs": "Equation4329"}, + {"rhs": "Equation4330", "lhs": "Equation4333"}, + {"rhs": "Equation4327", "lhs": "Equation4334"}, + {"rhs": "Equation4328", "lhs": "Equation4335"}, + {"rhs": "Equation4327", "lhs": "Equation4337"}, + {"rhs": "Equation4345", "lhs": "Equation4347"}, + {"rhs": "Equation4350", "lhs": "Equation4352"}, + {"rhs": "Equation4348", "lhs": "Equation4354"}, + {"rhs": "Equation4364", "lhs": "Equation4365"}, + {"rhs": "Equation4362", "lhs": "Equation4367"}, + {"rhs": "Equation4369", "lhs": "Equation4370"}, + {"rhs": "Equation4358", "lhs": "Equation4376"}, + {"rhs": "Equation4391", "lhs": "Equation4394"}, + {"rhs": "Equation4401", "lhs": "Equation4404"}, + {"rhs": "Equation4411", "lhs": "Equation4414"}, + {"rhs": "Equation4415", "lhs": "Equation4418"}, + {"rhs": "Equation4419", "lhs": "Equation4422"}, + {"rhs": "Equation4423", "lhs": "Equation4426"}, + {"rhs": "Equation4415", "lhs": "Equation4427"}, + {"rhs": "Equation4416", "lhs": "Equation4428"}, + {"rhs": "Equation4417", "lhs": "Equation4429"}, + {"rhs": "Equation4415", "lhs": "Equation4430"}, + {"rhs": "Equation4438", "lhs": "Equation4441"}, + {"rhs": "Equation4448", "lhs": "Equation4451"}, + {"rhs": "Equation4452", "lhs": "Equation4455"}, + {"rhs": "Equation4456", "lhs": "Equation4459"}, + {"rhs": "Equation4460", "lhs": "Equation4463"}, + {"rhs": "Equation4452", "lhs": "Equation4464"}, + {"rhs": "Equation4453", "lhs": "Equation4465"}, + {"rhs": "Equation4454", "lhs": "Equation4466"}, + {"rhs": "Equation4452", "lhs": "Equation4467"}, + {"rhs": "Equation4475", "lhs": "Equation4478"}, + {"rhs": "Equation4485", "lhs": "Equation4488"}, + {"rhs": "Equation4489", "lhs": "Equation4492"}, + {"rhs": "Equation4493", "lhs": "Equation4496"}, + {"rhs": "Equation4497", "lhs": "Equation4500"}, + {"rhs": "Equation4489", "lhs": "Equation4501"}, + {"rhs": "Equation4490", "lhs": "Equation4502"}, + {"rhs": "Equation4491", "lhs": "Equation4503"}, + {"rhs": "Equation4489", "lhs": "Equation4504"}, + {"rhs": "Equation4506", "lhs": "Equation4509"}, + {"rhs": "Equation4510", "lhs": "Equation4513"}, + {"rhs": "Equation4514", "lhs": "Equation4517"}, + {"rhs": "Equation4506", "lhs": "Equation4518"}, + {"rhs": "Equation4507", "lhs": "Equation4519"}, + {"rhs": "Equation4508", "lhs": "Equation4520"}, + {"rhs": "Equation4506", "lhs": "Equation4521"}, + {"rhs": "Equation4523", "lhs": "Equation4526"}, + {"rhs": "Equation4527", "lhs": "Equation4530"}, + {"rhs": "Equation4531", "lhs": "Equation4534"}, + {"rhs": "Equation4523", "lhs": "Equation4535"}, + {"rhs": "Equation4524", "lhs": "Equation4536"}, + {"rhs": "Equation4525", "lhs": "Equation4537"}, + {"rhs": "Equation4523", "lhs": "Equation4538"}, + {"rhs": "Equation4540", "lhs": "Equation4543"}, + {"rhs": "Equation4544", "lhs": "Equation4547"}, + {"rhs": "Equation4548", "lhs": "Equation4551"}, + {"rhs": "Equation4540", "lhs": "Equation4552"}, + {"rhs": "Equation4541", "lhs": "Equation4553"}, + {"rhs": "Equation4542", "lhs": "Equation4554"}, + {"rhs": "Equation4540", "lhs": "Equation4555"}, + {"rhs": "Equation4506", "lhs": "Equation4557"}, + {"rhs": "Equation4507", "lhs": "Equation4558"}, + {"rhs": "Equation4508", "lhs": "Equation4559"}, + {"rhs": "Equation4506", "lhs": "Equation4560"}, + {"rhs": "Equation4510", "lhs": "Equation4562"}, + {"rhs": "Equation4511", "lhs": "Equation4563"}, + {"rhs": "Equation4512", "lhs": "Equation4564"}, + {"rhs": "Equation4510", "lhs": "Equation4565"}, + {"rhs": "Equation4514", "lhs": "Equation4567"}, + {"rhs": "Equation4515", "lhs": "Equation4568"}, + {"rhs": "Equation4516", "lhs": "Equation4569"}, + {"rhs": "Equation4514", "lhs": "Equation4570"}, + {"rhs": "Equation4506", "lhs": "Equation4572"}, + {"rhs": "Equation4507", "lhs": "Equation4573"}, + {"rhs": "Equation4508", "lhs": "Equation4574"}, + {"rhs": "Equation4506", "lhs": "Equation4575"}, + {"rhs": "Equation4593", "lhs": "Equation4596"}, + {"rhs": "Equation4601", "lhs": "Equation4604"}, + {"rhs": "Equation4610", "lhs": "Equation4613"}, + {"rhs": "Equation4614", "lhs": "Equation4617"}, + {"rhs": "Equation4618", "lhs": "Equation4621"}, + {"rhs": "Equation4614", "lhs": "Equation4624"}, + {"rhs": "Equation4615", "lhs": "Equation4625"}, + {"rhs": "Equation4616", "lhs": "Equation4626"}, + {"rhs": "Equation4614", "lhs": "Equation4627"}, + {"rhs": "Equation4631", "lhs": "Equation4634"}, + {"rhs": "Equation4638", "lhs": "Equation4641"}, + {"rhs": "Equation4642", "lhs": "Equation4644"}, + {"rhs": "Equation4645", "lhs": "Equation4648"}, + {"rhs": "Equation4642", "lhs": "Equation4649"}, + {"rhs": "Equation4643", "lhs": "Equation4650"}, + {"rhs": "Equation4642", "lhs": "Equation4652"}, + {"rhs": "Equation4660", "lhs": "Equation4662"}, + {"rhs": "Equation4665", "lhs": "Equation4667"}, + {"rhs": "Equation4663", "lhs": "Equation4669"}, + {"rhs": "Equation4679", "lhs": "Equation4680"}, + {"rhs": "Equation4677", "lhs": "Equation4682"}, + {"rhs": "Equation4684", "lhs": "Equation4685"}, + {"rhs": "Equation4673", "lhs": "Equation4691"}, + {"rhs": "Equation20", "lhs": "Equation22"}, + {"rhs": "Equation35", "lhs": "Equation37"}, + {"rhs": "Equation45", "lhs": "Equation46"}, + {"rhs": "Equation59", "lhs": "Equation61"}, + {"rhs": "Equation69", "lhs": "Equation71"}, + {"rhs": "Equation79", "lhs": "Equation81"}, + {"rhs": "Equation83", "lhs": "Equation85"}, + {"rhs": "Equation87", "lhs": "Equation89"}, + {"rhs": "Equation91", "lhs": "Equation93"}, + {"rhs": "Equation86", "lhs": "Equation94"}, + {"rhs": "Equation87", "lhs": "Equation95"}, + {"rhs": "Equation88", "lhs": "Equation96"}, + {"rhs": "Equation87", "lhs": "Equation97"}, + {"rhs": "Equation111", "lhs": "Equation113"}, + {"rhs": "Equation121", "lhs": "Equation123"}, + {"rhs": "Equation131", "lhs": "Equation133"}, + {"rhs": "Equation135", "lhs": "Equation137"}, + {"rhs": "Equation139", "lhs": "Equation141"}, + {"rhs": "Equation143", "lhs": "Equation145"}, + {"rhs": "Equation138", "lhs": "Equation146"}, + {"rhs": "Equation139", "lhs": "Equation147"}, + {"rhs": "Equation140", "lhs": "Equation148"}, + {"rhs": "Equation139", "lhs": "Equation149"}, + {"rhs": "Equation163", "lhs": "Equation165"}, + {"rhs": "Equation173", "lhs": "Equation175"}, + {"rhs": "Equation183", "lhs": "Equation185"}, + {"rhs": "Equation187", "lhs": "Equation189"}, + {"rhs": "Equation191", "lhs": "Equation193"}, + {"rhs": "Equation195", "lhs": "Equation197"}, + {"rhs": "Equation190", "lhs": "Equation198"}, + {"rhs": "Equation191", "lhs": "Equation199"}, + {"rhs": "Equation192", "lhs": "Equation200"}, + {"rhs": "Equation191", "lhs": "Equation201"}, + {"rhs": "Equation215", "lhs": "Equation217"}, + {"rhs": "Equation225", "lhs": "Equation227"}, + {"rhs": "Equation235", "lhs": "Equation237"}, + {"rhs": "Equation239", "lhs": "Equation241"}, + {"rhs": "Equation243", "lhs": "Equation245"}, + {"rhs": "Equation247", "lhs": "Equation249"}, + {"rhs": "Equation242", "lhs": "Equation250"}, + {"rhs": "Equation243", "lhs": "Equation251"}, + {"rhs": "Equation244", "lhs": "Equation252"}, + {"rhs": "Equation243", "lhs": "Equation253"}, + {"rhs": "Equation267", "lhs": "Equation269"}, + {"rhs": "Equation277", "lhs": "Equation279"}, + {"rhs": "Equation287", "lhs": "Equation289"}, + {"rhs": "Equation291", "lhs": "Equation293"}, + {"rhs": "Equation295", "lhs": "Equation297"}, + {"rhs": "Equation299", "lhs": "Equation301"}, + {"rhs": "Equation294", "lhs": "Equation302"}, + {"rhs": "Equation295", "lhs": "Equation303"}, + {"rhs": "Equation296", "lhs": "Equation304"}, + {"rhs": "Equation295", "lhs": "Equation305"}, + {"rhs": "Equation319", "lhs": "Equation321"}, + {"rhs": "Equation329", "lhs": "Equation331"}, + {"rhs": "Equation339", "lhs": "Equation341"}, + {"rhs": "Equation343", "lhs": "Equation345"}, + {"rhs": "Equation347", "lhs": "Equation349"}, + {"rhs": "Equation351", "lhs": "Equation353"}, + {"rhs": "Equation346", "lhs": "Equation354"}, + {"rhs": "Equation347", "lhs": "Equation355"}, + {"rhs": "Equation348", "lhs": "Equation356"}, + {"rhs": "Equation347", "lhs": "Equation357"}, + {"rhs": "Equation371", "lhs": "Equation373"}, + {"rhs": "Equation381", "lhs": "Equation383"}, + {"rhs": "Equation391", "lhs": "Equation393"}, + {"rhs": "Equation395", "lhs": "Equation397"}, + {"rhs": "Equation399", "lhs": "Equation401"}, + {"rhs": "Equation403", "lhs": "Equation405"}, + {"rhs": "Equation398", "lhs": "Equation406"}, + {"rhs": "Equation399", "lhs": "Equation407"}, + {"rhs": "Equation400", "lhs": "Equation408"}, + {"rhs": "Equation399", "lhs": "Equation409"}, + {"rhs": "Equation423", "lhs": "Equation425"}, + {"rhs": "Equation433", "lhs": "Equation435"}, + {"rhs": "Equation443", "lhs": "Equation445"}, + {"rhs": "Equation447", "lhs": "Equation449"}, + {"rhs": "Equation451", "lhs": "Equation453"}, + {"rhs": "Equation455", "lhs": "Equation457"}, + {"rhs": "Equation450", "lhs": "Equation458"}, + {"rhs": "Equation451", "lhs": "Equation459"}, + {"rhs": "Equation452", "lhs": "Equation460"}, + {"rhs": "Equation451", "lhs": "Equation461"}, + {"rhs": "Equation470", "lhs": "Equation472"}, + {"rhs": "Equation480", "lhs": "Equation482"}, + {"rhs": "Equation484", "lhs": "Equation486"}, + {"rhs": "Equation488", "lhs": "Equation490"}, + {"rhs": "Equation492", "lhs": "Equation494"}, + {"rhs": "Equation487", "lhs": "Equation495"}, + {"rhs": "Equation488", "lhs": "Equation496"}, + {"rhs": "Equation489", "lhs": "Equation497"}, + {"rhs": "Equation488", "lhs": "Equation498"}, + {"rhs": "Equation507", "lhs": "Equation509"}, + {"rhs": "Equation517", "lhs": "Equation519"}, + {"rhs": "Equation521", "lhs": "Equation523"}, + {"rhs": "Equation525", "lhs": "Equation527"}, + {"rhs": "Equation529", "lhs": "Equation531"}, + {"rhs": "Equation524", "lhs": "Equation532"}, + {"rhs": "Equation525", "lhs": "Equation533"}, + {"rhs": "Equation526", "lhs": "Equation534"}, + {"rhs": "Equation525", "lhs": "Equation535"}, + {"rhs": "Equation538", "lhs": "Equation540"}, + {"rhs": "Equation542", "lhs": "Equation544"}, + {"rhs": "Equation546", "lhs": "Equation548"}, + {"rhs": "Equation541", "lhs": "Equation549"}, + {"rhs": "Equation542", "lhs": "Equation550"}, + {"rhs": "Equation543", "lhs": "Equation551"}, + {"rhs": "Equation542", "lhs": "Equation552"}, + {"rhs": "Equation555", "lhs": "Equation557"}, + {"rhs": "Equation559", "lhs": "Equation561"}, + {"rhs": "Equation563", "lhs": "Equation565"}, + {"rhs": "Equation558", "lhs": "Equation566"}, + {"rhs": "Equation559", "lhs": "Equation567"}, + {"rhs": "Equation560", "lhs": "Equation568"}, + {"rhs": "Equation559", 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{"rhs": "Equation691", "lhs": "Equation701"}, + {"rhs": "Equation710", "lhs": "Equation712"}, + {"rhs": "Equation720", "lhs": "Equation722"}, + {"rhs": "Equation724", "lhs": "Equation726"}, + {"rhs": "Equation728", "lhs": "Equation730"}, + {"rhs": "Equation732", "lhs": "Equation734"}, + {"rhs": "Equation727", "lhs": "Equation735"}, + {"rhs": "Equation728", "lhs": "Equation736"}, + {"rhs": "Equation729", "lhs": "Equation737"}, + {"rhs": "Equation728", "lhs": "Equation738"}, + {"rhs": "Equation741", "lhs": "Equation743"}, + {"rhs": "Equation745", "lhs": "Equation747"}, + {"rhs": "Equation749", "lhs": "Equation751"}, + {"rhs": "Equation744", "lhs": "Equation752"}, + {"rhs": "Equation745", "lhs": "Equation753"}, + {"rhs": "Equation746", "lhs": "Equation754"}, + {"rhs": "Equation745", "lhs": "Equation755"}, + {"rhs": "Equation758", "lhs": "Equation760"}, + {"rhs": "Equation762", "lhs": "Equation764"}, + {"rhs": "Equation766", "lhs": "Equation768"}, + {"rhs": "Equation761", "lhs": 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"lhs": "Equation803"}, + {"rhs": "Equation766", "lhs": "Equation804"}, + {"rhs": "Equation761", "lhs": "Equation806"}, + {"rhs": "Equation762", "lhs": "Equation807"}, + {"rhs": "Equation763", "lhs": "Equation808"}, + {"rhs": "Equation762", "lhs": "Equation809"}, + {"rhs": "Equation829", "lhs": "Equation831"}, + {"rhs": "Equation839", "lhs": "Equation841"}, + {"rhs": "Equation849", "lhs": "Equation851"}, + {"rhs": "Equation853", "lhs": "Equation855"}, + {"rhs": "Equation857", "lhs": "Equation859"}, + {"rhs": "Equation861", "lhs": "Equation863"}, + {"rhs": "Equation856", "lhs": "Equation864"}, + {"rhs": "Equation857", "lhs": "Equation865"}, + {"rhs": "Equation858", "lhs": "Equation866"}, + {"rhs": "Equation857", "lhs": "Equation867"}, + {"rhs": "Equation876", "lhs": "Equation878"}, + {"rhs": "Equation886", "lhs": "Equation888"}, + {"rhs": "Equation890", "lhs": "Equation892"}, + {"rhs": "Equation894", "lhs": "Equation896"}, + {"rhs": "Equation898", "lhs": "Equation900"}, + {"rhs": 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{"rhs": "Equation965", "lhs": "Equation967"}, + {"rhs": "Equation969", "lhs": "Equation971"}, + {"rhs": "Equation964", "lhs": "Equation972"}, + {"rhs": "Equation965", "lhs": "Equation973"}, + {"rhs": "Equation966", "lhs": "Equation974"}, + {"rhs": "Equation965", "lhs": "Equation975"}, + {"rhs": "Equation978", "lhs": "Equation980"}, + {"rhs": "Equation982", "lhs": "Equation984"}, + {"rhs": "Equation986", "lhs": "Equation988"}, + {"rhs": "Equation981", "lhs": "Equation989"}, + {"rhs": "Equation982", "lhs": "Equation990"}, + {"rhs": "Equation983", "lhs": "Equation991"}, + {"rhs": "Equation982", "lhs": "Equation992"}, + {"rhs": "Equation960", "lhs": "Equation994"}, + {"rhs": "Equation961", "lhs": "Equation995"}, + {"rhs": "Equation962", "lhs": "Equation996"}, + {"rhs": "Equation961", "lhs": "Equation997"}, + {"rhs": "Equation964", "lhs": "Equation999"}, + {"rhs": "Equation965", "lhs": "Equation1000"}, + {"rhs": "Equation966", "lhs": "Equation1001"}, + {"rhs": "Equation965", "lhs": 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{"rhs": "Equation454", "lhs": "Equation458"}, + {"rhs": "Equation455", "lhs": "Equation459"}, + {"rhs": "Equation456", "lhs": "Equation460"}, + {"rhs": "Equation456", "lhs": "Equation461"}, + {"rhs": "Equation471", "lhs": "Equation472"}, + {"rhs": "Equation481", "lhs": "Equation482"}, + {"rhs": "Equation485", "lhs": "Equation486"}, + {"rhs": "Equation489", "lhs": "Equation490"}, + {"rhs": "Equation493", "lhs": "Equation494"}, + {"rhs": "Equation491", "lhs": "Equation495"}, + {"rhs": "Equation492", "lhs": "Equation496"}, + {"rhs": "Equation493", "lhs": "Equation497"}, + {"rhs": "Equation493", "lhs": "Equation498"}, + {"rhs": "Equation508", "lhs": "Equation509"}, + {"rhs": "Equation518", "lhs": "Equation519"}, + {"rhs": "Equation522", "lhs": "Equation523"}, + {"rhs": "Equation526", "lhs": "Equation527"}, + {"rhs": "Equation530", "lhs": "Equation531"}, + {"rhs": "Equation528", "lhs": "Equation532"}, + {"rhs": "Equation529", "lhs": "Equation533"}, + {"rhs": "Equation530", "lhs": 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"lhs": "Equation585"}, + {"rhs": "Equation581", "lhs": "Equation586"}, + {"rhs": "Equation571", "lhs": "Equation588"}, + {"rhs": "Equation572", "lhs": "Equation589"}, + {"rhs": "Equation573", "lhs": "Equation590"}, + {"rhs": "Equation573", "lhs": "Equation591"}, + {"rhs": "Equation575", "lhs": "Equation593"}, + {"rhs": "Equation576", "lhs": "Equation594"}, + {"rhs": "Equation577", "lhs": "Equation595"}, + {"rhs": "Equation577", "lhs": "Equation596"}, + {"rhs": "Equation579", "lhs": "Equation598"}, + {"rhs": "Equation580", "lhs": "Equation599"}, + {"rhs": "Equation581", "lhs": "Equation600"}, + {"rhs": "Equation581", "lhs": "Equation601"}, + {"rhs": "Equation579", "lhs": "Equation603"}, + {"rhs": "Equation580", "lhs": "Equation604"}, + {"rhs": "Equation581", "lhs": "Equation605"}, + {"rhs": "Equation581", "lhs": "Equation606"}, + {"rhs": "Equation627", "lhs": "Equation628"}, + {"rhs": "Equation637", "lhs": "Equation638"}, + {"rhs": "Equation647", "lhs": "Equation648"}, + {"rhs": "Equation651", "lhs": "Equation652"}, + {"rhs": "Equation655", "lhs": "Equation656"}, + {"rhs": "Equation659", "lhs": "Equation660"}, + {"rhs": "Equation657", "lhs": "Equation661"}, + {"rhs": "Equation658", "lhs": "Equation662"}, + {"rhs": "Equation659", "lhs": "Equation663"}, + {"rhs": "Equation659", "lhs": "Equation664"}, + {"rhs": "Equation674", "lhs": "Equation675"}, + {"rhs": "Equation684", "lhs": "Equation685"}, + {"rhs": "Equation688", "lhs": "Equation689"}, + {"rhs": "Equation692", "lhs": "Equation693"}, + {"rhs": "Equation696", "lhs": "Equation697"}, + {"rhs": "Equation694", "lhs": "Equation698"}, + {"rhs": "Equation695", "lhs": "Equation699"}, + {"rhs": "Equation696", "lhs": "Equation700"}, + {"rhs": "Equation696", "lhs": "Equation701"}, + {"rhs": "Equation711", "lhs": "Equation712"}, + {"rhs": "Equation721", "lhs": "Equation722"}, + {"rhs": "Equation725", "lhs": "Equation726"}, + {"rhs": "Equation729", "lhs": "Equation730"}, + {"rhs": "Equation733", "lhs": "Equation734"}, + {"rhs": "Equation731", "lhs": "Equation735"}, + {"rhs": "Equation732", "lhs": "Equation736"}, + {"rhs": "Equation733", "lhs": "Equation737"}, + {"rhs": "Equation733", "lhs": "Equation738"}, + {"rhs": "Equation742", "lhs": "Equation743"}, + {"rhs": "Equation746", "lhs": "Equation747"}, + {"rhs": "Equation750", "lhs": "Equation751"}, + {"rhs": "Equation748", "lhs": "Equation752"}, + {"rhs": "Equation749", "lhs": "Equation753"}, + {"rhs": "Equation750", "lhs": "Equation754"}, + {"rhs": "Equation750", "lhs": "Equation755"}, + {"rhs": "Equation759", "lhs": "Equation760"}, + {"rhs": "Equation763", "lhs": "Equation764"}, + {"rhs": "Equation767", "lhs": "Equation768"}, + {"rhs": "Equation765", "lhs": "Equation769"}, + {"rhs": "Equation766", "lhs": "Equation770"}, + {"rhs": "Equation767", "lhs": "Equation771"}, + {"rhs": "Equation767", "lhs": "Equation772"}, + {"rhs": "Equation776", "lhs": "Equation777"}, + {"rhs": "Equation780", "lhs": "Equation781"}, + {"rhs": "Equation784", "lhs": "Equation785"}, + {"rhs": "Equation782", "lhs": "Equation786"}, + {"rhs": "Equation783", "lhs": "Equation787"}, + {"rhs": "Equation784", "lhs": "Equation788"}, + {"rhs": "Equation784", "lhs": "Equation789"}, + {"rhs": "Equation774", "lhs": "Equation791"}, + {"rhs": "Equation775", "lhs": "Equation792"}, + {"rhs": "Equation776", "lhs": "Equation793"}, + {"rhs": "Equation776", "lhs": "Equation794"}, + {"rhs": "Equation778", "lhs": "Equation796"}, + {"rhs": "Equation779", "lhs": "Equation797"}, + {"rhs": "Equation780", "lhs": "Equation798"}, + {"rhs": "Equation780", "lhs": "Equation799"}, + {"rhs": "Equation782", "lhs": "Equation801"}, + {"rhs": "Equation783", "lhs": "Equation802"}, + {"rhs": "Equation784", "lhs": "Equation803"}, + {"rhs": "Equation784", "lhs": "Equation804"}, + {"rhs": "Equation782", "lhs": "Equation806"}, + {"rhs": "Equation783", "lhs": "Equation807"}, + {"rhs": "Equation784", "lhs": "Equation808"}, + {"rhs": "Equation784", "lhs": "Equation809"}, + {"rhs": "Equation830", "lhs": "Equation831"}, + {"rhs": "Equation840", "lhs": "Equation841"}, + {"rhs": "Equation850", "lhs": "Equation851"}, + {"rhs": "Equation854", "lhs": "Equation855"}, + {"rhs": "Equation858", "lhs": "Equation859"}, + {"rhs": "Equation862", "lhs": "Equation863"}, + {"rhs": "Equation860", "lhs": "Equation864"}, + {"rhs": "Equation861", "lhs": "Equation865"}, + {"rhs": "Equation862", "lhs": "Equation866"}, + {"rhs": "Equation862", "lhs": "Equation867"}, + {"rhs": "Equation877", "lhs": "Equation878"}, + {"rhs": "Equation887", "lhs": "Equation888"}, + {"rhs": "Equation891", "lhs": "Equation892"}, + {"rhs": "Equation895", "lhs": "Equation896"}, + {"rhs": "Equation899", "lhs": "Equation900"}, + {"rhs": "Equation897", "lhs": "Equation901"}, + {"rhs": "Equation898", "lhs": "Equation902"}, + {"rhs": "Equation899", "lhs": "Equation903"}, + {"rhs": "Equation899", "lhs": "Equation904"}, + {"rhs": "Equation914", "lhs": "Equation915"}, + {"rhs": "Equation924", "lhs": "Equation925"}, + {"rhs": "Equation928", "lhs": "Equation929"}, + {"rhs": "Equation932", "lhs": "Equation933"}, + {"rhs": "Equation936", "lhs": "Equation937"}, + {"rhs": "Equation934", "lhs": "Equation938"}, + {"rhs": "Equation935", "lhs": "Equation939"}, + {"rhs": "Equation936", "lhs": "Equation940"}, + {"rhs": "Equation936", "lhs": "Equation941"}, + {"rhs": "Equation945", "lhs": "Equation946"}, + {"rhs": "Equation949", "lhs": "Equation950"}, + {"rhs": "Equation953", "lhs": "Equation954"}, + {"rhs": "Equation951", "lhs": "Equation955"}, + {"rhs": "Equation952", "lhs": "Equation956"}, + {"rhs": "Equation953", "lhs": "Equation957"}, + {"rhs": "Equation953", "lhs": "Equation958"}, + {"rhs": "Equation962", "lhs": "Equation963"}, + {"rhs": "Equation966", "lhs": "Equation967"}, + {"rhs": "Equation970", "lhs": "Equation971"}, + {"rhs": "Equation968", "lhs": "Equation972"}, + {"rhs": "Equation969", "lhs": "Equation973"}, + {"rhs": "Equation970", "lhs": "Equation974"}, + {"rhs": "Equation970", "lhs": "Equation975"}, + {"rhs": "Equation979", "lhs": "Equation980"}, + {"rhs": "Equation983", "lhs": "Equation984"}, + {"rhs": "Equation987", "lhs": "Equation988"}, + {"rhs": "Equation985", "lhs": "Equation989"}, + {"rhs": "Equation986", "lhs": "Equation990"}, + {"rhs": "Equation987", "lhs": "Equation991"}, + {"rhs": "Equation987", "lhs": "Equation992"}, + {"rhs": "Equation977", "lhs": "Equation994"}, + {"rhs": "Equation978", "lhs": "Equation995"}, + {"rhs": "Equation979", "lhs": "Equation996"}, + {"rhs": "Equation979", "lhs": "Equation997"}, + {"rhs": "Equation981", "lhs": "Equation999"}, + {"rhs": "Equation982", "lhs": "Equation1000"}, + {"rhs": "Equation983", "lhs": "Equation1001"}, + {"rhs": "Equation983", "lhs": "Equation1002"}, + {"rhs": "Equation985", "lhs": "Equation1004"}, + {"rhs": "Equation986", "lhs": "Equation1005"}, + {"rhs": "Equation987", "lhs": "Equation1006"}, + {"rhs": "Equation987", "lhs": "Equation1007"}, + {"rhs": "Equation985", "lhs": "Equation1009"}, + {"rhs": "Equation986", "lhs": "Equation1010"}, + {"rhs": "Equation987", "lhs": "Equation1011"}, + {"rhs": "Equation987", "lhs": "Equation1012"}, + {"rhs": "Equation1033", "lhs": "Equation1034"}, + {"rhs": "Equation1043", "lhs": "Equation1044"}, + {"rhs": "Equation1053", "lhs": "Equation1054"}, + {"rhs": "Equation1057", "lhs": "Equation1058"}, + {"rhs": "Equation1061", "lhs": "Equation1062"}, + {"rhs": "Equation1065", "lhs": "Equation1066"}, + {"rhs": "Equation1063", "lhs": "Equation1067"}, + {"rhs": "Equation1064", "lhs": "Equation1068"}, + {"rhs": "Equation1065", "lhs": "Equation1069"}, + {"rhs": "Equation1065", "lhs": "Equation1070"}, + {"rhs": "Equation1080", "lhs": "Equation1081"}, + {"rhs": "Equation1090", "lhs": "Equation1091"}, + {"rhs": "Equation1094", "lhs": "Equation1095"}, + {"rhs": "Equation1098", "lhs": "Equation1099"}, + {"rhs": "Equation1102", "lhs": "Equation1103"}, + {"rhs": "Equation1100", "lhs": "Equation1104"}, + {"rhs": "Equation1101", "lhs": "Equation1105"}, + {"rhs": "Equation1102", "lhs": 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"Equation1986"}, + {"rhs": "Equation1983", "lhs": "Equation1987"}, + {"rhs": "Equation1984", "lhs": "Equation1988"}, + {"rhs": "Equation1985", "lhs": "Equation1989"}, + {"rhs": "Equation1985", "lhs": "Equation1990"}, + {"rhs": "Equation1994", "lhs": "Equation1995"}, + {"rhs": "Equation1998", "lhs": "Equation1999"}, + {"rhs": "Equation2002", "lhs": "Equation2003"}, + {"rhs": "Equation2000", "lhs": "Equation2004"}, + {"rhs": "Equation2001", "lhs": "Equation2005"}, + {"rhs": "Equation2002", "lhs": "Equation2006"}, + {"rhs": "Equation2002", "lhs": "Equation2007"}, + {"rhs": "Equation1992", "lhs": "Equation2009"}, + {"rhs": "Equation1993", "lhs": "Equation2010"}, + {"rhs": "Equation1994", "lhs": "Equation2011"}, + {"rhs": "Equation1994", "lhs": "Equation2012"}, + {"rhs": "Equation1996", "lhs": "Equation2014"}, + {"rhs": "Equation1997", "lhs": "Equation2015"}, + {"rhs": "Equation1998", "lhs": "Equation2016"}, + {"rhs": "Equation1998", "lhs": "Equation2017"}, + {"rhs": "Equation2000", "lhs": 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"Equation3174"}, + {"rhs": "Equation3178", "lhs": "Equation3179"}, + {"rhs": "Equation3182", "lhs": "Equation3183"}, + {"rhs": "Equation3186", "lhs": "Equation3187"}, + {"rhs": "Equation3184", "lhs": "Equation3188"}, + {"rhs": "Equation3185", "lhs": "Equation3189"}, + {"rhs": "Equation3186", "lhs": "Equation3190"}, + {"rhs": "Equation3186", "lhs": "Equation3191"}, + {"rhs": "Equation3195", "lhs": "Equation3196"}, + {"rhs": "Equation3199", "lhs": "Equation3200"}, + {"rhs": "Equation3203", "lhs": "Equation3204"}, + {"rhs": "Equation3201", "lhs": "Equation3205"}, + {"rhs": "Equation3202", "lhs": "Equation3206"}, + {"rhs": "Equation3203", "lhs": "Equation3207"}, + {"rhs": "Equation3203", "lhs": "Equation3208"}, + {"rhs": "Equation3212", "lhs": "Equation3213"}, + {"rhs": "Equation3216", "lhs": "Equation3217"}, + {"rhs": "Equation3220", "lhs": "Equation3221"}, + {"rhs": "Equation3218", "lhs": "Equation3222"}, + {"rhs": "Equation3219", "lhs": "Equation3223"}, + {"rhs": "Equation3220", "lhs": 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{"rhs": "Equation492", "lhs": "Equation604"}, + {"rhs": "Equation491", "lhs": "Equation605"}, + {"rhs": "Equation493", "lhs": "Equation606"}, + {"rhs": "Equation621", "lhs": "Equation628"}, + {"rhs": "Equation631", "lhs": "Equation638"}, + {"rhs": "Equation641", "lhs": "Equation648"}, + {"rhs": "Equation631", "lhs": "Equation652"}, + {"rhs": "Equation634", "lhs": "Equation656"}, + {"rhs": "Equation631", "lhs": "Equation660"}, + {"rhs": "Equation635", "lhs": "Equation661"}, + {"rhs": "Equation636", "lhs": "Equation662"}, + {"rhs": "Equation635", "lhs": "Equation663"}, + {"rhs": "Equation637", "lhs": "Equation664"}, + {"rhs": "Equation668", "lhs": "Equation675"}, + {"rhs": "Equation678", "lhs": "Equation685"}, + {"rhs": "Equation668", "lhs": "Equation689"}, + {"rhs": "Equation671", "lhs": "Equation693"}, + {"rhs": "Equation668", "lhs": "Equation697"}, + {"rhs": "Equation672", "lhs": "Equation698"}, + {"rhs": "Equation673", "lhs": "Equation699"}, + {"rhs": "Equation672", "lhs": 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"lhs": "Equation769"}, + {"rhs": "Equation683", "lhs": "Equation770"}, + {"rhs": "Equation682", "lhs": "Equation771"}, + {"rhs": "Equation684", "lhs": "Equation772"}, + {"rhs": "Equation668", "lhs": "Equation777"}, + {"rhs": "Equation671", "lhs": "Equation781"}, + {"rhs": "Equation668", "lhs": "Equation785"}, + {"rhs": "Equation672", "lhs": "Equation786"}, + {"rhs": "Equation673", "lhs": "Equation787"}, + {"rhs": "Equation672", "lhs": "Equation788"}, + {"rhs": "Equation674", "lhs": "Equation789"}, + {"rhs": "Equation686", "lhs": "Equation791"}, + {"rhs": "Equation687", "lhs": "Equation792"}, + {"rhs": "Equation686", "lhs": "Equation793"}, + {"rhs": "Equation688", "lhs": "Equation794"}, + {"rhs": "Equation690", "lhs": "Equation796"}, + {"rhs": "Equation691", "lhs": "Equation797"}, + {"rhs": "Equation690", "lhs": "Equation798"}, + {"rhs": "Equation692", "lhs": "Equation799"}, + {"rhs": "Equation686", "lhs": "Equation801"}, + {"rhs": "Equation687", "lhs": "Equation802"}, + {"rhs": 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{"rhs": "Equation875", "lhs": "Equation901"}, + {"rhs": "Equation876", "lhs": "Equation902"}, + {"rhs": "Equation875", "lhs": "Equation903"}, + {"rhs": "Equation877", "lhs": "Equation904"}, + {"rhs": "Equation908", "lhs": "Equation915"}, + {"rhs": "Equation918", "lhs": "Equation925"}, + {"rhs": "Equation908", "lhs": "Equation929"}, + {"rhs": "Equation911", "lhs": "Equation933"}, + {"rhs": "Equation908", "lhs": "Equation937"}, + {"rhs": "Equation912", "lhs": "Equation938"}, + {"rhs": "Equation913", "lhs": "Equation939"}, + {"rhs": "Equation912", "lhs": "Equation940"}, + {"rhs": "Equation914", "lhs": "Equation941"}, + {"rhs": "Equation871", "lhs": "Equation946"}, + {"rhs": "Equation874", "lhs": "Equation950"}, + {"rhs": "Equation871", "lhs": "Equation954"}, + {"rhs": "Equation875", "lhs": "Equation955"}, + {"rhs": "Equation876", "lhs": "Equation956"}, + {"rhs": "Equation875", "lhs": "Equation957"}, + {"rhs": "Equation877", "lhs": "Equation958"}, + {"rhs": "Equation881", "lhs": 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{"rhs": "Equation479", "lhs": "Equation495"}, + {"rhs": "Equation480", "lhs": "Equation496"}, + {"rhs": "Equation480", "lhs": "Equation497"}, + {"rhs": "Equation481", "lhs": "Equation498"}, + {"rhs": "Equation505", "lhs": "Equation509"}, + {"rhs": "Equation515", "lhs": "Equation519"}, + {"rhs": "Equation512", "lhs": "Equation523"}, + {"rhs": "Equation515", "lhs": "Equation527"}, + {"rhs": "Equation515", "lhs": "Equation531"}, + {"rhs": "Equation516", "lhs": "Equation532"}, + {"rhs": "Equation517", "lhs": "Equation533"}, + {"rhs": "Equation517", "lhs": "Equation534"}, + {"rhs": "Equation518", "lhs": "Equation535"}, + {"rhs": "Equation502", "lhs": "Equation540"}, + {"rhs": "Equation505", "lhs": "Equation544"}, + {"rhs": "Equation505", "lhs": "Equation548"}, + {"rhs": "Equation506", "lhs": "Equation549"}, + {"rhs": "Equation507", "lhs": "Equation550"}, + {"rhs": "Equation507", "lhs": "Equation551"}, + {"rhs": "Equation508", "lhs": "Equation552"}, + {"rhs": "Equation512", "lhs": 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"lhs": "Equation596"}, + {"rhs": "Equation524", "lhs": "Equation598"}, + {"rhs": "Equation525", "lhs": "Equation599"}, + {"rhs": "Equation525", "lhs": "Equation600"}, + {"rhs": "Equation526", "lhs": "Equation601"}, + {"rhs": "Equation528", "lhs": "Equation603"}, + {"rhs": "Equation529", "lhs": "Equation604"}, + {"rhs": "Equation529", "lhs": "Equation605"}, + {"rhs": "Equation530", "lhs": "Equation606"}, + {"rhs": "Equation624", "lhs": "Equation628"}, + {"rhs": "Equation634", "lhs": "Equation638"}, + {"rhs": "Equation644", "lhs": "Equation648"}, + {"rhs": "Equation641", "lhs": "Equation652"}, + {"rhs": "Equation644", "lhs": "Equation656"}, + {"rhs": "Equation644", "lhs": "Equation660"}, + {"rhs": "Equation645", "lhs": "Equation661"}, + {"rhs": "Equation646", "lhs": "Equation662"}, + {"rhs": "Equation646", "lhs": "Equation663"}, + {"rhs": "Equation647", "lhs": "Equation664"}, + {"rhs": "Equation671", "lhs": "Equation675"}, + {"rhs": "Equation681", "lhs": "Equation685"}, + {"rhs": "Equation678", "lhs": "Equation689"}, + {"rhs": "Equation681", "lhs": "Equation693"}, + {"rhs": "Equation681", "lhs": "Equation697"}, + {"rhs": "Equation682", "lhs": "Equation698"}, + {"rhs": "Equation683", "lhs": "Equation699"}, + {"rhs": "Equation683", "lhs": "Equation700"}, + {"rhs": "Equation684", "lhs": "Equation701"}, + {"rhs": "Equation708", "lhs": "Equation712"}, + {"rhs": "Equation718", "lhs": "Equation722"}, + {"rhs": "Equation715", "lhs": "Equation726"}, + {"rhs": "Equation718", "lhs": "Equation730"}, + {"rhs": "Equation718", "lhs": "Equation734"}, + {"rhs": "Equation719", "lhs": "Equation735"}, + {"rhs": "Equation720", "lhs": "Equation736"}, + {"rhs": "Equation720", "lhs": "Equation737"}, + {"rhs": "Equation721", "lhs": "Equation738"}, + {"rhs": "Equation705", "lhs": "Equation743"}, + {"rhs": "Equation708", "lhs": "Equation747"}, + {"rhs": "Equation708", "lhs": "Equation751"}, + {"rhs": "Equation709", "lhs": "Equation752"}, + {"rhs": "Equation710", "lhs": "Equation753"}, + {"rhs": "Equation710", "lhs": "Equation754"}, + {"rhs": "Equation711", "lhs": "Equation755"}, + {"rhs": "Equation715", "lhs": "Equation760"}, + {"rhs": "Equation718", "lhs": "Equation764"}, + {"rhs": "Equation718", "lhs": "Equation768"}, + {"rhs": "Equation719", "lhs": "Equation769"}, + {"rhs": "Equation720", "lhs": "Equation770"}, + {"rhs": "Equation720", "lhs": "Equation771"}, + {"rhs": "Equation721", "lhs": "Equation772"}, + {"rhs": "Equation715", "lhs": "Equation777"}, + {"rhs": "Equation718", "lhs": "Equation781"}, + {"rhs": "Equation718", "lhs": "Equation785"}, + {"rhs": "Equation719", "lhs": "Equation786"}, + {"rhs": "Equation720", "lhs": "Equation787"}, + {"rhs": "Equation720", "lhs": "Equation788"}, + {"rhs": "Equation721", "lhs": "Equation789"}, + {"rhs": "Equation723", "lhs": "Equation791"}, + {"rhs": "Equation724", "lhs": "Equation792"}, + {"rhs": "Equation724", "lhs": "Equation793"}, + {"rhs": "Equation725", "lhs": "Equation794"}, + {"rhs": "Equation727", "lhs": "Equation796"}, + {"rhs": "Equation728", "lhs": "Equation797"}, + {"rhs": "Equation728", "lhs": "Equation798"}, + {"rhs": "Equation729", "lhs": "Equation799"}, + {"rhs": "Equation727", "lhs": "Equation801"}, + {"rhs": "Equation728", "lhs": "Equation802"}, + {"rhs": "Equation728", "lhs": "Equation803"}, + {"rhs": "Equation729", "lhs": "Equation804"}, + {"rhs": "Equation731", "lhs": "Equation806"}, + {"rhs": "Equation732", "lhs": "Equation807"}, + {"rhs": "Equation732", "lhs": "Equation808"}, + {"rhs": "Equation733", "lhs": "Equation809"}, + {"rhs": "Equation827", "lhs": "Equation831"}, + {"rhs": "Equation837", "lhs": "Equation841"}, + {"rhs": "Equation847", "lhs": "Equation851"}, + {"rhs": "Equation844", "lhs": "Equation855"}, + {"rhs": "Equation847", "lhs": "Equation859"}, + {"rhs": "Equation847", "lhs": "Equation863"}, + {"rhs": "Equation848", "lhs": "Equation864"}, + {"rhs": "Equation849", "lhs": "Equation865"}, + {"rhs": "Equation849", "lhs": "Equation866"}, + {"rhs": "Equation850", "lhs": "Equation867"}, + {"rhs": "Equation874", "lhs": "Equation878"}, + {"rhs": "Equation884", "lhs": "Equation888"}, + {"rhs": "Equation881", "lhs": "Equation892"}, + {"rhs": "Equation884", "lhs": "Equation896"}, + {"rhs": "Equation884", "lhs": "Equation900"}, + {"rhs": "Equation885", "lhs": "Equation901"}, + {"rhs": "Equation886", "lhs": "Equation902"}, + {"rhs": "Equation886", "lhs": "Equation903"}, + {"rhs": "Equation887", "lhs": "Equation904"}, + {"rhs": "Equation911", "lhs": "Equation915"}, + {"rhs": "Equation921", "lhs": "Equation925"}, + {"rhs": "Equation918", "lhs": "Equation929"}, + {"rhs": "Equation921", "lhs": "Equation933"}, + {"rhs": "Equation921", "lhs": "Equation937"}, + {"rhs": "Equation922", "lhs": "Equation938"}, + {"rhs": "Equation923", "lhs": "Equation939"}, + {"rhs": "Equation923", "lhs": "Equation940"}, + {"rhs": "Equation924", "lhs": "Equation941"}, + {"rhs": "Equation908", "lhs": "Equation946"}, + {"rhs": "Equation911", "lhs": "Equation950"}, + {"rhs": "Equation911", "lhs": "Equation954"}, + {"rhs": "Equation912", "lhs": "Equation955"}, + {"rhs": "Equation913", "lhs": "Equation956"}, + {"rhs": "Equation913", "lhs": "Equation957"}, + {"rhs": "Equation914", "lhs": "Equation958"}, + {"rhs": "Equation918", "lhs": "Equation963"}, + {"rhs": "Equation921", "lhs": "Equation967"}, + {"rhs": "Equation921", "lhs": "Equation971"}, + {"rhs": "Equation922", "lhs": "Equation972"}, + {"rhs": "Equation923", "lhs": "Equation973"}, + {"rhs": "Equation923", "lhs": "Equation974"}, + {"rhs": "Equation924", "lhs": "Equation975"}, + {"rhs": "Equation918", "lhs": "Equation980"}, + {"rhs": "Equation921", "lhs": "Equation984"}, + {"rhs": "Equation921", "lhs": "Equation988"}, + {"rhs": "Equation922", "lhs": "Equation989"}, + {"rhs": "Equation923", "lhs": "Equation990"}, + {"rhs": "Equation923", "lhs": "Equation991"}, + {"rhs": "Equation924", "lhs": "Equation992"}, + {"rhs": "Equation926", "lhs": "Equation994"}, + {"rhs": "Equation927", "lhs": "Equation995"}, + {"rhs": "Equation927", "lhs": "Equation996"}, + {"rhs": "Equation928", "lhs": "Equation997"}, + {"rhs": "Equation930", "lhs": "Equation999"}, + {"rhs": "Equation931", "lhs": "Equation1000"}, + {"rhs": "Equation931", "lhs": "Equation1001"}, + {"rhs": "Equation932", "lhs": "Equation1002"}, + {"rhs": "Equation930", "lhs": "Equation1004"}, + {"rhs": "Equation931", "lhs": "Equation1005"}, + {"rhs": "Equation931", "lhs": "Equation1006"}, + {"rhs": "Equation932", "lhs": "Equation1007"}, + {"rhs": "Equation934", "lhs": "Equation1009"}, + {"rhs": "Equation935", "lhs": "Equation1010"}, + {"rhs": "Equation935", "lhs": "Equation1011"}, + {"rhs": "Equation936", "lhs": "Equation1012"}, + {"rhs": "Equation1030", "lhs": "Equation1034"}, + {"rhs": "Equation1040", "lhs": "Equation1044"}, + {"rhs": "Equation1050", "lhs": "Equation1054"}, + {"rhs": "Equation1047", "lhs": "Equation1058"}, + {"rhs": "Equation1050", "lhs": "Equation1062"}, + {"rhs": "Equation1050", "lhs": "Equation1066"}, + {"rhs": "Equation1051", "lhs": "Equation1067"}, + {"rhs": "Equation1052", "lhs": "Equation1068"}, + {"rhs": "Equation1052", "lhs": "Equation1069"}, + {"rhs": "Equation1053", "lhs": "Equation1070"}, + {"rhs": "Equation1077", "lhs": "Equation1081"}, + {"rhs": "Equation1087", "lhs": "Equation1091"}, + {"rhs": "Equation1084", "lhs": "Equation1095"}, + {"rhs": "Equation1087", "lhs": "Equation1099"}, + {"rhs": "Equation1087", "lhs": "Equation1103"}, + {"rhs": "Equation1088", "lhs": "Equation1104"}, + {"rhs": "Equation1089", "lhs": "Equation1105"}, + {"rhs": "Equation1089", "lhs": "Equation1106"}, + {"rhs": "Equation1090", "lhs": "Equation1107"}, + {"rhs": "Equation1114", "lhs": "Equation1118"}, + {"rhs": "Equation1124", "lhs": "Equation1128"}, + {"rhs": "Equation1121", "lhs": "Equation1132"}, + {"rhs": "Equation1124", "lhs": "Equation1136"}, + {"rhs": "Equation1124", "lhs": "Equation1140"}, + {"rhs": "Equation1125", "lhs": "Equation1141"}, + {"rhs": "Equation1126", "lhs": "Equation1142"}, + {"rhs": "Equation1126", "lhs": "Equation1143"}, + {"rhs": "Equation1127", "lhs": "Equation1144"}, + {"rhs": "Equation1111", "lhs": "Equation1149"}, + {"rhs": "Equation1114", "lhs": "Equation1153"}, + {"rhs": "Equation1114", "lhs": "Equation1157"}, + {"rhs": "Equation1115", "lhs": "Equation1158"}, + {"rhs": "Equation1116", "lhs": "Equation1159"}, + {"rhs": "Equation1116", "lhs": "Equation1160"}, + {"rhs": "Equation1117", "lhs": "Equation1161"}, + {"rhs": "Equation1121", "lhs": "Equation1166"}, + {"rhs": "Equation1124", "lhs": "Equation1170"}, + {"rhs": "Equation1124", "lhs": "Equation1174"}, + {"rhs": "Equation1125", "lhs": "Equation1175"}, + {"rhs": "Equation1126", "lhs": "Equation1176"}, + {"rhs": "Equation1126", "lhs": "Equation1177"}, + {"rhs": "Equation1127", "lhs": "Equation1178"}, + {"rhs": "Equation1121", "lhs": "Equation1183"}, + {"rhs": "Equation1124", "lhs": "Equation1187"}, + {"rhs": "Equation1124", "lhs": "Equation1191"}, + {"rhs": "Equation1125", "lhs": "Equation1192"}, + {"rhs": "Equation1126", "lhs": "Equation1193"}, + {"rhs": "Equation1126", "lhs": "Equation1194"}, + {"rhs": "Equation1127", "lhs": "Equation1195"}, + {"rhs": "Equation1129", "lhs": "Equation1197"}, + {"rhs": "Equation1130", "lhs": "Equation1198"}, + {"rhs": "Equation1130", "lhs": "Equation1199"}, + {"rhs": "Equation1131", "lhs": "Equation1200"}, + {"rhs": "Equation1133", "lhs": "Equation1202"}, + {"rhs": "Equation1134", "lhs": "Equation1203"}, + {"rhs": "Equation1134", "lhs": "Equation1204"}, + {"rhs": "Equation1135", "lhs": "Equation1205"}, + {"rhs": "Equation1133", "lhs": "Equation1207"}, + {"rhs": "Equation1134", "lhs": "Equation1208"}, + {"rhs": "Equation1134", "lhs": "Equation1209"}, + {"rhs": "Equation1135", "lhs": "Equation1210"}, + {"rhs": "Equation1137", "lhs": "Equation1212"}, + {"rhs": "Equation1138", "lhs": "Equation1213"}, + {"rhs": "Equation1138", "lhs": "Equation1214"}, + {"rhs": "Equation1139", "lhs": "Equation1215"}, + {"rhs": "Equation1233", "lhs": "Equation1237"}, + {"rhs": "Equation1243", "lhs": "Equation1247"}, + {"rhs": "Equation1253", "lhs": "Equation1257"}, + {"rhs": "Equation1250", "lhs": "Equation1261"}, + {"rhs": "Equation1253", "lhs": "Equation1265"}, + {"rhs": "Equation1253", "lhs": "Equation1269"}, + {"rhs": "Equation1254", "lhs": "Equation1270"}, + {"rhs": "Equation1255", "lhs": "Equation1271"}, + {"rhs": "Equation1255", "lhs": "Equation1272"}, + {"rhs": "Equation1256", "lhs": "Equation1273"}, + {"rhs": "Equation1280", "lhs": "Equation1284"}, + {"rhs": "Equation1290", "lhs": "Equation1294"}, + {"rhs": "Equation1287", "lhs": "Equation1298"}, + {"rhs": "Equation1290", "lhs": "Equation1302"}, + {"rhs": "Equation1290", "lhs": "Equation1306"}, + {"rhs": "Equation1291", "lhs": "Equation1307"}, + {"rhs": "Equation1292", "lhs": "Equation1308"}, + {"rhs": "Equation1292", "lhs": "Equation1309"}, + {"rhs": "Equation1293", "lhs": "Equation1310"}, + {"rhs": "Equation1317", "lhs": "Equation1321"}, + {"rhs": "Equation1327", "lhs": "Equation1331"}, + {"rhs": "Equation1324", "lhs": "Equation1335"}, + {"rhs": "Equation1327", "lhs": "Equation1339"}, + {"rhs": "Equation1327", "lhs": "Equation1343"}, + {"rhs": "Equation1328", "lhs": "Equation1344"}, + {"rhs": "Equation1329", "lhs": "Equation1345"}, + {"rhs": "Equation1329", "lhs": "Equation1346"}, + {"rhs": "Equation1330", "lhs": "Equation1347"}, + {"rhs": "Equation1314", "lhs": "Equation1352"}, + {"rhs": "Equation1317", "lhs": "Equation1356"}, + {"rhs": "Equation1317", "lhs": "Equation1360"}, + {"rhs": "Equation1318", "lhs": "Equation1361"}, + {"rhs": "Equation1319", "lhs": "Equation1362"}, + {"rhs": "Equation1319", "lhs": "Equation1363"}, + {"rhs": "Equation1320", "lhs": "Equation1364"}, + {"rhs": "Equation1324", "lhs": "Equation1369"}, + {"rhs": "Equation1327", "lhs": "Equation1373"}, + {"rhs": "Equation1327", "lhs": "Equation1377"}, + {"rhs": "Equation1328", "lhs": "Equation1378"}, + {"rhs": "Equation1329", "lhs": "Equation1379"}, + {"rhs": "Equation1329", "lhs": "Equation1380"}, + {"rhs": "Equation1330", "lhs": "Equation1381"}, + {"rhs": "Equation1324", "lhs": "Equation1386"}, + {"rhs": "Equation1327", "lhs": "Equation1390"}, + {"rhs": "Equation1327", "lhs": "Equation1394"}, + {"rhs": "Equation1328", "lhs": "Equation1395"}, + {"rhs": "Equation1329", "lhs": "Equation1396"}, + {"rhs": "Equation1329", "lhs": "Equation1397"}, + {"rhs": "Equation1330", "lhs": "Equation1398"}, + {"rhs": "Equation1332", "lhs": "Equation1400"}, + {"rhs": "Equation1333", "lhs": "Equation1401"}, + {"rhs": "Equation1333", "lhs": "Equation1402"}, + {"rhs": "Equation1334", "lhs": "Equation1403"}, + {"rhs": "Equation1336", "lhs": "Equation1405"}, + {"rhs": "Equation1337", "lhs": "Equation1406"}, + {"rhs": "Equation1337", "lhs": "Equation1407"}, + {"rhs": "Equation1338", "lhs": "Equation1408"}, + {"rhs": "Equation1336", "lhs": "Equation1410"}, + {"rhs": "Equation1337", "lhs": "Equation1411"}, + {"rhs": "Equation1337", "lhs": "Equation1412"}, + {"rhs": "Equation1338", "lhs": "Equation1413"}, + {"rhs": "Equation1340", "lhs": "Equation1415"}, + {"rhs": "Equation1341", "lhs": "Equation1416"}, + {"rhs": "Equation1341", "lhs": "Equation1417"}, + {"rhs": "Equation1342", "lhs": "Equation1418"}, + {"rhs": "Equation1436", "lhs": "Equation1440"}, + {"rhs": "Equation1446", "lhs": "Equation1450"}, + {"rhs": "Equation1456", "lhs": "Equation1460"}, + {"rhs": "Equation1453", "lhs": "Equation1464"}, + {"rhs": "Equation1456", "lhs": "Equation1468"}, + {"rhs": "Equation1456", "lhs": "Equation1472"}, + {"rhs": "Equation1457", "lhs": "Equation1473"}, + {"rhs": "Equation1458", "lhs": "Equation1474"}, + {"rhs": "Equation1458", "lhs": "Equation1475"}, + {"rhs": "Equation1459", "lhs": "Equation1476"}, + {"rhs": "Equation1483", "lhs": "Equation1487"}, + {"rhs": "Equation1493", "lhs": "Equation1497"}, + {"rhs": "Equation1490", "lhs": "Equation1501"}, + {"rhs": "Equation1493", "lhs": "Equation1505"}, + {"rhs": "Equation1493", "lhs": "Equation1509"}, + {"rhs": "Equation1494", "lhs": "Equation1510"}, + {"rhs": 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"Equation1541", "lhs": "Equation1611"}, + {"rhs": "Equation1539", "lhs": "Equation1613"}, + {"rhs": "Equation1540", "lhs": "Equation1614"}, + {"rhs": "Equation1540", "lhs": "Equation1615"}, + {"rhs": "Equation1541", "lhs": "Equation1616"}, + {"rhs": "Equation1543", "lhs": "Equation1618"}, + {"rhs": "Equation1544", "lhs": "Equation1619"}, + {"rhs": "Equation1544", "lhs": "Equation1620"}, + {"rhs": "Equation1545", "lhs": "Equation1621"}, + {"rhs": "Equation1639", "lhs": "Equation1643"}, + {"rhs": "Equation1649", "lhs": "Equation1653"}, + {"rhs": "Equation1659", "lhs": "Equation1663"}, + {"rhs": "Equation1656", "lhs": "Equation1667"}, + {"rhs": "Equation1659", "lhs": "Equation1671"}, + {"rhs": "Equation1659", "lhs": "Equation1675"}, + {"rhs": "Equation1660", "lhs": "Equation1676"}, + {"rhs": "Equation1661", "lhs": "Equation1677"}, + {"rhs": "Equation1661", "lhs": "Equation1678"}, + {"rhs": "Equation1662", "lhs": "Equation1679"}, + {"rhs": "Equation1686", "lhs": "Equation1690"}, + {"rhs": "Equation1696", "lhs": "Equation1700"}, + {"rhs": "Equation1693", "lhs": "Equation1704"}, + {"rhs": "Equation1696", "lhs": "Equation1708"}, + {"rhs": "Equation1696", "lhs": "Equation1712"}, + {"rhs": "Equation1697", "lhs": "Equation1713"}, + {"rhs": "Equation1698", "lhs": "Equation1714"}, + {"rhs": "Equation1698", "lhs": "Equation1715"}, + {"rhs": "Equation1699", "lhs": "Equation1716"}, + {"rhs": "Equation1723", "lhs": "Equation1727"}, + {"rhs": "Equation1733", "lhs": "Equation1737"}, + {"rhs": "Equation1730", "lhs": "Equation1741"}, + {"rhs": "Equation1733", "lhs": "Equation1745"}, + {"rhs": "Equation1733", "lhs": "Equation1749"}, + {"rhs": "Equation1734", "lhs": "Equation1750"}, + {"rhs": "Equation1735", "lhs": "Equation1751"}, + {"rhs": "Equation1735", "lhs": "Equation1752"}, + {"rhs": "Equation1736", "lhs": "Equation1753"}, + {"rhs": "Equation1720", "lhs": "Equation1758"}, + {"rhs": "Equation1723", "lhs": "Equation1762"}, + {"rhs": "Equation1723", "lhs": "Equation1766"}, + {"rhs": "Equation1724", "lhs": "Equation1767"}, + {"rhs": "Equation1725", "lhs": "Equation1768"}, + {"rhs": "Equation1725", "lhs": "Equation1769"}, + {"rhs": "Equation1726", "lhs": "Equation1770"}, + {"rhs": "Equation1730", "lhs": "Equation1775"}, + {"rhs": "Equation1733", "lhs": "Equation1779"}, + {"rhs": "Equation1733", "lhs": "Equation1783"}, + {"rhs": "Equation1734", "lhs": "Equation1784"}, + {"rhs": "Equation1735", "lhs": "Equation1785"}, + {"rhs": "Equation1735", "lhs": "Equation1786"}, + {"rhs": "Equation1736", "lhs": "Equation1787"}, + {"rhs": "Equation1730", "lhs": "Equation1792"}, + {"rhs": "Equation1733", "lhs": "Equation1796"}, + {"rhs": "Equation1733", "lhs": "Equation1800"}, + {"rhs": "Equation1734", "lhs": "Equation1801"}, + {"rhs": "Equation1735", "lhs": "Equation1802"}, + {"rhs": "Equation1735", "lhs": "Equation1803"}, + {"rhs": "Equation1736", "lhs": "Equation1804"}, + {"rhs": "Equation1738", "lhs": "Equation1806"}, + {"rhs": "Equation1739", "lhs": "Equation1807"}, + {"rhs": 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"Equation1863", "lhs": "Equation1879"}, + {"rhs": "Equation1864", "lhs": "Equation1880"}, + {"rhs": "Equation1864", "lhs": "Equation1881"}, + {"rhs": "Equation1865", "lhs": "Equation1882"}, + {"rhs": "Equation1889", "lhs": "Equation1893"}, + {"rhs": "Equation1899", "lhs": "Equation1903"}, + {"rhs": "Equation1896", "lhs": "Equation1907"}, + {"rhs": "Equation1899", "lhs": "Equation1911"}, + {"rhs": "Equation1899", "lhs": "Equation1915"}, + {"rhs": "Equation1900", "lhs": "Equation1916"}, + {"rhs": "Equation1901", "lhs": "Equation1917"}, + {"rhs": "Equation1901", "lhs": "Equation1918"}, + {"rhs": "Equation1902", "lhs": "Equation1919"}, + {"rhs": "Equation1926", "lhs": "Equation1930"}, + {"rhs": "Equation1936", "lhs": "Equation1940"}, + {"rhs": "Equation1933", "lhs": "Equation1944"}, + {"rhs": "Equation1936", "lhs": "Equation1948"}, + {"rhs": "Equation1936", "lhs": "Equation1952"}, + {"rhs": "Equation1937", "lhs": "Equation1953"}, + {"rhs": "Equation1938", "lhs": "Equation1954"}, + {"rhs": 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"Equation1938", "lhs": "Equation2005"}, + {"rhs": "Equation1938", "lhs": "Equation2006"}, + {"rhs": "Equation1939", "lhs": "Equation2007"}, + {"rhs": "Equation1941", "lhs": "Equation2009"}, + {"rhs": "Equation1942", "lhs": "Equation2010"}, + {"rhs": "Equation1942", "lhs": "Equation2011"}, + {"rhs": "Equation1943", "lhs": "Equation2012"}, + {"rhs": "Equation1945", "lhs": "Equation2014"}, + {"rhs": "Equation1946", "lhs": "Equation2015"}, + {"rhs": "Equation1946", "lhs": "Equation2016"}, + {"rhs": "Equation1947", "lhs": "Equation2017"}, + {"rhs": "Equation1945", "lhs": "Equation2019"}, + {"rhs": "Equation1946", "lhs": "Equation2020"}, + {"rhs": "Equation1946", "lhs": "Equation2021"}, + {"rhs": "Equation1947", "lhs": "Equation2022"}, + {"rhs": "Equation1949", "lhs": "Equation2024"}, + {"rhs": "Equation1950", "lhs": "Equation2025"}, + {"rhs": "Equation1950", "lhs": "Equation2026"}, + {"rhs": "Equation1951", "lhs": "Equation2027"}, + {"rhs": "Equation2045", "lhs": "Equation2049"}, + {"rhs": 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"Equation2353", "lhs": "Equation2423"}, + {"rhs": "Equation2351", "lhs": "Equation2425"}, + {"rhs": "Equation2352", "lhs": "Equation2426"}, + {"rhs": "Equation2352", "lhs": "Equation2427"}, + {"rhs": "Equation2353", "lhs": "Equation2428"}, + {"rhs": "Equation2355", "lhs": "Equation2430"}, + {"rhs": "Equation2356", "lhs": "Equation2431"}, + {"rhs": "Equation2356", "lhs": "Equation2432"}, + {"rhs": "Equation2357", "lhs": "Equation2433"}, + {"rhs": "Equation2451", "lhs": "Equation2455"}, + {"rhs": "Equation2461", "lhs": "Equation2465"}, + {"rhs": "Equation2471", "lhs": "Equation2475"}, + {"rhs": "Equation2468", "lhs": "Equation2479"}, + {"rhs": "Equation2471", "lhs": "Equation2483"}, + {"rhs": "Equation2471", "lhs": "Equation2487"}, + {"rhs": "Equation2472", "lhs": "Equation2488"}, + {"rhs": "Equation2473", "lhs": "Equation2489"}, + {"rhs": "Equation2473", "lhs": "Equation2490"}, + {"rhs": "Equation2474", "lhs": "Equation2491"}, + {"rhs": "Equation2498", "lhs": "Equation2502"}, + {"rhs": 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"Equation2551", "lhs": "Equation2620"}, + {"rhs": "Equation2552", "lhs": "Equation2621"}, + {"rhs": "Equation2554", "lhs": "Equation2623"}, + {"rhs": "Equation2555", "lhs": "Equation2624"}, + {"rhs": "Equation2555", "lhs": "Equation2625"}, + {"rhs": "Equation2556", "lhs": "Equation2626"}, + {"rhs": "Equation2554", "lhs": "Equation2628"}, + {"rhs": "Equation2555", "lhs": "Equation2629"}, + {"rhs": "Equation2555", "lhs": "Equation2630"}, + {"rhs": "Equation2556", "lhs": "Equation2631"}, + {"rhs": "Equation2558", "lhs": "Equation2633"}, + {"rhs": "Equation2559", "lhs": "Equation2634"}, + {"rhs": "Equation2559", "lhs": "Equation2635"}, + {"rhs": "Equation2560", "lhs": "Equation2636"}, + {"rhs": "Equation2654", "lhs": "Equation2658"}, + {"rhs": "Equation2664", "lhs": "Equation2668"}, + {"rhs": "Equation2674", "lhs": "Equation2678"}, + {"rhs": "Equation2671", "lhs": "Equation2682"}, + {"rhs": "Equation2674", "lhs": "Equation2686"}, + {"rhs": "Equation2674", "lhs": "Equation2690"}, + {"rhs": 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"lhs": "Equation778"}, + {"rhs": "Equation639", "lhs": "Equation779"}, + {"rhs": "Equation640", "lhs": "Equation780"}, + {"rhs": "Equation642", "lhs": "Equation782"}, + {"rhs": "Equation642", "lhs": "Equation783"}, + {"rhs": "Equation643", "lhs": "Equation784"}, + {"rhs": "Equation818", "lhs": "Equation821"}, + {"rhs": "Equation818", "lhs": "Equation824"}, + {"rhs": "Equation818", "lhs": "Equation827"}, + {"rhs": "Equation819", "lhs": "Equation828"}, + {"rhs": "Equation819", "lhs": "Equation829"}, + {"rhs": "Equation820", "lhs": "Equation830"}, + {"rhs": "Equation818", "lhs": "Equation834"}, + {"rhs": "Equation818", "lhs": "Equation837"}, + {"rhs": "Equation819", "lhs": "Equation838"}, + {"rhs": "Equation819", "lhs": "Equation839"}, + {"rhs": "Equation820", "lhs": "Equation840"}, + {"rhs": "Equation818", "lhs": "Equation844"}, + {"rhs": "Equation818", "lhs": "Equation847"}, + {"rhs": "Equation819", "lhs": "Equation848"}, + {"rhs": "Equation819", "lhs": "Equation849"}, + {"rhs": "Equation820", "lhs": "Equation850"}, + {"rhs": "Equation822", "lhs": "Equation852"}, + {"rhs": "Equation822", "lhs": "Equation853"}, + {"rhs": "Equation823", "lhs": "Equation854"}, + {"rhs": "Equation822", "lhs": "Equation856"}, + {"rhs": "Equation822", "lhs": "Equation857"}, + {"rhs": "Equation823", "lhs": "Equation858"}, + {"rhs": "Equation825", "lhs": "Equation860"}, + {"rhs": "Equation825", "lhs": "Equation861"}, + {"rhs": "Equation826", "lhs": "Equation862"}, + {"rhs": "Equation818", "lhs": "Equation871"}, + {"rhs": "Equation818", "lhs": "Equation874"}, + {"rhs": "Equation819", "lhs": "Equation875"}, + {"rhs": "Equation819", "lhs": "Equation876"}, + {"rhs": "Equation820", "lhs": "Equation877"}, + {"rhs": "Equation818", "lhs": "Equation881"}, + {"rhs": "Equation818", "lhs": "Equation884"}, + {"rhs": "Equation819", "lhs": "Equation885"}, + {"rhs": "Equation819", "lhs": "Equation886"}, + {"rhs": "Equation820", "lhs": "Equation887"}, + {"rhs": "Equation822", "lhs": "Equation889"}, + {"rhs": "Equation822", "lhs": "Equation890"}, + {"rhs": "Equation823", "lhs": "Equation891"}, + {"rhs": "Equation822", "lhs": "Equation893"}, + {"rhs": "Equation822", "lhs": "Equation894"}, + {"rhs": "Equation823", "lhs": "Equation895"}, + {"rhs": "Equation825", "lhs": "Equation897"}, + {"rhs": "Equation825", "lhs": "Equation898"}, + {"rhs": "Equation826", "lhs": "Equation899"}, + {"rhs": "Equation818", "lhs": "Equation908"}, + {"rhs": "Equation818", "lhs": "Equation911"}, + {"rhs": "Equation819", "lhs": "Equation912"}, + {"rhs": "Equation819", "lhs": "Equation913"}, + {"rhs": "Equation820", "lhs": "Equation914"}, + {"rhs": "Equation818", "lhs": "Equation918"}, + {"rhs": "Equation818", "lhs": "Equation921"}, + {"rhs": "Equation819", "lhs": "Equation922"}, + {"rhs": "Equation819", "lhs": "Equation923"}, + {"rhs": "Equation820", "lhs": "Equation924"}, + {"rhs": "Equation822", "lhs": "Equation926"}, + {"rhs": "Equation822", "lhs": "Equation927"}, + {"rhs": "Equation823", "lhs": "Equation928"}, + {"rhs": "Equation822", "lhs": "Equation930"}, + {"rhs": "Equation822", "lhs": "Equation931"}, + {"rhs": "Equation823", "lhs": "Equation932"}, + {"rhs": "Equation825", "lhs": "Equation934"}, + {"rhs": "Equation825", "lhs": "Equation935"}, + {"rhs": "Equation826", "lhs": "Equation936"}, + {"rhs": "Equation832", "lhs": "Equation943"}, + {"rhs": "Equation832", "lhs": "Equation944"}, + {"rhs": "Equation833", "lhs": "Equation945"}, + {"rhs": "Equation832", "lhs": "Equation947"}, + {"rhs": "Equation832", "lhs": "Equation948"}, + {"rhs": "Equation833", "lhs": "Equation949"}, + {"rhs": "Equation835", "lhs": "Equation951"}, + {"rhs": "Equation835", "lhs": "Equation952"}, + {"rhs": "Equation836", "lhs": "Equation953"}, + {"rhs": "Equation832", "lhs": "Equation960"}, + {"rhs": "Equation832", "lhs": "Equation961"}, + {"rhs": "Equation833", "lhs": "Equation962"}, + {"rhs": "Equation832", "lhs": "Equation964"}, + {"rhs": "Equation832", "lhs": "Equation965"}, + {"rhs": "Equation833", "lhs": "Equation966"}, + {"rhs": "Equation835", "lhs": "Equation968"}, + {"rhs": "Equation835", "lhs": "Equation969"}, + {"rhs": "Equation836", "lhs": "Equation970"}, + {"rhs": "Equation842", "lhs": "Equation977"}, + {"rhs": "Equation842", "lhs": "Equation978"}, + {"rhs": "Equation843", "lhs": "Equation979"}, + {"rhs": "Equation842", "lhs": "Equation981"}, + {"rhs": "Equation842", "lhs": "Equation982"}, + {"rhs": "Equation843", "lhs": "Equation983"}, + {"rhs": "Equation845", "lhs": "Equation985"}, + {"rhs": "Equation845", "lhs": "Equation986"}, + {"rhs": "Equation846", "lhs": "Equation987"}, + {"rhs": "Equation1021", "lhs": "Equation1024"}, + {"rhs": "Equation1021", "lhs": "Equation1027"}, + {"rhs": "Equation1021", "lhs": "Equation1030"}, + {"rhs": "Equation1022", "lhs": "Equation1031"}, + {"rhs": "Equation1022", "lhs": "Equation1032"}, + {"rhs": "Equation1023", "lhs": "Equation1033"}, + {"rhs": "Equation1021", "lhs": "Equation1037"}, + {"rhs": "Equation1021", "lhs": "Equation1040"}, + {"rhs": "Equation1022", "lhs": "Equation1041"}, + {"rhs": "Equation1022", "lhs": "Equation1042"}, + {"rhs": "Equation1023", "lhs": "Equation1043"}, + {"rhs": "Equation1021", "lhs": "Equation1047"}, + {"rhs": "Equation1021", "lhs": "Equation1050"}, + {"rhs": "Equation1022", "lhs": "Equation1051"}, + {"rhs": "Equation1022", "lhs": "Equation1052"}, + {"rhs": "Equation1023", "lhs": "Equation1053"}, + {"rhs": "Equation1025", "lhs": "Equation1055"}, + {"rhs": "Equation1025", "lhs": "Equation1056"}, + {"rhs": "Equation1026", "lhs": "Equation1057"}, + {"rhs": "Equation1025", "lhs": "Equation1059"}, + {"rhs": "Equation1025", "lhs": "Equation1060"}, + {"rhs": "Equation1026", "lhs": "Equation1061"}, + {"rhs": "Equation1028", "lhs": "Equation1063"}, + {"rhs": "Equation1028", "lhs": "Equation1064"}, + {"rhs": "Equation1029", "lhs": "Equation1065"}, + {"rhs": "Equation1021", "lhs": "Equation1074"}, + {"rhs": "Equation1021", "lhs": "Equation1077"}, + {"rhs": "Equation1022", "lhs": "Equation1078"}, + {"rhs": "Equation1022", "lhs": "Equation1079"}, + {"rhs": "Equation1023", "lhs": "Equation1080"}, + {"rhs": "Equation1021", "lhs": "Equation1084"}, + {"rhs": "Equation1021", "lhs": "Equation1087"}, + {"rhs": "Equation1022", "lhs": "Equation1088"}, + {"rhs": "Equation1022", "lhs": "Equation1089"}, + {"rhs": "Equation1023", "lhs": "Equation1090"}, + {"rhs": "Equation1025", "lhs": "Equation1092"}, + {"rhs": "Equation1025", "lhs": "Equation1093"}, + {"rhs": "Equation1026", "lhs": "Equation1094"}, + {"rhs": "Equation1025", "lhs": "Equation1096"}, + {"rhs": "Equation1025", "lhs": "Equation1097"}, + {"rhs": "Equation1026", "lhs": "Equation1098"}, + {"rhs": "Equation1028", "lhs": "Equation1100"}, + {"rhs": "Equation1028", "lhs": "Equation1101"}, + {"rhs": "Equation1029", "lhs": "Equation1102"}, + {"rhs": "Equation1021", "lhs": "Equation1111"}, + {"rhs": "Equation1021", "lhs": "Equation1114"}, + {"rhs": "Equation1022", "lhs": "Equation1115"}, + {"rhs": "Equation1022", "lhs": "Equation1116"}, + {"rhs": "Equation1023", "lhs": "Equation1117"}, + {"rhs": "Equation1021", "lhs": "Equation1121"}, + {"rhs": "Equation1021", "lhs": "Equation1124"}, + {"rhs": "Equation1022", "lhs": "Equation1125"}, + {"rhs": "Equation1022", "lhs": "Equation1126"}, + {"rhs": "Equation1023", "lhs": "Equation1127"}, + {"rhs": "Equation1025", "lhs": "Equation1129"}, + {"rhs": "Equation1025", "lhs": "Equation1130"}, + {"rhs": "Equation1026", "lhs": "Equation1131"}, + {"rhs": "Equation1025", "lhs": "Equation1133"}, + {"rhs": "Equation1025", "lhs": "Equation1134"}, + {"rhs": "Equation1026", "lhs": "Equation1135"}, + {"rhs": "Equation1028", "lhs": "Equation1137"}, + {"rhs": "Equation1028", "lhs": "Equation1138"}, + {"rhs": "Equation1029", "lhs": "Equation1139"}, + {"rhs": "Equation1035", "lhs": "Equation1146"}, + {"rhs": "Equation1035", "lhs": "Equation1147"}, + {"rhs": "Equation1036", "lhs": "Equation1148"}, + {"rhs": "Equation1035", "lhs": "Equation1150"}, + {"rhs": "Equation1035", "lhs": "Equation1151"}, + {"rhs": "Equation1036", "lhs": "Equation1152"}, + {"rhs": "Equation1038", "lhs": "Equation1154"}, + {"rhs": "Equation1038", "lhs": "Equation1155"}, + {"rhs": "Equation1039", "lhs": "Equation1156"}, + {"rhs": "Equation1035", "lhs": "Equation1163"}, + {"rhs": "Equation1035", "lhs": "Equation1164"}, + {"rhs": "Equation1036", "lhs": "Equation1165"}, + {"rhs": "Equation1035", "lhs": "Equation1167"}, + {"rhs": "Equation1035", "lhs": "Equation1168"}, + {"rhs": "Equation1036", "lhs": "Equation1169"}, + {"rhs": "Equation1038", "lhs": "Equation1171"}, + {"rhs": "Equation1038", "lhs": "Equation1172"}, + {"rhs": "Equation1039", "lhs": "Equation1173"}, + {"rhs": "Equation1045", "lhs": "Equation1180"}, + {"rhs": "Equation1045", "lhs": "Equation1181"}, + {"rhs": "Equation1046", "lhs": "Equation1182"}, + {"rhs": "Equation1045", "lhs": "Equation1184"}, + {"rhs": "Equation1045", "lhs": "Equation1185"}, + {"rhs": "Equation1046", "lhs": "Equation1186"}, + {"rhs": "Equation1048", "lhs": "Equation1188"}, + {"rhs": "Equation1048", "lhs": "Equation1189"}, + {"rhs": "Equation1049", "lhs": "Equation1190"}, + {"rhs": "Equation1224", "lhs": "Equation1227"}, + {"rhs": "Equation1224", "lhs": "Equation1230"}, + {"rhs": "Equation1224", "lhs": "Equation1233"}, + {"rhs": "Equation1225", "lhs": "Equation1234"}, + {"rhs": "Equation1225", "lhs": "Equation1235"}, + {"rhs": "Equation1226", "lhs": "Equation1236"}, + {"rhs": "Equation1224", "lhs": "Equation1240"}, + {"rhs": "Equation1224", "lhs": "Equation1243"}, + {"rhs": "Equation1225", "lhs": "Equation1244"}, + {"rhs": "Equation1225", "lhs": "Equation1245"}, + {"rhs": "Equation1226", "lhs": "Equation1246"}, + {"rhs": "Equation1224", "lhs": "Equation1250"}, + {"rhs": "Equation1224", "lhs": "Equation1253"}, + {"rhs": "Equation1225", "lhs": "Equation1254"}, + {"rhs": "Equation1225", "lhs": "Equation1255"}, + {"rhs": "Equation1226", "lhs": "Equation1256"}, + {"rhs": "Equation1228", "lhs": "Equation1258"}, + {"rhs": "Equation1228", "lhs": "Equation1259"}, + {"rhs": "Equation1229", "lhs": "Equation1260"}, + {"rhs": "Equation1228", "lhs": "Equation1262"}, + {"rhs": "Equation1228", "lhs": "Equation1263"}, + {"rhs": "Equation1229", "lhs": "Equation1264"}, + {"rhs": "Equation1231", "lhs": "Equation1266"}, + {"rhs": "Equation1231", "lhs": "Equation1267"}, + {"rhs": "Equation1232", "lhs": "Equation1268"}, + {"rhs": "Equation1224", "lhs": "Equation1277"}, + {"rhs": "Equation1224", "lhs": "Equation1280"}, + {"rhs": "Equation1225", "lhs": "Equation1281"}, + {"rhs": "Equation1225", "lhs": "Equation1282"}, + {"rhs": "Equation1226", "lhs": "Equation1283"}, + {"rhs": "Equation1224", "lhs": "Equation1287"}, + {"rhs": "Equation1224", "lhs": "Equation1290"}, + {"rhs": "Equation1225", "lhs": "Equation1291"}, + {"rhs": "Equation1225", "lhs": "Equation1292"}, + {"rhs": "Equation1226", "lhs": "Equation1293"}, + {"rhs": "Equation1228", "lhs": "Equation1295"}, + {"rhs": "Equation1228", "lhs": "Equation1296"}, + {"rhs": "Equation1229", "lhs": "Equation1297"}, + {"rhs": "Equation1228", "lhs": "Equation1299"}, + {"rhs": "Equation1228", "lhs": "Equation1300"}, + {"rhs": "Equation1229", "lhs": "Equation1301"}, + {"rhs": "Equation1231", "lhs": "Equation1303"}, + {"rhs": "Equation1231", "lhs": "Equation1304"}, + {"rhs": "Equation1232", "lhs": "Equation1305"}, + {"rhs": "Equation1224", "lhs": "Equation1314"}, + {"rhs": "Equation1224", "lhs": "Equation1317"}, + {"rhs": "Equation1225", "lhs": "Equation1318"}, + {"rhs": "Equation1225", "lhs": "Equation1319"}, + {"rhs": "Equation1226", "lhs": "Equation1320"}, + {"rhs": "Equation1224", "lhs": "Equation1324"}, + {"rhs": "Equation1224", "lhs": "Equation1327"}, + {"rhs": "Equation1225", "lhs": "Equation1328"}, + {"rhs": "Equation1225", "lhs": "Equation1329"}, + {"rhs": "Equation1226", "lhs": "Equation1330"}, + {"rhs": "Equation1228", "lhs": "Equation1332"}, + {"rhs": "Equation1228", "lhs": "Equation1333"}, + {"rhs": "Equation1229", "lhs": "Equation1334"}, + {"rhs": "Equation1228", "lhs": "Equation1336"}, + {"rhs": "Equation1228", "lhs": "Equation1337"}, + {"rhs": "Equation1229", "lhs": "Equation1338"}, + {"rhs": "Equation1231", "lhs": "Equation1340"}, + {"rhs": "Equation1231", "lhs": "Equation1341"}, + {"rhs": "Equation1232", "lhs": "Equation1342"}, + {"rhs": "Equation1238", "lhs": "Equation1349"}, + {"rhs": "Equation1238", "lhs": "Equation1350"}, + {"rhs": "Equation1239", "lhs": "Equation1351"}, + {"rhs": "Equation1238", "lhs": "Equation1353"}, + {"rhs": "Equation1238", "lhs": "Equation1354"}, + {"rhs": "Equation1239", "lhs": "Equation1355"}, + {"rhs": "Equation1241", "lhs": "Equation1357"}, + {"rhs": "Equation1241", "lhs": "Equation1358"}, + {"rhs": "Equation1242", "lhs": "Equation1359"}, + {"rhs": "Equation1238", "lhs": "Equation1366"}, + {"rhs": "Equation1238", "lhs": "Equation1367"}, + {"rhs": "Equation1239", "lhs": "Equation1368"}, + {"rhs": "Equation1238", "lhs": "Equation1370"}, + {"rhs": "Equation1238", "lhs": "Equation1371"}, + {"rhs": "Equation1239", "lhs": "Equation1372"}, + {"rhs": "Equation1241", "lhs": "Equation1374"}, + {"rhs": "Equation1241", "lhs": "Equation1375"}, + {"rhs": "Equation1242", "lhs": "Equation1376"}, + {"rhs": "Equation1248", "lhs": "Equation1383"}, + {"rhs": "Equation1248", "lhs": "Equation1384"}, + {"rhs": "Equation1249", "lhs": "Equation1385"}, + {"rhs": "Equation1248", "lhs": "Equation1387"}, + {"rhs": "Equation1248", "lhs": "Equation1388"}, + {"rhs": "Equation1249", "lhs": "Equation1389"}, + {"rhs": "Equation1251", "lhs": "Equation1391"}, + {"rhs": "Equation1251", "lhs": "Equation1392"}, + {"rhs": "Equation1252", "lhs": "Equation1393"}, + {"rhs": "Equation1427", "lhs": "Equation1430"}, + {"rhs": "Equation1427", "lhs": "Equation1433"}, + {"rhs": "Equation1427", "lhs": "Equation1436"}, + {"rhs": "Equation1428", "lhs": "Equation1437"}, + {"rhs": "Equation1428", "lhs": "Equation1438"}, + {"rhs": "Equation1429", "lhs": "Equation1439"}, + {"rhs": "Equation1427", "lhs": "Equation1443"}, + {"rhs": "Equation1427", "lhs": "Equation1446"}, + {"rhs": "Equation1428", "lhs": "Equation1447"}, + {"rhs": "Equation1428", "lhs": "Equation1448"}, + {"rhs": "Equation1429", "lhs": "Equation1449"}, + {"rhs": "Equation1427", "lhs": "Equation1453"}, + {"rhs": "Equation1427", "lhs": "Equation1456"}, + {"rhs": "Equation1428", "lhs": "Equation1457"}, + {"rhs": "Equation1428", "lhs": "Equation1458"}, + {"rhs": "Equation1429", "lhs": "Equation1459"}, + {"rhs": "Equation1431", "lhs": "Equation1461"}, + {"rhs": "Equation1431", "lhs": "Equation1462"}, + {"rhs": "Equation1432", "lhs": "Equation1463"}, + {"rhs": "Equation1431", "lhs": "Equation1465"}, + {"rhs": "Equation1431", "lhs": "Equation1466"}, + {"rhs": "Equation1432", "lhs": "Equation1467"}, + {"rhs": "Equation1434", "lhs": "Equation1469"}, + {"rhs": "Equation1434", "lhs": "Equation1470"}, + {"rhs": "Equation1435", "lhs": "Equation1471"}, + {"rhs": "Equation1427", "lhs": "Equation1480"}, + {"rhs": "Equation1427", "lhs": "Equation1483"}, + {"rhs": "Equation1428", "lhs": "Equation1484"}, + {"rhs": "Equation1428", "lhs": "Equation1485"}, + {"rhs": "Equation1429", "lhs": "Equation1486"}, + {"rhs": "Equation1427", "lhs": "Equation1490"}, + {"rhs": "Equation1427", "lhs": "Equation1493"}, + {"rhs": "Equation1428", "lhs": "Equation1494"}, + {"rhs": "Equation1428", "lhs": "Equation1495"}, + {"rhs": "Equation1429", "lhs": "Equation1496"}, + {"rhs": "Equation1431", "lhs": "Equation1498"}, + {"rhs": "Equation1431", "lhs": "Equation1499"}, + {"rhs": "Equation1432", "lhs": "Equation1500"}, + {"rhs": "Equation1431", "lhs": "Equation1502"}, + {"rhs": "Equation1431", "lhs": "Equation1503"}, + {"rhs": "Equation1432", "lhs": "Equation1504"}, + {"rhs": "Equation1434", "lhs": "Equation1506"}, + {"rhs": "Equation1434", "lhs": "Equation1507"}, + {"rhs": "Equation1435", "lhs": "Equation1508"}, + {"rhs": "Equation1427", "lhs": "Equation1517"}, + {"rhs": "Equation1427", "lhs": "Equation1520"}, + {"rhs": "Equation1428", "lhs": "Equation1521"}, + {"rhs": "Equation1428", "lhs": "Equation1522"}, + {"rhs": "Equation1429", "lhs": "Equation1523"}, + {"rhs": "Equation1427", "lhs": "Equation1527"}, + {"rhs": "Equation1427", "lhs": "Equation1530"}, + {"rhs": "Equation1428", "lhs": "Equation1531"}, + {"rhs": "Equation1428", "lhs": "Equation1532"}, + {"rhs": "Equation1429", "lhs": "Equation1533"}, + {"rhs": "Equation1431", "lhs": "Equation1535"}, + {"rhs": "Equation1431", "lhs": "Equation1536"}, + {"rhs": "Equation1432", "lhs": "Equation1537"}, + {"rhs": "Equation1431", "lhs": "Equation1539"}, + {"rhs": "Equation1431", "lhs": "Equation1540"}, + {"rhs": "Equation1432", "lhs": "Equation1541"}, + {"rhs": "Equation1434", "lhs": "Equation1543"}, + {"rhs": "Equation1434", "lhs": "Equation1544"}, + {"rhs": "Equation1435", "lhs": "Equation1545"}, + {"rhs": "Equation1441", "lhs": "Equation1552"}, + {"rhs": "Equation1441", "lhs": "Equation1553"}, + {"rhs": "Equation1442", "lhs": "Equation1554"}, + {"rhs": "Equation1441", "lhs": "Equation1556"}, + {"rhs": "Equation1441", "lhs": "Equation1557"}, + {"rhs": "Equation1442", "lhs": "Equation1558"}, + {"rhs": "Equation1444", "lhs": "Equation1560"}, + {"rhs": "Equation1444", "lhs": "Equation1561"}, + {"rhs": "Equation1445", "lhs": "Equation1562"}, + {"rhs": "Equation1441", "lhs": "Equation1569"}, + {"rhs": "Equation1441", "lhs": "Equation1570"}, + {"rhs": "Equation1442", "lhs": "Equation1571"}, + {"rhs": "Equation1441", "lhs": "Equation1573"}, + {"rhs": "Equation1441", "lhs": "Equation1574"}, + {"rhs": "Equation1442", "lhs": "Equation1575"}, + {"rhs": "Equation1444", "lhs": "Equation1577"}, + {"rhs": "Equation1444", "lhs": "Equation1578"}, + {"rhs": "Equation1445", "lhs": "Equation1579"}, + {"rhs": "Equation1451", "lhs": "Equation1586"}, + {"rhs": "Equation1451", "lhs": "Equation1587"}, + {"rhs": "Equation1452", "lhs": "Equation1588"}, + {"rhs": "Equation1451", "lhs": "Equation1590"}, + {"rhs": "Equation1451", "lhs": "Equation1591"}, + {"rhs": "Equation1452", "lhs": "Equation1592"}, + {"rhs": "Equation1454", "lhs": "Equation1594"}, + {"rhs": "Equation1454", "lhs": "Equation1595"}, + {"rhs": "Equation1455", "lhs": "Equation1596"}, + {"rhs": "Equation1630", "lhs": "Equation1633"}, + {"rhs": "Equation1630", "lhs": "Equation1636"}, + {"rhs": "Equation1630", "lhs": "Equation1639"}, + {"rhs": "Equation1631", "lhs": "Equation1640"}, + {"rhs": "Equation1631", "lhs": "Equation1641"}, + {"rhs": "Equation1632", "lhs": "Equation1642"}, + {"rhs": "Equation1630", "lhs": "Equation1646"}, + {"rhs": "Equation1630", "lhs": "Equation1649"}, + {"rhs": "Equation1631", "lhs": "Equation1650"}, + {"rhs": "Equation1631", "lhs": "Equation1651"}, + {"rhs": "Equation1632", "lhs": "Equation1652"}, + {"rhs": "Equation1630", "lhs": "Equation1656"}, + {"rhs": "Equation1630", "lhs": "Equation1659"}, + {"rhs": "Equation1631", "lhs": "Equation1660"}, + {"rhs": "Equation1631", "lhs": "Equation1661"}, + {"rhs": "Equation1632", "lhs": "Equation1662"}, + {"rhs": "Equation1634", "lhs": "Equation1664"}, + {"rhs": "Equation1634", "lhs": "Equation1665"}, + {"rhs": "Equation1635", "lhs": "Equation1666"}, + {"rhs": "Equation1634", "lhs": "Equation1668"}, + {"rhs": "Equation1634", "lhs": "Equation1669"}, + {"rhs": "Equation1635", "lhs": "Equation1670"}, + {"rhs": "Equation1637", "lhs": "Equation1672"}, + {"rhs": "Equation1637", "lhs": "Equation1673"}, + {"rhs": "Equation1638", "lhs": "Equation1674"}, + {"rhs": "Equation1630", "lhs": "Equation1683"}, + {"rhs": "Equation1630", "lhs": "Equation1686"}, + {"rhs": "Equation1631", "lhs": "Equation1687"}, + {"rhs": "Equation1631", "lhs": "Equation1688"}, + {"rhs": "Equation1632", "lhs": "Equation1689"}, + {"rhs": "Equation1630", "lhs": "Equation1693"}, + {"rhs": "Equation1630", "lhs": "Equation1696"}, + {"rhs": "Equation1631", "lhs": "Equation1697"}, + {"rhs": "Equation1631", "lhs": "Equation1698"}, + {"rhs": "Equation1632", "lhs": "Equation1699"}, + {"rhs": "Equation1634", "lhs": "Equation1701"}, + {"rhs": "Equation1634", "lhs": "Equation1702"}, + {"rhs": "Equation1635", "lhs": "Equation1703"}, + {"rhs": "Equation1634", "lhs": "Equation1705"}, + {"rhs": "Equation1634", "lhs": "Equation1706"}, + {"rhs": "Equation1635", "lhs": "Equation1707"}, + {"rhs": "Equation1637", "lhs": "Equation1709"}, + {"rhs": "Equation1637", "lhs": "Equation1710"}, + {"rhs": "Equation1638", "lhs": "Equation1711"}, + {"rhs": "Equation1630", "lhs": "Equation1720"}, + {"rhs": "Equation1630", "lhs": "Equation1723"}, + {"rhs": "Equation1631", "lhs": "Equation1724"}, + {"rhs": "Equation1631", "lhs": "Equation1725"}, + {"rhs": "Equation1632", "lhs": "Equation1726"}, + {"rhs": "Equation1630", "lhs": "Equation1730"}, + {"rhs": "Equation1630", "lhs": "Equation1733"}, + {"rhs": "Equation1631", "lhs": "Equation1734"}, + {"rhs": "Equation1631", "lhs": "Equation1735"}, + {"rhs": "Equation1632", "lhs": "Equation1736"}, + {"rhs": "Equation1634", "lhs": "Equation1738"}, + {"rhs": "Equation1634", "lhs": "Equation1739"}, + {"rhs": "Equation1635", "lhs": "Equation1740"}, + {"rhs": "Equation1634", "lhs": "Equation1742"}, + {"rhs": "Equation1634", "lhs": "Equation1743"}, + {"rhs": "Equation1635", "lhs": "Equation1744"}, + {"rhs": "Equation1637", "lhs": "Equation1746"}, + {"rhs": "Equation1637", "lhs": "Equation1747"}, + {"rhs": "Equation1638", "lhs": "Equation1748"}, + {"rhs": "Equation1644", "lhs": "Equation1755"}, + {"rhs": "Equation1644", "lhs": "Equation1756"}, + {"rhs": "Equation1645", "lhs": "Equation1757"}, + {"rhs": "Equation1644", "lhs": "Equation1759"}, + {"rhs": "Equation1644", "lhs": "Equation1760"}, + {"rhs": "Equation1645", "lhs": "Equation1761"}, + {"rhs": "Equation1647", "lhs": "Equation1763"}, + {"rhs": "Equation1647", "lhs": "Equation1764"}, + {"rhs": "Equation1648", "lhs": "Equation1765"}, + {"rhs": "Equation1644", "lhs": "Equation1772"}, + {"rhs": "Equation1644", "lhs": "Equation1773"}, + {"rhs": "Equation1645", "lhs": "Equation1774"}, + {"rhs": "Equation1644", "lhs": "Equation1776"}, + {"rhs": "Equation1644", "lhs": "Equation1777"}, + {"rhs": "Equation1645", "lhs": "Equation1778"}, + {"rhs": "Equation1647", "lhs": "Equation1780"}, + {"rhs": "Equation1647", "lhs": "Equation1781"}, + {"rhs": "Equation1648", "lhs": "Equation1782"}, + {"rhs": "Equation1654", "lhs": "Equation1789"}, + {"rhs": "Equation1654", "lhs": "Equation1790"}, + {"rhs": "Equation1655", "lhs": "Equation1791"}, + {"rhs": "Equation1654", "lhs": "Equation1793"}, + {"rhs": "Equation1654", "lhs": "Equation1794"}, + {"rhs": "Equation1655", "lhs": "Equation1795"}, + {"rhs": "Equation1657", "lhs": "Equation1797"}, + {"rhs": "Equation1657", "lhs": "Equation1798"}, + {"rhs": "Equation1658", "lhs": "Equation1799"}, + {"rhs": "Equation1833", "lhs": "Equation1836"}, + {"rhs": "Equation1833", "lhs": "Equation1839"}, + {"rhs": "Equation1833", "lhs": "Equation1842"}, + {"rhs": "Equation1834", "lhs": "Equation1843"}, + {"rhs": "Equation1834", "lhs": "Equation1844"}, + {"rhs": "Equation1835", "lhs": "Equation1845"}, + {"rhs": "Equation1833", "lhs": "Equation1849"}, + {"rhs": "Equation1833", "lhs": "Equation1852"}, + {"rhs": "Equation1834", "lhs": "Equation1853"}, + {"rhs": "Equation1834", "lhs": "Equation1854"}, + {"rhs": "Equation1835", "lhs": "Equation1855"}, + {"rhs": "Equation1833", "lhs": "Equation1859"}, + {"rhs": "Equation1833", "lhs": "Equation1862"}, + {"rhs": "Equation1834", "lhs": "Equation1863"}, + {"rhs": "Equation1834", "lhs": "Equation1864"}, + {"rhs": "Equation1835", "lhs": "Equation1865"}, + {"rhs": "Equation1837", "lhs": "Equation1867"}, + {"rhs": "Equation1837", "lhs": "Equation1868"}, + {"rhs": "Equation1838", "lhs": "Equation1869"}, + {"rhs": "Equation1837", "lhs": "Equation1871"}, + {"rhs": "Equation1837", "lhs": "Equation1872"}, + {"rhs": "Equation1838", "lhs": "Equation1873"}, + {"rhs": "Equation1840", "lhs": "Equation1875"}, + {"rhs": "Equation1840", "lhs": "Equation1876"}, + {"rhs": "Equation1841", "lhs": "Equation1877"}, + {"rhs": "Equation1833", "lhs": "Equation1886"}, + {"rhs": "Equation1833", "lhs": "Equation1889"}, + {"rhs": "Equation1834", "lhs": "Equation1890"}, + {"rhs": "Equation1834", "lhs": "Equation1891"}, + {"rhs": "Equation1835", "lhs": "Equation1892"}, + {"rhs": "Equation1833", "lhs": "Equation1896"}, + {"rhs": "Equation1833", "lhs": "Equation1899"}, + {"rhs": "Equation1834", "lhs": "Equation1900"}, + {"rhs": "Equation1834", "lhs": "Equation1901"}, + {"rhs": "Equation1835", "lhs": "Equation1902"}, + {"rhs": "Equation1837", "lhs": "Equation1904"}, + {"rhs": "Equation1837", "lhs": "Equation1905"}, + {"rhs": "Equation1838", "lhs": "Equation1906"}, + {"rhs": "Equation1837", "lhs": "Equation1908"}, + {"rhs": "Equation1837", "lhs": "Equation1909"}, + {"rhs": "Equation1838", "lhs": "Equation1910"}, + {"rhs": "Equation1840", "lhs": "Equation1912"}, + {"rhs": "Equation1840", "lhs": "Equation1913"}, + {"rhs": "Equation1841", "lhs": "Equation1914"}, + {"rhs": "Equation1833", "lhs": "Equation1923"}, + {"rhs": "Equation1833", "lhs": "Equation1926"}, + {"rhs": "Equation1834", "lhs": "Equation1927"}, + {"rhs": "Equation1834", "lhs": "Equation1928"}, + {"rhs": "Equation1835", "lhs": "Equation1929"}, + {"rhs": "Equation1833", "lhs": "Equation1933"}, + {"rhs": "Equation1833", "lhs": "Equation1936"}, + {"rhs": "Equation1834", "lhs": "Equation1937"}, + {"rhs": "Equation1834", "lhs": "Equation1938"}, + {"rhs": "Equation1835", "lhs": "Equation1939"}, + {"rhs": "Equation1837", "lhs": "Equation1941"}, + {"rhs": "Equation1837", "lhs": "Equation1942"}, + {"rhs": "Equation1838", "lhs": "Equation1943"}, + {"rhs": "Equation1837", "lhs": "Equation1945"}, + {"rhs": "Equation1837", "lhs": "Equation1946"}, + {"rhs": "Equation1838", "lhs": "Equation1947"}, + {"rhs": "Equation1840", "lhs": "Equation1949"}, + {"rhs": "Equation1840", "lhs": "Equation1950"}, + {"rhs": "Equation1841", "lhs": "Equation1951"}, + {"rhs": "Equation1847", "lhs": "Equation1958"}, + {"rhs": "Equation1847", "lhs": "Equation1959"}, + {"rhs": "Equation1848", "lhs": "Equation1960"}, + {"rhs": "Equation1847", "lhs": "Equation1962"}, + {"rhs": "Equation1847", "lhs": "Equation1963"}, + {"rhs": "Equation1848", "lhs": "Equation1964"}, + {"rhs": "Equation1850", "lhs": "Equation1966"}, + {"rhs": "Equation1850", "lhs": "Equation1967"}, + {"rhs": "Equation1851", "lhs": "Equation1968"}, + {"rhs": "Equation1847", "lhs": "Equation1975"}, + {"rhs": "Equation1847", "lhs": "Equation1976"}, + {"rhs": "Equation1848", "lhs": "Equation1977"}, + {"rhs": "Equation1847", "lhs": "Equation1979"}, + {"rhs": "Equation1847", "lhs": "Equation1980"}, + {"rhs": "Equation1848", "lhs": "Equation1981"}, + {"rhs": "Equation1850", "lhs": "Equation1983"}, + {"rhs": "Equation1850", "lhs": "Equation1984"}, + {"rhs": "Equation1851", "lhs": "Equation1985"}, + {"rhs": "Equation1857", "lhs": "Equation1992"}, + {"rhs": "Equation1857", "lhs": "Equation1993"}, + {"rhs": "Equation1858", "lhs": "Equation1994"}, + {"rhs": "Equation1857", "lhs": "Equation1996"}, + {"rhs": "Equation1857", "lhs": "Equation1997"}, + {"rhs": "Equation1858", "lhs": "Equation1998"}, + {"rhs": "Equation1860", "lhs": "Equation2000"}, + {"rhs": "Equation1860", "lhs": "Equation2001"}, + {"rhs": "Equation1861", "lhs": "Equation2002"}, + {"rhs": "Equation2036", "lhs": "Equation2039"}, + {"rhs": "Equation2036", "lhs": "Equation2042"}, + {"rhs": "Equation2036", "lhs": "Equation2045"}, + {"rhs": "Equation2037", "lhs": "Equation2046"}, + {"rhs": "Equation2037", "lhs": "Equation2047"}, + {"rhs": "Equation2038", "lhs": "Equation2048"}, + {"rhs": "Equation2036", "lhs": "Equation2052"}, + {"rhs": "Equation2036", "lhs": "Equation2055"}, + {"rhs": "Equation2037", "lhs": "Equation2056"}, + {"rhs": "Equation2037", "lhs": "Equation2057"}, + {"rhs": "Equation2038", "lhs": "Equation2058"}, + {"rhs": "Equation2036", "lhs": "Equation2062"}, + {"rhs": "Equation2036", "lhs": "Equation2065"}, + {"rhs": "Equation2037", "lhs": "Equation2066"}, + {"rhs": "Equation2037", "lhs": "Equation2067"}, + {"rhs": "Equation2038", "lhs": "Equation2068"}, + {"rhs": "Equation2040", "lhs": "Equation2070"}, + {"rhs": "Equation2040", "lhs": "Equation2071"}, + {"rhs": "Equation2041", "lhs": "Equation2072"}, + {"rhs": "Equation2040", "lhs": "Equation2074"}, + {"rhs": "Equation2040", "lhs": "Equation2075"}, + {"rhs": "Equation2041", "lhs": "Equation2076"}, + {"rhs": "Equation2043", "lhs": "Equation2078"}, + {"rhs": "Equation2043", "lhs": "Equation2079"}, + {"rhs": "Equation2044", "lhs": "Equation2080"}, + {"rhs": "Equation2036", "lhs": "Equation2089"}, + {"rhs": "Equation2036", "lhs": "Equation2092"}, + {"rhs": "Equation2037", "lhs": "Equation2093"}, + {"rhs": "Equation2037", "lhs": "Equation2094"}, + {"rhs": "Equation2038", "lhs": "Equation2095"}, + {"rhs": "Equation2036", "lhs": "Equation2099"}, + {"rhs": "Equation2036", "lhs": "Equation2102"}, + {"rhs": "Equation2037", "lhs": "Equation2103"}, + {"rhs": "Equation2037", "lhs": "Equation2104"}, + {"rhs": "Equation2038", "lhs": "Equation2105"}, + {"rhs": "Equation2040", "lhs": "Equation2107"}, + {"rhs": "Equation2040", "lhs": "Equation2108"}, + {"rhs": "Equation2041", "lhs": "Equation2109"}, + {"rhs": "Equation2040", "lhs": "Equation2111"}, + {"rhs": "Equation2040", "lhs": "Equation2112"}, + {"rhs": "Equation2041", "lhs": "Equation2113"}, + {"rhs": "Equation2043", "lhs": "Equation2115"}, + {"rhs": "Equation2043", "lhs": "Equation2116"}, + {"rhs": "Equation2044", "lhs": "Equation2117"}, + {"rhs": "Equation2036", "lhs": "Equation2126"}, + {"rhs": "Equation2036", "lhs": "Equation2129"}, + {"rhs": "Equation2037", "lhs": "Equation2130"}, + {"rhs": "Equation2037", "lhs": "Equation2131"}, + {"rhs": "Equation2038", "lhs": "Equation2132"}, + {"rhs": "Equation2036", "lhs": "Equation2136"}, + {"rhs": "Equation2036", "lhs": "Equation2139"}, + {"rhs": "Equation2037", "lhs": "Equation2140"}, + {"rhs": "Equation2037", "lhs": "Equation2141"}, + {"rhs": "Equation2038", "lhs": "Equation2142"}, + {"rhs": "Equation2040", "lhs": "Equation2144"}, + {"rhs": "Equation2040", "lhs": "Equation2145"}, + {"rhs": "Equation2041", "lhs": "Equation2146"}, + {"rhs": "Equation2040", "lhs": "Equation2148"}, + {"rhs": "Equation2040", "lhs": "Equation2149"}, + {"rhs": "Equation2041", "lhs": "Equation2150"}, + {"rhs": "Equation2043", "lhs": "Equation2152"}, + {"rhs": "Equation2043", "lhs": "Equation2153"}, + {"rhs": "Equation2044", "lhs": "Equation2154"}, + {"rhs": "Equation2050", "lhs": "Equation2161"}, + {"rhs": "Equation2050", "lhs": "Equation2162"}, + {"rhs": "Equation2051", "lhs": "Equation2163"}, + {"rhs": "Equation2050", "lhs": "Equation2165"}, + {"rhs": "Equation2050", "lhs": "Equation2166"}, + {"rhs": "Equation2051", "lhs": "Equation2167"}, + {"rhs": "Equation2053", "lhs": "Equation2169"}, + {"rhs": "Equation2053", "lhs": "Equation2170"}, + {"rhs": "Equation2054", "lhs": "Equation2171"}, + {"rhs": "Equation2050", "lhs": "Equation2178"}, + {"rhs": "Equation2050", "lhs": "Equation2179"}, + {"rhs": "Equation2051", "lhs": "Equation2180"}, + {"rhs": "Equation2050", "lhs": "Equation2182"}, + {"rhs": "Equation2050", "lhs": "Equation2183"}, + {"rhs": "Equation2051", "lhs": "Equation2184"}, + {"rhs": "Equation2053", "lhs": "Equation2186"}, + {"rhs": "Equation2053", "lhs": "Equation2187"}, + {"rhs": "Equation2054", "lhs": "Equation2188"}, + {"rhs": "Equation2060", "lhs": "Equation2195"}, + {"rhs": "Equation2060", "lhs": "Equation2196"}, + {"rhs": "Equation2061", "lhs": "Equation2197"}, + {"rhs": "Equation2060", "lhs": "Equation2199"}, + {"rhs": "Equation2060", "lhs": "Equation2200"}, + {"rhs": "Equation2061", "lhs": "Equation2201"}, + {"rhs": "Equation2063", "lhs": "Equation2203"}, + {"rhs": "Equation2063", "lhs": "Equation2204"}, + {"rhs": "Equation2064", "lhs": "Equation2205"}, + {"rhs": "Equation2239", "lhs": "Equation2242"}, + {"rhs": "Equation2239", "lhs": "Equation2245"}, + {"rhs": "Equation2239", "lhs": "Equation2248"}, + {"rhs": "Equation2240", "lhs": "Equation2249"}, + {"rhs": "Equation2240", "lhs": "Equation2250"}, + {"rhs": "Equation2241", "lhs": "Equation2251"}, + {"rhs": "Equation2239", "lhs": "Equation2255"}, + {"rhs": "Equation2239", "lhs": "Equation2258"}, + {"rhs": "Equation2240", "lhs": "Equation2259"}, + {"rhs": "Equation2240", "lhs": "Equation2260"}, + {"rhs": "Equation2241", "lhs": "Equation2261"}, + {"rhs": "Equation2239", "lhs": "Equation2265"}, + {"rhs": "Equation2239", "lhs": "Equation2268"}, + {"rhs": "Equation2240", "lhs": "Equation2269"}, + {"rhs": "Equation2240", "lhs": "Equation2270"}, + {"rhs": "Equation2241", "lhs": "Equation2271"}, + {"rhs": "Equation2243", "lhs": "Equation2273"}, + {"rhs": "Equation2243", "lhs": "Equation2274"}, + {"rhs": "Equation2244", "lhs": "Equation2275"}, + {"rhs": "Equation2243", "lhs": "Equation2277"}, + {"rhs": "Equation2243", "lhs": "Equation2278"}, + {"rhs": "Equation2244", "lhs": "Equation2279"}, + {"rhs": "Equation2246", "lhs": "Equation2281"}, + {"rhs": "Equation2246", "lhs": "Equation2282"}, + {"rhs": "Equation2247", "lhs": "Equation2283"}, + {"rhs": "Equation2239", "lhs": "Equation2292"}, + {"rhs": "Equation2239", "lhs": "Equation2295"}, + {"rhs": "Equation2240", "lhs": "Equation2296"}, + {"rhs": "Equation2240", "lhs": "Equation2297"}, + {"rhs": "Equation2241", "lhs": "Equation2298"}, + {"rhs": "Equation2239", "lhs": "Equation2302"}, + {"rhs": "Equation2239", "lhs": "Equation2305"}, + {"rhs": "Equation2240", "lhs": "Equation2306"}, + {"rhs": "Equation2240", "lhs": "Equation2307"}, + {"rhs": "Equation2241", "lhs": "Equation2308"}, + {"rhs": "Equation2243", "lhs": "Equation2310"}, + {"rhs": "Equation2243", "lhs": "Equation2311"}, + {"rhs": "Equation2244", "lhs": "Equation2312"}, + {"rhs": "Equation2243", "lhs": "Equation2314"}, + {"rhs": "Equation2243", "lhs": "Equation2315"}, + {"rhs": "Equation2244", "lhs": "Equation2316"}, + {"rhs": "Equation2246", "lhs": "Equation2318"}, + {"rhs": "Equation2246", "lhs": "Equation2319"}, + {"rhs": "Equation2247", "lhs": "Equation2320"}, + {"rhs": "Equation2239", "lhs": "Equation2329"}, + {"rhs": "Equation2239", "lhs": "Equation2332"}, + {"rhs": "Equation2240", "lhs": "Equation2333"}, + {"rhs": "Equation2240", "lhs": "Equation2334"}, + {"rhs": "Equation2241", "lhs": "Equation2335"}, + {"rhs": "Equation2239", "lhs": "Equation2339"}, + {"rhs": "Equation2239", "lhs": "Equation2342"}, + {"rhs": "Equation2240", "lhs": "Equation2343"}, + {"rhs": "Equation2240", "lhs": "Equation2344"}, + {"rhs": "Equation2241", "lhs": "Equation2345"}, + {"rhs": "Equation2243", "lhs": "Equation2347"}, + {"rhs": "Equation2243", "lhs": "Equation2348"}, + {"rhs": "Equation2244", "lhs": "Equation2349"}, + {"rhs": "Equation2243", "lhs": "Equation2351"}, + {"rhs": "Equation2243", "lhs": "Equation2352"}, + {"rhs": "Equation2244", "lhs": "Equation2353"}, + {"rhs": "Equation2246", "lhs": "Equation2355"}, + {"rhs": "Equation2246", "lhs": "Equation2356"}, + {"rhs": "Equation2247", "lhs": "Equation2357"}, + {"rhs": "Equation2253", "lhs": "Equation2364"}, + {"rhs": "Equation2253", "lhs": "Equation2365"}, + {"rhs": "Equation2254", "lhs": "Equation2366"}, + {"rhs": "Equation2253", "lhs": "Equation2368"}, + {"rhs": "Equation2253", "lhs": "Equation2369"}, + {"rhs": "Equation2254", "lhs": "Equation2370"}, + {"rhs": "Equation2256", "lhs": "Equation2372"}, + {"rhs": "Equation2256", "lhs": "Equation2373"}, + {"rhs": "Equation2257", "lhs": "Equation2374"}, + {"rhs": "Equation2253", "lhs": "Equation2381"}, + {"rhs": "Equation2253", "lhs": "Equation2382"}, + {"rhs": "Equation2254", "lhs": "Equation2383"}, + {"rhs": "Equation2253", "lhs": "Equation2385"}, + {"rhs": "Equation2253", "lhs": "Equation2386"}, + {"rhs": "Equation2254", "lhs": "Equation2387"}, + {"rhs": "Equation2256", "lhs": "Equation2389"}, + {"rhs": "Equation2256", "lhs": "Equation2390"}, + {"rhs": "Equation2257", "lhs": "Equation2391"}, + {"rhs": "Equation2263", "lhs": "Equation2398"}, + {"rhs": "Equation2263", "lhs": "Equation2399"}, + {"rhs": "Equation2264", "lhs": "Equation2400"}, + {"rhs": "Equation2263", "lhs": "Equation2402"}, + {"rhs": "Equation2263", "lhs": "Equation2403"}, + {"rhs": "Equation2264", "lhs": "Equation2404"}, + {"rhs": "Equation2266", "lhs": "Equation2406"}, + {"rhs": "Equation2266", "lhs": "Equation2407"}, + {"rhs": "Equation2267", "lhs": "Equation2408"}, + {"rhs": "Equation2442", "lhs": "Equation2445"}, + {"rhs": "Equation2442", "lhs": "Equation2448"}, + {"rhs": "Equation2442", "lhs": "Equation2451"}, + {"rhs": "Equation2443", "lhs": "Equation2452"}, + {"rhs": "Equation2443", "lhs": "Equation2453"}, + {"rhs": "Equation2444", "lhs": "Equation2454"}, + {"rhs": "Equation2442", "lhs": "Equation2458"}, + {"rhs": "Equation2442", "lhs": "Equation2461"}, + {"rhs": "Equation2443", "lhs": "Equation2462"}, + {"rhs": "Equation2443", "lhs": "Equation2463"}, + {"rhs": "Equation2444", "lhs": "Equation2464"}, + {"rhs": "Equation2442", "lhs": "Equation2468"}, + {"rhs": "Equation2442", "lhs": "Equation2471"}, + {"rhs": "Equation2443", "lhs": "Equation2472"}, + {"rhs": "Equation2443", "lhs": "Equation2473"}, + {"rhs": "Equation2444", "lhs": "Equation2474"}, + {"rhs": "Equation2446", "lhs": "Equation2476"}, + {"rhs": "Equation2446", "lhs": "Equation2477"}, + {"rhs": "Equation2447", "lhs": "Equation2478"}, + {"rhs": "Equation2446", "lhs": "Equation2480"}, + {"rhs": "Equation2446", "lhs": "Equation2481"}, + {"rhs": "Equation2447", "lhs": "Equation2482"}, + {"rhs": "Equation2449", "lhs": "Equation2484"}, + {"rhs": "Equation2449", "lhs": "Equation2485"}, + {"rhs": "Equation2450", "lhs": "Equation2486"}, + {"rhs": "Equation2442", "lhs": "Equation2495"}, + {"rhs": "Equation2442", "lhs": "Equation2498"}, + {"rhs": "Equation2443", "lhs": "Equation2499"}, + {"rhs": "Equation2443", "lhs": "Equation2500"}, + {"rhs": "Equation2444", "lhs": "Equation2501"}, + {"rhs": "Equation2442", "lhs": "Equation2505"}, + {"rhs": "Equation2442", "lhs": "Equation2508"}, + {"rhs": "Equation2443", "lhs": "Equation2509"}, + {"rhs": "Equation2443", "lhs": "Equation2510"}, + {"rhs": "Equation2444", "lhs": "Equation2511"}, + {"rhs": "Equation2446", "lhs": "Equation2513"}, + {"rhs": "Equation2446", "lhs": "Equation2514"}, + {"rhs": "Equation2447", "lhs": "Equation2515"}, + {"rhs": "Equation2446", "lhs": "Equation2517"}, + {"rhs": "Equation2446", "lhs": "Equation2518"}, + {"rhs": "Equation2447", "lhs": "Equation2519"}, + {"rhs": "Equation2449", "lhs": "Equation2521"}, + {"rhs": "Equation2449", "lhs": "Equation2522"}, + {"rhs": "Equation2450", "lhs": "Equation2523"}, + {"rhs": "Equation2442", "lhs": "Equation2532"}, + {"rhs": "Equation2442", "lhs": "Equation2535"}, + {"rhs": "Equation2443", "lhs": "Equation2536"}, + {"rhs": "Equation2443", "lhs": "Equation2537"}, + {"rhs": "Equation2444", "lhs": "Equation2538"}, + {"rhs": "Equation2442", "lhs": "Equation2542"}, + {"rhs": "Equation2442", "lhs": "Equation2545"}, + {"rhs": "Equation2443", "lhs": "Equation2546"}, + {"rhs": "Equation2443", "lhs": "Equation2547"}, + {"rhs": "Equation2444", "lhs": "Equation2548"}, + {"rhs": "Equation2446", "lhs": "Equation2550"}, + {"rhs": "Equation2446", "lhs": "Equation2551"}, + {"rhs": "Equation2447", "lhs": "Equation2552"}, + {"rhs": "Equation2446", "lhs": "Equation2554"}, + {"rhs": "Equation2446", "lhs": "Equation2555"}, + {"rhs": "Equation2447", "lhs": "Equation2556"}, + {"rhs": "Equation2449", "lhs": "Equation2558"}, + {"rhs": "Equation2449", "lhs": "Equation2559"}, + {"rhs": "Equation2450", "lhs": "Equation2560"}, + {"rhs": "Equation2456", "lhs": "Equation2567"}, + {"rhs": "Equation2456", "lhs": "Equation2568"}, + {"rhs": "Equation2457", "lhs": "Equation2569"}, + {"rhs": "Equation2456", "lhs": "Equation2571"}, + {"rhs": "Equation2456", "lhs": "Equation2572"}, + {"rhs": "Equation2457", "lhs": "Equation2573"}, + {"rhs": "Equation2459", "lhs": "Equation2575"}, + {"rhs": "Equation2459", "lhs": "Equation2576"}, + {"rhs": "Equation2460", "lhs": "Equation2577"}, + {"rhs": "Equation2456", "lhs": "Equation2584"}, + {"rhs": "Equation2456", "lhs": "Equation2585"}, + {"rhs": "Equation2457", "lhs": "Equation2586"}, + {"rhs": "Equation2456", "lhs": "Equation2588"}, + {"rhs": "Equation2456", "lhs": "Equation2589"}, + {"rhs": "Equation2457", "lhs": "Equation2590"}, + {"rhs": "Equation2459", "lhs": "Equation2592"}, + {"rhs": "Equation2459", "lhs": "Equation2593"}, + {"rhs": "Equation2460", "lhs": "Equation2594"}, + {"rhs": "Equation2466", "lhs": "Equation2601"}, + {"rhs": "Equation2466", "lhs": "Equation2602"}, + {"rhs": "Equation2467", "lhs": "Equation2603"}, + {"rhs": "Equation2466", "lhs": "Equation2605"}, + {"rhs": "Equation2466", "lhs": "Equation2606"}, + {"rhs": "Equation2467", "lhs": "Equation2607"}, + {"rhs": "Equation2469", "lhs": "Equation2609"}, + {"rhs": "Equation2469", "lhs": "Equation2610"}, + {"rhs": "Equation2470", "lhs": "Equation2611"}, + {"rhs": "Equation2645", "lhs": "Equation2648"}, + {"rhs": "Equation2645", "lhs": "Equation2651"}, + {"rhs": "Equation2645", "lhs": "Equation2654"}, + {"rhs": "Equation2646", "lhs": "Equation2655"}, + {"rhs": "Equation2646", "lhs": "Equation2656"}, + {"rhs": "Equation2647", "lhs": "Equation2657"}, + {"rhs": "Equation2645", "lhs": "Equation2661"}, + {"rhs": "Equation2645", "lhs": "Equation2664"}, + {"rhs": "Equation2646", "lhs": "Equation2665"}, + {"rhs": "Equation2646", "lhs": "Equation2666"}, + {"rhs": "Equation2647", "lhs": "Equation2667"}, + {"rhs": "Equation2645", "lhs": "Equation2671"}, + {"rhs": "Equation2645", "lhs": "Equation2674"}, + {"rhs": "Equation2646", "lhs": "Equation2675"}, + {"rhs": "Equation2646", "lhs": "Equation2676"}, + {"rhs": "Equation2647", "lhs": "Equation2677"}, + {"rhs": "Equation2649", "lhs": "Equation2679"}, + {"rhs": "Equation2649", "lhs": "Equation2680"}, + {"rhs": "Equation2650", "lhs": "Equation2681"}, + {"rhs": "Equation2649", "lhs": "Equation2683"}, + {"rhs": "Equation2649", "lhs": "Equation2684"}, + {"rhs": "Equation2650", "lhs": "Equation2685"}, + {"rhs": "Equation2652", "lhs": "Equation2687"}, + {"rhs": "Equation2652", "lhs": "Equation2688"}, + {"rhs": "Equation2653", "lhs": "Equation2689"}, + {"rhs": "Equation2645", "lhs": "Equation2698"}, + {"rhs": "Equation2645", "lhs": "Equation2701"}, + {"rhs": "Equation2646", "lhs": "Equation2702"}, + {"rhs": "Equation2646", "lhs": "Equation2703"}, + {"rhs": "Equation2647", "lhs": "Equation2704"}, + {"rhs": "Equation2645", "lhs": "Equation2708"}, + {"rhs": "Equation2645", "lhs": "Equation2711"}, + {"rhs": "Equation2646", "lhs": "Equation2712"}, + {"rhs": "Equation2646", "lhs": "Equation2713"}, + {"rhs": "Equation2647", "lhs": "Equation2714"}, + {"rhs": "Equation2649", "lhs": "Equation2716"}, + {"rhs": "Equation2649", "lhs": "Equation2717"}, + {"rhs": "Equation2650", "lhs": "Equation2718"}, + {"rhs": "Equation2649", "lhs": "Equation2720"}, + {"rhs": "Equation2649", "lhs": "Equation2721"}, + {"rhs": "Equation2650", "lhs": "Equation2722"}, + {"rhs": "Equation2652", "lhs": "Equation2724"}, + {"rhs": "Equation2652", "lhs": "Equation2725"}, + {"rhs": "Equation2653", "lhs": "Equation2726"}, + {"rhs": "Equation2645", "lhs": "Equation2735"}, + {"rhs": "Equation2645", "lhs": "Equation2738"}, + {"rhs": "Equation2646", "lhs": "Equation2739"}, + {"rhs": "Equation2646", "lhs": "Equation2740"}, + {"rhs": "Equation2647", "lhs": "Equation2741"}, + {"rhs": "Equation2645", "lhs": "Equation2745"}, + {"rhs": "Equation2645", "lhs": "Equation2748"}, + {"rhs": "Equation2646", "lhs": "Equation2749"}, + {"rhs": "Equation2646", "lhs": "Equation2750"}, + {"rhs": "Equation2647", "lhs": "Equation2751"}, + {"rhs": "Equation2649", "lhs": "Equation2753"}, + {"rhs": "Equation2649", "lhs": "Equation2754"}, + {"rhs": "Equation2650", "lhs": "Equation2755"}, + {"rhs": "Equation2649", "lhs": "Equation2757"}, + {"rhs": "Equation2649", "lhs": "Equation2758"}, + {"rhs": "Equation2650", "lhs": "Equation2759"}, + {"rhs": "Equation2652", "lhs": "Equation2761"}, + {"rhs": "Equation2652", "lhs": "Equation2762"}, + {"rhs": "Equation2653", "lhs": "Equation2763"}, + {"rhs": "Equation2659", "lhs": "Equation2770"}, + {"rhs": "Equation2659", "lhs": "Equation2771"}, + {"rhs": "Equation2660", "lhs": "Equation2772"}, + {"rhs": "Equation2659", "lhs": "Equation2774"}, + {"rhs": "Equation2659", "lhs": "Equation2775"}, + {"rhs": "Equation2660", "lhs": "Equation2776"}, + {"rhs": "Equation2662", "lhs": "Equation2778"}, + {"rhs": "Equation2662", "lhs": "Equation2779"}, + {"rhs": "Equation2663", "lhs": "Equation2780"}, + {"rhs": "Equation2659", "lhs": "Equation2787"}, + {"rhs": "Equation2659", "lhs": "Equation2788"}, + {"rhs": "Equation2660", "lhs": "Equation2789"}, + {"rhs": "Equation2659", "lhs": "Equation2791"}, + {"rhs": "Equation2659", "lhs": "Equation2792"}, + {"rhs": "Equation2660", "lhs": "Equation2793"}, + {"rhs": "Equation2662", "lhs": "Equation2795"}, + {"rhs": "Equation2662", "lhs": "Equation2796"}, + {"rhs": "Equation2663", "lhs": "Equation2797"}, + {"rhs": "Equation2669", "lhs": "Equation2804"}, + {"rhs": "Equation2669", "lhs": "Equation2805"}, + {"rhs": "Equation2670", "lhs": "Equation2806"}, + {"rhs": "Equation2669", "lhs": "Equation2808"}, + {"rhs": "Equation2669", "lhs": "Equation2809"}, + {"rhs": "Equation2670", "lhs": "Equation2810"}, + {"rhs": "Equation2672", "lhs": "Equation2812"}, + {"rhs": "Equation2672", "lhs": "Equation2813"}, + {"rhs": "Equation2673", "lhs": "Equation2814"}, + {"rhs": "Equation2848", "lhs": "Equation2851"}, + {"rhs": "Equation2848", "lhs": "Equation2854"}, + {"rhs": "Equation2848", "lhs": "Equation2857"}, + {"rhs": "Equation2849", "lhs": "Equation2858"}, + {"rhs": "Equation2849", "lhs": "Equation2859"}, + {"rhs": "Equation2850", "lhs": "Equation2860"}, + {"rhs": "Equation2848", "lhs": "Equation2864"}, + {"rhs": "Equation2848", "lhs": "Equation2867"}, + {"rhs": "Equation2849", "lhs": "Equation2868"}, + {"rhs": "Equation2849", "lhs": "Equation2869"}, + {"rhs": "Equation2850", "lhs": "Equation2870"}, + {"rhs": "Equation2848", "lhs": "Equation2874"}, + {"rhs": "Equation2848", "lhs": "Equation2877"}, + {"rhs": "Equation2849", "lhs": "Equation2878"}, + {"rhs": "Equation2849", "lhs": "Equation2879"}, + {"rhs": "Equation2850", "lhs": "Equation2880"}, + {"rhs": "Equation2852", "lhs": "Equation2882"}, + {"rhs": "Equation2852", "lhs": "Equation2883"}, + {"rhs": "Equation2853", "lhs": "Equation2884"}, + {"rhs": "Equation2852", "lhs": "Equation2886"}, + {"rhs": "Equation2852", "lhs": "Equation2887"}, + {"rhs": "Equation2853", "lhs": "Equation2888"}, + {"rhs": "Equation2855", "lhs": "Equation2890"}, + {"rhs": "Equation2855", "lhs": "Equation2891"}, + {"rhs": "Equation2856", "lhs": "Equation2892"}, + {"rhs": "Equation2848", "lhs": "Equation2901"}, + {"rhs": "Equation2848", "lhs": "Equation2904"}, + {"rhs": "Equation2849", "lhs": "Equation2905"}, + {"rhs": "Equation2849", "lhs": "Equation2906"}, + {"rhs": "Equation2850", "lhs": "Equation2907"}, + {"rhs": "Equation2848", "lhs": "Equation2911"}, + {"rhs": "Equation2848", "lhs": "Equation2914"}, + {"rhs": "Equation2849", "lhs": "Equation2915"}, + {"rhs": "Equation2849", "lhs": "Equation2916"}, + {"rhs": "Equation2850", "lhs": "Equation2917"}, + {"rhs": "Equation2852", "lhs": "Equation2919"}, + {"rhs": "Equation2852", "lhs": "Equation2920"}, + {"rhs": "Equation2853", "lhs": "Equation2921"}, + {"rhs": "Equation2852", "lhs": "Equation2923"}, + {"rhs": "Equation2852", "lhs": "Equation2924"}, + {"rhs": "Equation2853", "lhs": "Equation2925"}, + {"rhs": "Equation2855", "lhs": "Equation2927"}, + {"rhs": "Equation2855", "lhs": "Equation2928"}, + {"rhs": "Equation2856", "lhs": "Equation2929"}, + {"rhs": "Equation2848", "lhs": "Equation2938"}, + {"rhs": "Equation2848", "lhs": "Equation2941"}, + {"rhs": "Equation2849", "lhs": "Equation2942"}, + {"rhs": "Equation2849", "lhs": "Equation2943"}, + {"rhs": "Equation2850", "lhs": "Equation2944"}, + {"rhs": "Equation2848", "lhs": "Equation2948"}, + {"rhs": "Equation2848", "lhs": "Equation2951"}, + {"rhs": "Equation2849", "lhs": "Equation2952"}, + {"rhs": "Equation2849", "lhs": "Equation2953"}, + {"rhs": "Equation2850", "lhs": "Equation2954"}, + {"rhs": "Equation2852", "lhs": "Equation2956"}, + {"rhs": "Equation2852", "lhs": "Equation2957"}, + {"rhs": "Equation2853", "lhs": "Equation2958"}, + {"rhs": "Equation2852", "lhs": "Equation2960"}, + {"rhs": "Equation2852", "lhs": "Equation2961"}, + {"rhs": "Equation2853", "lhs": "Equation2962"}, + {"rhs": "Equation2855", "lhs": "Equation2964"}, + {"rhs": "Equation2855", "lhs": "Equation2965"}, + {"rhs": "Equation2856", "lhs": "Equation2966"}, + {"rhs": "Equation2862", "lhs": "Equation2973"}, + {"rhs": "Equation2862", "lhs": "Equation2974"}, + {"rhs": "Equation2863", "lhs": "Equation2975"}, + {"rhs": "Equation2862", "lhs": "Equation2977"}, + {"rhs": "Equation2862", "lhs": "Equation2978"}, + {"rhs": "Equation2863", "lhs": "Equation2979"}, + {"rhs": "Equation2865", "lhs": "Equation2981"}, + {"rhs": "Equation2865", "lhs": "Equation2982"}, + {"rhs": "Equation2866", "lhs": "Equation2983"}, + {"rhs": "Equation2862", "lhs": "Equation2990"}, + {"rhs": "Equation2862", "lhs": "Equation2991"}, + {"rhs": "Equation2863", "lhs": "Equation2992"}, + {"rhs": "Equation2862", "lhs": "Equation2994"}, + {"rhs": "Equation2862", "lhs": "Equation2995"}, + {"rhs": "Equation2863", "lhs": "Equation2996"}, + {"rhs": "Equation2865", "lhs": "Equation2998"}, + {"rhs": "Equation2865", "lhs": "Equation2999"}, + {"rhs": "Equation2866", "lhs": "Equation3000"}, + {"rhs": "Equation2872", "lhs": "Equation3007"}, + {"rhs": "Equation2872", "lhs": "Equation3008"}, + {"rhs": "Equation2873", "lhs": "Equation3009"}, + {"rhs": "Equation2872", "lhs": "Equation3011"}, + {"rhs": "Equation2872", "lhs": "Equation3012"}, + {"rhs": "Equation2873", "lhs": "Equation3013"}, + {"rhs": "Equation2875", "lhs": "Equation3015"}, + {"rhs": "Equation2875", "lhs": "Equation3016"}, + {"rhs": "Equation2876", "lhs": "Equation3017"}, + {"rhs": "Equation3051", "lhs": "Equation3054"}, + {"rhs": "Equation3051", "lhs": "Equation3057"}, + {"rhs": "Equation3051", "lhs": "Equation3060"}, + {"rhs": "Equation3052", "lhs": "Equation3061"}, + {"rhs": "Equation3052", "lhs": "Equation3062"}, + {"rhs": "Equation3053", "lhs": "Equation3063"}, + {"rhs": "Equation3051", "lhs": "Equation3067"}, + {"rhs": "Equation3051", "lhs": "Equation3070"}, + {"rhs": "Equation3052", "lhs": "Equation3071"}, + {"rhs": "Equation3052", "lhs": "Equation3072"}, + {"rhs": "Equation3053", "lhs": "Equation3073"}, + {"rhs": "Equation3051", "lhs": "Equation3077"}, + {"rhs": "Equation3051", "lhs": "Equation3080"}, + {"rhs": "Equation3052", "lhs": "Equation3081"}, + {"rhs": "Equation3052", "lhs": "Equation3082"}, + {"rhs": "Equation3053", "lhs": "Equation3083"}, + {"rhs": "Equation3055", "lhs": "Equation3085"}, + {"rhs": "Equation3055", "lhs": "Equation3086"}, + {"rhs": "Equation3056", "lhs": "Equation3087"}, + {"rhs": "Equation3055", "lhs": "Equation3089"}, + {"rhs": "Equation3055", "lhs": "Equation3090"}, + {"rhs": "Equation3056", "lhs": "Equation3091"}, + {"rhs": "Equation3058", "lhs": "Equation3093"}, + {"rhs": "Equation3058", "lhs": "Equation3094"}, + {"rhs": "Equation3059", "lhs": "Equation3095"}, + {"rhs": "Equation3051", "lhs": "Equation3104"}, + {"rhs": "Equation3051", "lhs": "Equation3107"}, + {"rhs": "Equation3052", "lhs": "Equation3108"}, + {"rhs": "Equation3052", "lhs": "Equation3109"}, + {"rhs": "Equation3053", "lhs": "Equation3110"}, + {"rhs": "Equation3051", "lhs": "Equation3114"}, + {"rhs": "Equation3051", "lhs": "Equation3117"}, + {"rhs": "Equation3052", "lhs": "Equation3118"}, + {"rhs": "Equation3052", "lhs": "Equation3119"}, + {"rhs": "Equation3053", "lhs": "Equation3120"}, + {"rhs": "Equation3055", "lhs": "Equation3122"}, + {"rhs": "Equation3055", "lhs": "Equation3123"}, + {"rhs": "Equation3056", "lhs": "Equation3124"}, + {"rhs": "Equation3055", "lhs": "Equation3126"}, + {"rhs": "Equation3055", "lhs": "Equation3127"}, + {"rhs": "Equation3056", "lhs": "Equation3128"}, + {"rhs": "Equation3058", "lhs": "Equation3130"}, + {"rhs": "Equation3058", "lhs": "Equation3131"}, + {"rhs": "Equation3059", "lhs": "Equation3132"}, + {"rhs": "Equation3051", "lhs": "Equation3141"}, + {"rhs": "Equation3051", "lhs": "Equation3144"}, + {"rhs": "Equation3052", "lhs": "Equation3145"}, + {"rhs": "Equation3052", "lhs": "Equation3146"}, + {"rhs": "Equation3053", "lhs": "Equation3147"}, + {"rhs": "Equation3051", "lhs": "Equation3151"}, + {"rhs": "Equation3051", "lhs": "Equation3154"}, + {"rhs": "Equation3052", "lhs": "Equation3155"}, + {"rhs": "Equation3052", "lhs": "Equation3156"}, + {"rhs": "Equation3053", "lhs": "Equation3157"}, + {"rhs": "Equation3055", "lhs": "Equation3159"}, + {"rhs": "Equation3055", "lhs": "Equation3160"}, + {"rhs": "Equation3056", "lhs": "Equation3161"}, + {"rhs": "Equation3055", "lhs": "Equation3163"}, + {"rhs": "Equation3055", "lhs": "Equation3164"}, + {"rhs": "Equation3056", "lhs": "Equation3165"}, + {"rhs": "Equation3058", "lhs": "Equation3167"}, + {"rhs": "Equation3058", "lhs": "Equation3168"}, + {"rhs": "Equation3059", "lhs": "Equation3169"}, + {"rhs": "Equation3065", "lhs": "Equation3176"}, + {"rhs": "Equation3065", "lhs": "Equation3177"}, + {"rhs": "Equation3066", "lhs": "Equation3178"}, + {"rhs": "Equation3065", "lhs": "Equation3180"}, + {"rhs": "Equation3065", "lhs": "Equation3181"}, + {"rhs": "Equation3066", "lhs": "Equation3182"}, + {"rhs": "Equation3068", "lhs": "Equation3184"}, + {"rhs": "Equation3068", "lhs": "Equation3185"}, + {"rhs": "Equation3069", "lhs": "Equation3186"}, + {"rhs": "Equation3065", "lhs": "Equation3193"}, + {"rhs": "Equation3065", "lhs": "Equation3194"}, + {"rhs": "Equation3066", "lhs": "Equation3195"}, + {"rhs": "Equation3065", "lhs": "Equation3197"}, + {"rhs": "Equation3065", "lhs": "Equation3198"}, + {"rhs": "Equation3066", "lhs": "Equation3199"}, + {"rhs": "Equation3068", "lhs": "Equation3201"}, + {"rhs": "Equation3068", "lhs": "Equation3202"}, + {"rhs": "Equation3069", "lhs": "Equation3203"}, + {"rhs": "Equation3075", "lhs": "Equation3210"}, + {"rhs": "Equation3075", "lhs": "Equation3211"}, + {"rhs": "Equation3076", "lhs": "Equation3212"}, + {"rhs": "Equation3075", "lhs": "Equation3214"}, + {"rhs": "Equation3075", "lhs": "Equation3215"}, + {"rhs": "Equation3076", "lhs": "Equation3216"}, + {"rhs": "Equation3078", "lhs": "Equation3218"}, + {"rhs": "Equation3078", "lhs": "Equation3219"}, + {"rhs": "Equation3079", "lhs": "Equation3220"}, + {"rhs": "Equation3254", "lhs": "Equation3257"}, + {"rhs": "Equation3254", "lhs": "Equation3260"}, + {"rhs": "Equation3254", "lhs": "Equation3263"}, + {"rhs": "Equation3255", "lhs": "Equation3264"}, + {"rhs": "Equation3255", "lhs": "Equation3265"}, + {"rhs": "Equation3256", "lhs": "Equation3266"}, + {"rhs": "Equation3254", "lhs": "Equation3270"}, + {"rhs": "Equation3254", "lhs": "Equation3273"}, + {"rhs": "Equation3255", "lhs": "Equation3274"}, + {"rhs": "Equation3255", "lhs": "Equation3275"}, + {"rhs": "Equation3256", "lhs": "Equation3276"}, + {"rhs": "Equation3254", "lhs": "Equation3280"}, + {"rhs": "Equation3254", "lhs": "Equation3283"}, + {"rhs": "Equation3255", "lhs": "Equation3284"}, + {"rhs": "Equation3255", "lhs": "Equation3285"}, + {"rhs": "Equation3256", "lhs": "Equation3286"}, + {"rhs": "Equation3258", "lhs": "Equation3288"}, + {"rhs": "Equation3258", "lhs": "Equation3289"}, + {"rhs": "Equation3259", "lhs": "Equation3290"}, + {"rhs": "Equation3258", "lhs": "Equation3292"}, + {"rhs": "Equation3258", "lhs": "Equation3293"}, + {"rhs": "Equation3259", "lhs": "Equation3294"}, + {"rhs": "Equation3261", "lhs": "Equation3296"}, + {"rhs": "Equation3261", "lhs": "Equation3297"}, + {"rhs": "Equation3262", "lhs": "Equation3298"}, + {"rhs": "Equation3254", "lhs": "Equation3307"}, + {"rhs": "Equation3254", "lhs": "Equation3310"}, + {"rhs": "Equation3255", "lhs": "Equation3311"}, + {"rhs": "Equation3255", "lhs": "Equation3312"}, + {"rhs": "Equation3256", "lhs": "Equation3313"}, + {"rhs": "Equation3254", "lhs": "Equation3317"}, + {"rhs": "Equation3254", "lhs": "Equation3320"}, + {"rhs": "Equation3255", "lhs": "Equation3321"}, + {"rhs": "Equation3255", "lhs": "Equation3322"}, + {"rhs": "Equation3256", "lhs": "Equation3323"}, + {"rhs": "Equation3258", "lhs": "Equation3325"}, + {"rhs": "Equation3258", "lhs": "Equation3326"}, + {"rhs": "Equation3259", "lhs": "Equation3327"}, + {"rhs": "Equation3258", "lhs": "Equation3329"}, + {"rhs": "Equation3258", "lhs": "Equation3330"}, + {"rhs": "Equation3259", "lhs": "Equation3331"}, + {"rhs": "Equation3261", "lhs": "Equation3333"}, + {"rhs": "Equation3261", "lhs": "Equation3334"}, + {"rhs": "Equation3262", "lhs": "Equation3335"}, + {"rhs": "Equation3254", "lhs": "Equation3344"}, + {"rhs": "Equation3254", "lhs": "Equation3347"}, + {"rhs": "Equation3255", "lhs": "Equation3348"}, + {"rhs": "Equation3255", "lhs": "Equation3349"}, + {"rhs": "Equation3256", "lhs": "Equation3350"}, + {"rhs": "Equation3254", "lhs": "Equation3354"}, + {"rhs": "Equation3254", "lhs": "Equation3357"}, + {"rhs": "Equation3255", "lhs": "Equation3358"}, + {"rhs": "Equation3255", "lhs": "Equation3359"}, + {"rhs": "Equation3256", "lhs": "Equation3360"}, + {"rhs": "Equation3258", "lhs": "Equation3362"}, + {"rhs": "Equation3258", "lhs": "Equation3363"}, + {"rhs": "Equation3259", "lhs": "Equation3364"}, + {"rhs": "Equation3258", "lhs": "Equation3366"}, + {"rhs": "Equation3258", "lhs": "Equation3367"}, + {"rhs": "Equation3259", "lhs": "Equation3368"}, + {"rhs": "Equation3261", "lhs": "Equation3370"}, + {"rhs": "Equation3261", "lhs": "Equation3371"}, + {"rhs": "Equation3262", "lhs": "Equation3372"}, + {"rhs": "Equation3268", "lhs": "Equation3379"}, + {"rhs": "Equation3268", "lhs": "Equation3380"}, + {"rhs": "Equation3269", "lhs": "Equation3381"}, + {"rhs": "Equation3268", "lhs": "Equation3383"}, + {"rhs": "Equation3268", "lhs": "Equation3384"}, + {"rhs": "Equation3269", "lhs": "Equation3385"}, + {"rhs": "Equation3271", "lhs": "Equation3387"}, + {"rhs": "Equation3271", "lhs": "Equation3388"}, + {"rhs": "Equation3272", "lhs": "Equation3389"}, + {"rhs": "Equation3268", "lhs": "Equation3396"}, + {"rhs": "Equation3268", "lhs": "Equation3397"}, + {"rhs": "Equation3269", "lhs": "Equation3398"}, + {"rhs": "Equation3268", "lhs": "Equation3400"}, + {"rhs": "Equation3268", "lhs": "Equation3401"}, + {"rhs": "Equation3269", "lhs": "Equation3402"}, + {"rhs": "Equation3271", "lhs": "Equation3404"}, + {"rhs": "Equation3271", "lhs": "Equation3405"}, + {"rhs": "Equation3272", "lhs": "Equation3406"}, + {"rhs": "Equation3278", "lhs": "Equation3413"}, + {"rhs": "Equation3278", "lhs": "Equation3414"}, + {"rhs": "Equation3279", "lhs": "Equation3415"}, + {"rhs": "Equation3278", "lhs": "Equation3417"}, + {"rhs": "Equation3278", "lhs": "Equation3418"}, + {"rhs": "Equation3279", "lhs": "Equation3419"}, + {"rhs": "Equation3281", "lhs": "Equation3421"}, + {"rhs": "Equation3281", "lhs": "Equation3422"}, + {"rhs": "Equation3282", "lhs": "Equation3423"}, + {"rhs": "Equation3457", "lhs": "Equation3460"}, + {"rhs": "Equation3457", "lhs": "Equation3463"}, + {"rhs": "Equation3457", "lhs": "Equation3466"}, + {"rhs": "Equation3458", "lhs": "Equation3467"}, + {"rhs": "Equation3458", "lhs": "Equation3468"}, + {"rhs": "Equation3459", "lhs": "Equation3469"}, + {"rhs": "Equation3457", "lhs": "Equation3473"}, + {"rhs": "Equation3457", "lhs": "Equation3476"}, + 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{"rhs": "Equation4269", "lhs": "Equation4286"}, + {"rhs": "Equation4269", "lhs": "Equation4287"}, + {"rhs": "Equation4270", "lhs": "Equation4288"}, + {"rhs": "Equation4268", "lhs": "Equation4292"}, + {"rhs": "Equation4268", "lhs": "Equation4294"}, + {"rhs": "Equation4269", "lhs": "Equation4295"}, + {"rhs": "Equation4269", "lhs": "Equation4296"}, + {"rhs": "Equation4270", "lhs": "Equation4297"}, + {"rhs": "Equation4272", "lhs": "Equation4299"}, + {"rhs": "Equation4272", "lhs": "Equation4300"}, + {"rhs": "Equation4273", "lhs": "Equation4301"}, + {"rhs": "Equation4272", "lhs": "Equation4303"}, + {"rhs": "Equation4272", "lhs": "Equation4304"}, + {"rhs": "Equation4273", "lhs": "Equation4305"}, + {"rhs": "Equation4275", "lhs": "Equation4307"}, + {"rhs": "Equation4268", "lhs": "Equation4315"}, + {"rhs": "Equation4269", "lhs": "Equation4316"}, + {"rhs": "Equation4269", "lhs": "Equation4317"}, + {"rhs": "Equation4270", "lhs": "Equation4318"}, + {"rhs": "Equation4268", "lhs": "Equation4322"}, + {"rhs": "Equation4269", "lhs": "Equation4323"}, + {"rhs": "Equation4269", "lhs": "Equation4324"}, + {"rhs": "Equation4270", "lhs": "Equation4325"}, + {"rhs": "Equation4272", "lhs": "Equation4327"}, + {"rhs": "Equation4272", "lhs": "Equation4328"}, + {"rhs": "Equation4272", "lhs": "Equation4330"}, + {"rhs": "Equation4272", "lhs": "Equation4331"}, + {"rhs": "Equation4273", "lhs": "Equation4332"}, + {"rhs": "Equation4268", "lhs": "Equation4339"}, + {"rhs": "Equation4269", "lhs": "Equation4340"}, + {"rhs": "Equation4270", "lhs": "Equation4341"}, + {"rhs": "Equation4268", "lhs": "Equation4344"}, + {"rhs": "Equation4269", "lhs": "Equation4345"}, + {"rhs": "Equation4270", "lhs": "Equation4346"}, + {"rhs": "Equation4272", "lhs": "Equation4348"}, + {"rhs": "Equation4272", "lhs": "Equation4350"}, + {"rhs": "Equation4272", "lhs": "Equation4351"}, + {"rhs": "Equation4283", "lhs": "Equation4358"}, + {"rhs": "Equation4283", "lhs": "Equation4364"}, + {"rhs": "Equation4290", "lhs": "Equation4369"}, + {"rhs": "Equation4381", "lhs": "Equation4384"}, + {"rhs": "Equation4381", "lhs": "Equation4387"}, + {"rhs": "Equation4381", "lhs": "Equation4390"}, + {"rhs": "Equation4382", "lhs": "Equation4391"}, + {"rhs": "Equation4382", "lhs": "Equation4392"}, + {"rhs": "Equation4383", "lhs": "Equation4393"}, + {"rhs": "Equation4381", "lhs": "Equation4397"}, + {"rhs": "Equation4381", "lhs": "Equation4400"}, + {"rhs": "Equation4382", "lhs": "Equation4401"}, + {"rhs": "Equation4382", "lhs": "Equation4402"}, + {"rhs": "Equation4383", "lhs": "Equation4403"}, + {"rhs": "Equation4381", "lhs": "Equation4407"}, + {"rhs": "Equation4381", "lhs": "Equation4410"}, + {"rhs": "Equation4382", "lhs": "Equation4411"}, + {"rhs": "Equation4382", "lhs": "Equation4412"}, + {"rhs": "Equation4383", "lhs": "Equation4413"}, + {"rhs": "Equation4385", "lhs": "Equation4415"}, + {"rhs": "Equation4385", "lhs": "Equation4416"}, + {"rhs": "Equation4386", "lhs": "Equation4417"}, + {"rhs": "Equation4385", "lhs": "Equation4419"}, + {"rhs": "Equation4385", "lhs": "Equation4420"}, + {"rhs": "Equation4386", "lhs": "Equation4421"}, + {"rhs": "Equation4388", "lhs": "Equation4423"}, + {"rhs": "Equation4388", "lhs": "Equation4424"}, + {"rhs": "Equation4389", "lhs": "Equation4425"}, + {"rhs": "Equation4381", "lhs": "Equation4434"}, + {"rhs": "Equation4381", "lhs": "Equation4437"}, + {"rhs": "Equation4382", "lhs": "Equation4438"}, + {"rhs": "Equation4382", "lhs": "Equation4439"}, + {"rhs": "Equation4383", "lhs": "Equation4440"}, + {"rhs": "Equation4381", "lhs": "Equation4444"}, + {"rhs": "Equation4381", "lhs": "Equation4447"}, + {"rhs": "Equation4382", "lhs": "Equation4448"}, + {"rhs": "Equation4382", "lhs": "Equation4449"}, + {"rhs": "Equation4383", "lhs": "Equation4450"}, + {"rhs": "Equation4385", "lhs": "Equation4452"}, + {"rhs": "Equation4385", "lhs": "Equation4453"}, + {"rhs": "Equation4386", "lhs": "Equation4454"}, + {"rhs": "Equation4385", "lhs": "Equation4456"}, + {"rhs": "Equation4385", "lhs": "Equation4457"}, + {"rhs": "Equation4386", "lhs": "Equation4458"}, + {"rhs": "Equation4388", "lhs": "Equation4460"}, + {"rhs": "Equation4388", "lhs": "Equation4461"}, + {"rhs": "Equation4389", "lhs": "Equation4462"}, + {"rhs": "Equation4381", "lhs": "Equation4471"}, + {"rhs": "Equation4381", "lhs": "Equation4474"}, + {"rhs": "Equation4382", "lhs": "Equation4475"}, + {"rhs": "Equation4382", "lhs": "Equation4476"}, + {"rhs": "Equation4383", "lhs": "Equation4477"}, + {"rhs": "Equation4381", "lhs": "Equation4481"}, + {"rhs": "Equation4381", "lhs": "Equation4484"}, + {"rhs": "Equation4382", "lhs": "Equation4485"}, + {"rhs": "Equation4382", "lhs": "Equation4486"}, + {"rhs": "Equation4383", "lhs": "Equation4487"}, + {"rhs": "Equation4385", "lhs": "Equation4489"}, + {"rhs": "Equation4385", "lhs": "Equation4490"}, + {"rhs": "Equation4386", "lhs": "Equation4491"}, + {"rhs": "Equation4385", "lhs": "Equation4493"}, + {"rhs": "Equation4385", "lhs": "Equation4494"}, + {"rhs": "Equation4386", "lhs": "Equation4495"}, + {"rhs": "Equation4388", "lhs": "Equation4497"}, + {"rhs": "Equation4388", "lhs": "Equation4498"}, + {"rhs": "Equation4389", "lhs": "Equation4499"}, + {"rhs": "Equation4395", "lhs": "Equation4506"}, + {"rhs": "Equation4395", "lhs": "Equation4507"}, + {"rhs": "Equation4396", "lhs": "Equation4508"}, + {"rhs": "Equation4395", "lhs": "Equation4510"}, + {"rhs": "Equation4395", "lhs": "Equation4511"}, + {"rhs": "Equation4396", "lhs": "Equation4512"}, + {"rhs": "Equation4398", "lhs": "Equation4514"}, + {"rhs": "Equation4398", "lhs": "Equation4515"}, + {"rhs": "Equation4399", "lhs": "Equation4516"}, + {"rhs": "Equation4395", "lhs": "Equation4523"}, + {"rhs": "Equation4395", "lhs": "Equation4524"}, + {"rhs": "Equation4396", "lhs": "Equation4525"}, + {"rhs": "Equation4395", "lhs": "Equation4527"}, + {"rhs": "Equation4395", "lhs": "Equation4528"}, + {"rhs": "Equation4396", "lhs": "Equation4529"}, + {"rhs": "Equation4398", "lhs": "Equation4531"}, + {"rhs": "Equation4398", "lhs": "Equation4532"}, + {"rhs": "Equation4399", "lhs": "Equation4533"}, + {"rhs": "Equation4405", "lhs": "Equation4540"}, + {"rhs": "Equation4405", "lhs": "Equation4541"}, + {"rhs": "Equation4406", "lhs": "Equation4542"}, + {"rhs": "Equation4405", "lhs": "Equation4544"}, + {"rhs": "Equation4405", "lhs": "Equation4545"}, + {"rhs": "Equation4406", "lhs": "Equation4546"}, + {"rhs": "Equation4408", "lhs": "Equation4548"}, + {"rhs": "Equation4408", "lhs": "Equation4549"}, + {"rhs": "Equation4409", "lhs": "Equation4550"}, + {"rhs": "Equation4583", "lhs": "Equation4586"}, + {"rhs": "Equation4583", "lhs": "Equation4589"}, + {"rhs": "Equation4583", "lhs": "Equation4592"}, + {"rhs": "Equation4584", "lhs": "Equation4593"}, + {"rhs": "Equation4584", "lhs": "Equation4594"}, + {"rhs": "Equation4585", "lhs": "Equation4595"}, + {"rhs": "Equation4583", "lhs": "Equation4597"}, + {"rhs": "Equation4583", "lhs": "Equation4600"}, + {"rhs": "Equation4584", "lhs": "Equation4601"}, + {"rhs": "Equation4584", "lhs": "Equation4602"}, + {"rhs": "Equation4585", "lhs": "Equation4603"}, + {"rhs": "Equation4583", "lhs": "Equation4607"}, + {"rhs": "Equation4583", "lhs": "Equation4609"}, + {"rhs": "Equation4584", "lhs": "Equation4610"}, + {"rhs": "Equation4584", "lhs": "Equation4611"}, + {"rhs": "Equation4585", "lhs": "Equation4612"}, + {"rhs": "Equation4587", "lhs": "Equation4614"}, + {"rhs": "Equation4587", "lhs": "Equation4615"}, + {"rhs": "Equation4588", "lhs": "Equation4616"}, + {"rhs": "Equation4587", "lhs": "Equation4618"}, + {"rhs": "Equation4587", "lhs": "Equation4619"}, + {"rhs": "Equation4588", "lhs": "Equation4620"}, + {"rhs": "Equation4590", "lhs": "Equation4622"}, + {"rhs": "Equation4583", "lhs": "Equation4630"}, + {"rhs": "Equation4584", "lhs": "Equation4631"}, + {"rhs": "Equation4584", "lhs": "Equation4632"}, + {"rhs": "Equation4585", "lhs": "Equation4633"}, + {"rhs": "Equation4583", "lhs": "Equation4637"}, + {"rhs": "Equation4584", "lhs": "Equation4638"}, + {"rhs": "Equation4584", "lhs": "Equation4639"}, + {"rhs": "Equation4585", "lhs": "Equation4640"}, + {"rhs": "Equation4587", "lhs": "Equation4642"}, + {"rhs": "Equation4587", "lhs": "Equation4643"}, + {"rhs": "Equation4587", "lhs": "Equation4645"}, + {"rhs": "Equation4587", "lhs": "Equation4646"}, + {"rhs": "Equation4588", "lhs": "Equation4647"}, + {"rhs": "Equation4583", "lhs": "Equation4654"}, + {"rhs": "Equation4584", "lhs": "Equation4655"}, + {"rhs": "Equation4585", "lhs": "Equation4656"}, + {"rhs": "Equation4583", "lhs": "Equation4659"}, + {"rhs": "Equation4584", "lhs": "Equation4660"}, + {"rhs": "Equation4585", "lhs": "Equation4661"}, + {"rhs": "Equation4587", "lhs": "Equation4663"}, + {"rhs": "Equation4587", "lhs": "Equation4665"}, + {"rhs": "Equation4587", "lhs": "Equation4666"}, + {"rhs": "Equation4598", "lhs": "Equation4673"}, + {"rhs": "Equation4598", "lhs": "Equation4679"}, + {"rhs": "Equation4605", "lhs": "Equation4684"}, + {"rhs": "Equation5", "lhs": "Equation7"}, + {"rhs": "Equation10", "lhs": "Equation12"}, + {"rhs": "Equation13", "lhs": "Equation15"}, + {"rhs": "Equation16", "lhs": "Equation18"}, + {"rhs": "Equation13", "lhs": "Equation19"}, + {"rhs": "Equation14", "lhs": "Equation20"}, + {"rhs": "Equation13", "lhs": "Equation21"}, + {"rhs": "Equation25", "lhs": "Equation27"}, + {"rhs": "Equation28", "lhs": "Equation30"}, + {"rhs": "Equation31", "lhs": "Equation33"}, + {"rhs": "Equation28", "lhs": "Equation34"}, + {"rhs": "Equation29", "lhs": "Equation35"}, + {"rhs": "Equation28", "lhs": "Equation36"}, + {"rhs": "Equation39", "lhs": "Equation41"}, + {"rhs": "Equation43", "lhs": "Equation44"}, + {"rhs": "Equation49", "lhs": "Equation51"}, + {"rhs": "Equation52", "lhs": "Equation54"}, + {"rhs": "Equation55", "lhs": "Equation57"}, + {"rhs": "Equation52", "lhs": "Equation58"}, + {"rhs": "Equation53", "lhs": "Equation59"}, + {"rhs": "Equation52", "lhs": "Equation60"}, + {"rhs": "Equation62", "lhs": "Equation64"}, + {"rhs": "Equation65", "lhs": "Equation67"}, + {"rhs": "Equation62", "lhs": "Equation68"}, + {"rhs": "Equation63", "lhs": "Equation69"}, + {"rhs": "Equation62", "lhs": "Equation70"}, + {"rhs": "Equation72", "lhs": "Equation74"}, + {"rhs": "Equation75", "lhs": "Equation77"}, + {"rhs": "Equation72", "lhs": "Equation78"}, + {"rhs": "Equation73", "lhs": "Equation79"}, + {"rhs": "Equation72", "lhs": "Equation80"}, + {"rhs": "Equation62", "lhs": "Equation82"}, + {"rhs": "Equation63", "lhs": "Equation83"}, + {"rhs": "Equation62", "lhs": "Equation84"}, + {"rhs": "Equation65", "lhs": "Equation86"}, + {"rhs": "Equation66", "lhs": "Equation87"}, + {"rhs": "Equation65", "lhs": "Equation88"}, + {"rhs": "Equation62", "lhs": "Equation90"}, + {"rhs": "Equation63", "lhs": "Equation91"}, + {"rhs": "Equation62", "lhs": "Equation92"}, + {"rhs": "Equation101", "lhs": "Equation103"}, + {"rhs": "Equation104", "lhs": "Equation106"}, + {"rhs": "Equation107", "lhs": "Equation109"}, + {"rhs": "Equation104", "lhs": "Equation110"}, + {"rhs": "Equation105", "lhs": "Equation111"}, + {"rhs": "Equation104", "lhs": "Equation112"}, + {"rhs": "Equation114", "lhs": "Equation116"}, + {"rhs": "Equation117", "lhs": "Equation119"}, + {"rhs": "Equation114", "lhs": "Equation120"}, + {"rhs": "Equation115", "lhs": "Equation121"}, + {"rhs": "Equation114", "lhs": "Equation122"}, + {"rhs": "Equation124", "lhs": "Equation126"}, + {"rhs": "Equation127", "lhs": "Equation129"}, + {"rhs": "Equation124", "lhs": "Equation130"}, + {"rhs": "Equation125", "lhs": "Equation131"}, + {"rhs": "Equation124", "lhs": "Equation132"}, + {"rhs": "Equation114", "lhs": "Equation134"}, + {"rhs": "Equation115", "lhs": "Equation135"}, + {"rhs": "Equation114", "lhs": "Equation136"}, + {"rhs": "Equation117", "lhs": "Equation138"}, + {"rhs": "Equation118", "lhs": "Equation139"}, + {"rhs": "Equation117", "lhs": "Equation140"}, + {"rhs": "Equation114", "lhs": "Equation142"}, + {"rhs": "Equation115", "lhs": "Equation143"}, + {"rhs": "Equation114", "lhs": "Equation144"}, + {"rhs": "Equation153", "lhs": "Equation155"}, + {"rhs": "Equation156", "lhs": "Equation158"}, + {"rhs": "Equation159", "lhs": "Equation161"}, + {"rhs": "Equation156", "lhs": "Equation162"}, + {"rhs": "Equation157", "lhs": "Equation163"}, + {"rhs": "Equation156", "lhs": "Equation164"}, + {"rhs": "Equation166", "lhs": "Equation168"}, + {"rhs": "Equation169", "lhs": "Equation171"}, + {"rhs": "Equation166", "lhs": "Equation172"}, + {"rhs": "Equation167", "lhs": "Equation173"}, + {"rhs": "Equation166", "lhs": "Equation174"}, + {"rhs": "Equation176", "lhs": "Equation178"}, + {"rhs": "Equation179", "lhs": "Equation181"}, + {"rhs": "Equation176", "lhs": "Equation182"}, + {"rhs": "Equation177", "lhs": "Equation183"}, + {"rhs": "Equation176", "lhs": "Equation184"}, + {"rhs": "Equation166", "lhs": "Equation186"}, + {"rhs": "Equation167", "lhs": "Equation187"}, + {"rhs": "Equation166", "lhs": "Equation188"}, + {"rhs": "Equation169", "lhs": "Equation190"}, + {"rhs": "Equation170", "lhs": "Equation191"}, + {"rhs": "Equation169", "lhs": "Equation192"}, + {"rhs": "Equation166", "lhs": "Equation194"}, + {"rhs": "Equation167", "lhs": "Equation195"}, + {"rhs": "Equation166", "lhs": "Equation196"}, + {"rhs": "Equation205", "lhs": "Equation207"}, + {"rhs": "Equation208", "lhs": "Equation210"}, + {"rhs": "Equation211", "lhs": "Equation213"}, + {"rhs": "Equation208", "lhs": "Equation214"}, + {"rhs": "Equation209", "lhs": "Equation215"}, + {"rhs": "Equation208", "lhs": "Equation216"}, + {"rhs": "Equation218", "lhs": "Equation220"}, + {"rhs": "Equation221", "lhs": "Equation223"}, + {"rhs": "Equation218", "lhs": "Equation224"}, + {"rhs": "Equation219", "lhs": "Equation225"}, + {"rhs": "Equation218", "lhs": "Equation226"}, + {"rhs": "Equation228", "lhs": "Equation230"}, + {"rhs": "Equation231", "lhs": "Equation233"}, + {"rhs": "Equation228", "lhs": "Equation234"}, + {"rhs": "Equation229", "lhs": "Equation235"}, + {"rhs": "Equation228", "lhs": "Equation236"}, + {"rhs": "Equation218", "lhs": "Equation238"}, + {"rhs": "Equation219", "lhs": "Equation239"}, + {"rhs": "Equation218", "lhs": "Equation240"}, + {"rhs": "Equation221", "lhs": "Equation242"}, + {"rhs": "Equation222", "lhs": "Equation243"}, + {"rhs": "Equation221", "lhs": "Equation244"}, + {"rhs": "Equation218", "lhs": "Equation246"}, + {"rhs": "Equation219", "lhs": "Equation247"}, + {"rhs": "Equation218", "lhs": "Equation248"}, + {"rhs": "Equation257", "lhs": "Equation259"}, + {"rhs": "Equation260", "lhs": "Equation262"}, + {"rhs": "Equation263", "lhs": "Equation265"}, + {"rhs": "Equation260", "lhs": "Equation266"}, + {"rhs": "Equation261", "lhs": "Equation267"}, + {"rhs": "Equation260", "lhs": "Equation268"}, + {"rhs": "Equation270", "lhs": "Equation272"}, + {"rhs": "Equation273", "lhs": "Equation275"}, + {"rhs": "Equation270", "lhs": "Equation276"}, + {"rhs": "Equation271", "lhs": "Equation277"}, + {"rhs": "Equation270", "lhs": "Equation278"}, + {"rhs": "Equation280", "lhs": "Equation282"}, + {"rhs": "Equation283", "lhs": "Equation285"}, + {"rhs": "Equation280", "lhs": "Equation286"}, + {"rhs": "Equation281", "lhs": "Equation287"}, + {"rhs": "Equation280", "lhs": "Equation288"}, + {"rhs": "Equation270", "lhs": "Equation290"}, + {"rhs": "Equation271", "lhs": "Equation291"}, + {"rhs": "Equation270", "lhs": "Equation292"}, + {"rhs": "Equation273", "lhs": "Equation294"}, + {"rhs": "Equation274", "lhs": "Equation295"}, + {"rhs": "Equation273", "lhs": "Equation296"}, + {"rhs": "Equation270", "lhs": "Equation298"}, + {"rhs": "Equation271", "lhs": "Equation299"}, + {"rhs": "Equation270", "lhs": "Equation300"}, + {"rhs": "Equation309", "lhs": "Equation311"}, + {"rhs": "Equation312", "lhs": "Equation314"}, + {"rhs": "Equation315", "lhs": "Equation317"}, + {"rhs": "Equation312", "lhs": "Equation318"}, + {"rhs": "Equation313", "lhs": "Equation319"}, + {"rhs": "Equation312", "lhs": "Equation320"}, + {"rhs": "Equation322", "lhs": "Equation324"}, + {"rhs": "Equation325", "lhs": "Equation327"}, + {"rhs": "Equation322", "lhs": "Equation328"}, + {"rhs": "Equation323", "lhs": "Equation329"}, + {"rhs": "Equation322", "lhs": "Equation330"}, + {"rhs": "Equation332", "lhs": "Equation334"}, + {"rhs": "Equation335", "lhs": "Equation337"}, + {"rhs": "Equation332", "lhs": "Equation338"}, + {"rhs": "Equation333", "lhs": "Equation339"}, + {"rhs": "Equation332", "lhs": "Equation340"}, + {"rhs": "Equation322", "lhs": "Equation342"}, + {"rhs": "Equation323", "lhs": "Equation343"}, + {"rhs": "Equation322", "lhs": "Equation344"}, + {"rhs": "Equation325", "lhs": "Equation346"}, + {"rhs": "Equation326", "lhs": "Equation347"}, + {"rhs": "Equation325", "lhs": "Equation348"}, + {"rhs": "Equation322", "lhs": "Equation350"}, + {"rhs": "Equation323", "lhs": "Equation351"}, + {"rhs": "Equation322", "lhs": "Equation352"}, + {"rhs": "Equation361", "lhs": "Equation363"}, + {"rhs": "Equation364", "lhs": "Equation366"}, + {"rhs": "Equation367", "lhs": "Equation369"}, + {"rhs": "Equation364", "lhs": "Equation370"}, + {"rhs": "Equation365", "lhs": "Equation371"}, + {"rhs": "Equation364", "lhs": "Equation372"}, + {"rhs": "Equation374", "lhs": "Equation376"}, + {"rhs": "Equation377", "lhs": "Equation379"}, + {"rhs": "Equation374", "lhs": "Equation380"}, + {"rhs": "Equation375", "lhs": "Equation381"}, + {"rhs": "Equation374", "lhs": "Equation382"}, + {"rhs": "Equation384", "lhs": "Equation386"}, + {"rhs": "Equation387", "lhs": "Equation389"}, + {"rhs": "Equation384", "lhs": "Equation390"}, + {"rhs": "Equation385", "lhs": "Equation391"}, + {"rhs": "Equation384", "lhs": "Equation392"}, + {"rhs": "Equation374", "lhs": "Equation394"}, + {"rhs": "Equation375", "lhs": "Equation395"}, + {"rhs": "Equation374", "lhs": "Equation396"}, + {"rhs": "Equation377", "lhs": "Equation398"}, + {"rhs": "Equation378", "lhs": "Equation399"}, + {"rhs": "Equation377", "lhs": "Equation400"}, + {"rhs": "Equation374", "lhs": "Equation402"}, + {"rhs": "Equation375", "lhs": "Equation403"}, + {"rhs": "Equation374", "lhs": "Equation404"}, + {"rhs": "Equation413", "lhs": "Equation415"}, + {"rhs": "Equation416", "lhs": "Equation418"}, + {"rhs": "Equation419", "lhs": "Equation421"}, + {"rhs": "Equation416", "lhs": "Equation422"}, + {"rhs": "Equation417", "lhs": "Equation423"}, + {"rhs": "Equation416", "lhs": "Equation424"}, + {"rhs": "Equation426", "lhs": "Equation428"}, + {"rhs": "Equation429", "lhs": "Equation431"}, + {"rhs": "Equation426", "lhs": "Equation432"}, + {"rhs": "Equation427", "lhs": "Equation433"}, + {"rhs": "Equation426", "lhs": "Equation434"}, + {"rhs": "Equation436", "lhs": "Equation438"}, + {"rhs": "Equation439", "lhs": "Equation441"}, + {"rhs": "Equation436", "lhs": "Equation442"}, + {"rhs": "Equation437", "lhs": "Equation443"}, + {"rhs": "Equation436", "lhs": "Equation444"}, + {"rhs": "Equation426", "lhs": "Equation446"}, + {"rhs": "Equation427", "lhs": "Equation447"}, + {"rhs": "Equation426", "lhs": "Equation448"}, + {"rhs": "Equation429", "lhs": "Equation450"}, + {"rhs": "Equation430", "lhs": "Equation451"}, + {"rhs": "Equation429", "lhs": "Equation452"}, + {"rhs": "Equation426", "lhs": "Equation454"}, + {"rhs": "Equation427", "lhs": "Equation455"}, + {"rhs": "Equation426", "lhs": "Equation456"}, + {"rhs": "Equation463", "lhs": "Equation465"}, + {"rhs": "Equation466", "lhs": "Equation468"}, + {"rhs": "Equation463", "lhs": "Equation469"}, + {"rhs": "Equation464", "lhs": "Equation470"}, + {"rhs": "Equation463", "lhs": "Equation471"}, + {"rhs": "Equation473", "lhs": "Equation475"}, + {"rhs": "Equation476", "lhs": "Equation478"}, + {"rhs": "Equation473", "lhs": "Equation479"}, + {"rhs": "Equation474", "lhs": "Equation480"}, + {"rhs": "Equation473", "lhs": "Equation481"}, + {"rhs": "Equation463", "lhs": "Equation483"}, + {"rhs": "Equation464", "lhs": "Equation484"}, + {"rhs": "Equation463", "lhs": "Equation485"}, + {"rhs": "Equation466", "lhs": "Equation487"}, + {"rhs": "Equation467", "lhs": "Equation488"}, + {"rhs": "Equation466", "lhs": "Equation489"}, + {"rhs": "Equation463", "lhs": "Equation491"}, + {"rhs": "Equation464", "lhs": "Equation492"}, + {"rhs": "Equation463", "lhs": "Equation493"}, + {"rhs": "Equation500", "lhs": "Equation502"}, + {"rhs": "Equation503", "lhs": "Equation505"}, + {"rhs": "Equation500", "lhs": "Equation506"}, + {"rhs": "Equation501", "lhs": "Equation507"}, + {"rhs": "Equation500", "lhs": "Equation508"}, + {"rhs": "Equation510", "lhs": "Equation512"}, + {"rhs": "Equation513", "lhs": "Equation515"}, + {"rhs": "Equation510", "lhs": "Equation516"}, + {"rhs": "Equation511", "lhs": "Equation517"}, + {"rhs": "Equation510", "lhs": "Equation518"}, + {"rhs": "Equation500", "lhs": "Equation520"}, + {"rhs": "Equation501", "lhs": "Equation521"}, + {"rhs": "Equation500", "lhs": "Equation522"}, + {"rhs": "Equation503", "lhs": "Equation524"}, + {"rhs": "Equation504", "lhs": "Equation525"}, + {"rhs": "Equation503", "lhs": "Equation526"}, + {"rhs": "Equation500", "lhs": "Equation528"}, + {"rhs": "Equation501", "lhs": "Equation529"}, + {"rhs": "Equation500", "lhs": 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"lhs": "Equation573"}, + {"rhs": "Equation466", "lhs": "Equation575"}, + {"rhs": "Equation467", "lhs": "Equation576"}, + {"rhs": "Equation466", "lhs": "Equation577"}, + {"rhs": "Equation463", "lhs": "Equation579"}, + {"rhs": "Equation464", "lhs": "Equation580"}, + {"rhs": "Equation463", "lhs": "Equation581"}, + {"rhs": "Equation616", "lhs": "Equation618"}, + {"rhs": "Equation619", "lhs": "Equation621"}, + {"rhs": "Equation622", "lhs": "Equation624"}, + {"rhs": "Equation619", "lhs": "Equation625"}, + {"rhs": "Equation620", "lhs": "Equation626"}, + {"rhs": "Equation619", "lhs": "Equation627"}, + {"rhs": "Equation629", "lhs": "Equation631"}, + {"rhs": "Equation632", "lhs": "Equation634"}, + {"rhs": "Equation629", "lhs": "Equation635"}, + {"rhs": "Equation630", "lhs": "Equation636"}, + {"rhs": "Equation629", "lhs": "Equation637"}, + {"rhs": "Equation639", "lhs": "Equation641"}, + {"rhs": "Equation642", "lhs": "Equation644"}, + {"rhs": "Equation639", "lhs": "Equation645"}, + {"rhs": "Equation640", "lhs": "Equation646"}, + {"rhs": "Equation639", "lhs": "Equation647"}, + {"rhs": "Equation629", "lhs": "Equation649"}, + {"rhs": "Equation630", "lhs": "Equation650"}, + {"rhs": "Equation629", "lhs": "Equation651"}, + {"rhs": "Equation632", "lhs": "Equation653"}, + {"rhs": "Equation633", "lhs": "Equation654"}, + {"rhs": "Equation632", "lhs": "Equation655"}, + {"rhs": "Equation629", "lhs": "Equation657"}, + {"rhs": "Equation630", "lhs": "Equation658"}, + {"rhs": "Equation629", "lhs": "Equation659"}, + {"rhs": "Equation666", "lhs": "Equation668"}, + {"rhs": "Equation669", "lhs": "Equation671"}, + {"rhs": "Equation666", "lhs": "Equation672"}, + {"rhs": "Equation667", "lhs": "Equation673"}, + {"rhs": "Equation666", "lhs": "Equation674"}, + {"rhs": "Equation676", "lhs": "Equation678"}, + {"rhs": "Equation679", "lhs": "Equation681"}, + {"rhs": "Equation676", "lhs": "Equation682"}, + {"rhs": "Equation677", "lhs": "Equation683"}, + {"rhs": "Equation676", "lhs": "Equation684"}, + {"rhs": "Equation666", "lhs": "Equation686"}, + {"rhs": "Equation667", "lhs": "Equation687"}, + {"rhs": "Equation666", "lhs": "Equation688"}, + {"rhs": "Equation669", "lhs": "Equation690"}, + {"rhs": "Equation670", "lhs": "Equation691"}, + {"rhs": "Equation669", "lhs": "Equation692"}, + {"rhs": "Equation666", "lhs": "Equation694"}, + {"rhs": "Equation667", "lhs": "Equation695"}, + {"rhs": "Equation666", "lhs": "Equation696"}, + {"rhs": "Equation703", "lhs": "Equation705"}, + {"rhs": "Equation706", "lhs": "Equation708"}, + {"rhs": "Equation703", "lhs": "Equation709"}, + {"rhs": "Equation704", "lhs": "Equation710"}, + {"rhs": "Equation703", "lhs": "Equation711"}, + {"rhs": "Equation713", "lhs": "Equation715"}, + {"rhs": "Equation716", "lhs": "Equation718"}, + {"rhs": "Equation713", "lhs": "Equation719"}, + {"rhs": "Equation714", "lhs": "Equation720"}, + {"rhs": "Equation713", "lhs": "Equation721"}, + {"rhs": "Equation703", "lhs": "Equation723"}, + {"rhs": "Equation704", "lhs": "Equation724"}, + {"rhs": "Equation703", "lhs": "Equation725"}, + {"rhs": "Equation706", "lhs": "Equation727"}, + {"rhs": "Equation707", "lhs": "Equation728"}, + {"rhs": "Equation706", "lhs": "Equation729"}, + {"rhs": "Equation703", "lhs": "Equation731"}, + {"rhs": "Equation704", "lhs": "Equation732"}, + {"rhs": "Equation703", "lhs": "Equation733"}, + {"rhs": "Equation666", "lhs": "Equation740"}, + {"rhs": "Equation667", "lhs": "Equation741"}, + {"rhs": "Equation666", "lhs": "Equation742"}, + {"rhs": "Equation669", "lhs": "Equation744"}, + {"rhs": "Equation670", "lhs": "Equation745"}, + {"rhs": "Equation669", "lhs": "Equation746"}, + {"rhs": "Equation666", "lhs": "Equation748"}, + {"rhs": "Equation667", "lhs": "Equation749"}, + {"rhs": "Equation666", "lhs": "Equation750"}, + {"rhs": "Equation676", "lhs": "Equation757"}, + {"rhs": "Equation677", "lhs": "Equation758"}, + {"rhs": "Equation676", "lhs": "Equation759"}, + {"rhs": "Equation679", "lhs": "Equation761"}, + {"rhs": "Equation680", "lhs": "Equation762"}, + {"rhs": "Equation679", "lhs": "Equation763"}, + {"rhs": "Equation676", "lhs": "Equation765"}, + {"rhs": "Equation677", "lhs": "Equation766"}, + {"rhs": "Equation676", "lhs": "Equation767"}, + {"rhs": "Equation666", "lhs": "Equation774"}, + {"rhs": "Equation667", "lhs": "Equation775"}, + {"rhs": "Equation666", "lhs": "Equation776"}, + {"rhs": "Equation669", "lhs": "Equation778"}, + {"rhs": "Equation670", "lhs": "Equation779"}, + {"rhs": "Equation669", "lhs": "Equation780"}, + {"rhs": "Equation666", "lhs": "Equation782"}, + {"rhs": "Equation667", "lhs": "Equation783"}, + {"rhs": "Equation666", "lhs": "Equation784"}, + {"rhs": "Equation819", "lhs": "Equation821"}, + {"rhs": "Equation822", "lhs": "Equation824"}, + {"rhs": "Equation825", "lhs": "Equation827"}, + {"rhs": "Equation822", "lhs": "Equation828"}, + {"rhs": "Equation823", "lhs": "Equation829"}, + {"rhs": "Equation822", "lhs": "Equation830"}, + {"rhs": "Equation832", "lhs": "Equation834"}, + {"rhs": "Equation835", "lhs": "Equation837"}, + {"rhs": "Equation832", "lhs": "Equation838"}, + {"rhs": "Equation833", "lhs": "Equation839"}, + {"rhs": "Equation832", "lhs": "Equation840"}, + {"rhs": "Equation842", "lhs": "Equation844"}, + {"rhs": "Equation845", "lhs": "Equation847"}, + {"rhs": "Equation842", "lhs": "Equation848"}, + {"rhs": "Equation843", "lhs": "Equation849"}, + {"rhs": "Equation842", "lhs": "Equation850"}, + {"rhs": "Equation832", "lhs": "Equation852"}, + {"rhs": "Equation833", "lhs": "Equation853"}, + {"rhs": "Equation832", "lhs": "Equation854"}, + {"rhs": "Equation835", "lhs": "Equation856"}, + {"rhs": "Equation836", "lhs": "Equation857"}, + {"rhs": "Equation835", "lhs": "Equation858"}, + {"rhs": "Equation832", "lhs": "Equation860"}, + {"rhs": "Equation833", "lhs": "Equation861"}, + {"rhs": "Equation832", "lhs": "Equation862"}, + {"rhs": "Equation869", "lhs": "Equation871"}, + {"rhs": "Equation872", "lhs": "Equation874"}, + {"rhs": "Equation869", "lhs": "Equation875"}, + {"rhs": "Equation870", "lhs": "Equation876"}, + {"rhs": "Equation869", "lhs": "Equation877"}, + {"rhs": "Equation879", "lhs": "Equation881"}, + {"rhs": "Equation882", "lhs": "Equation884"}, + {"rhs": "Equation879", "lhs": "Equation885"}, + {"rhs": "Equation880", "lhs": "Equation886"}, + {"rhs": "Equation879", "lhs": "Equation887"}, + {"rhs": "Equation869", "lhs": "Equation889"}, + {"rhs": "Equation870", "lhs": "Equation890"}, + {"rhs": "Equation869", "lhs": "Equation891"}, + {"rhs": "Equation872", "lhs": "Equation893"}, + {"rhs": "Equation873", "lhs": "Equation894"}, + {"rhs": "Equation872", "lhs": "Equation895"}, + {"rhs": "Equation869", "lhs": "Equation897"}, + {"rhs": "Equation870", "lhs": "Equation898"}, + {"rhs": "Equation869", "lhs": "Equation899"}, + {"rhs": "Equation906", "lhs": "Equation908"}, + {"rhs": "Equation909", "lhs": "Equation911"}, + {"rhs": "Equation906", "lhs": "Equation912"}, + {"rhs": "Equation907", "lhs": "Equation913"}, + {"rhs": "Equation906", "lhs": 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"Equation3924", "lhs": "Equation4015"}, + {"rhs": "Equation3914", "lhs": "Equation4022"}, + {"rhs": "Equation3915", "lhs": "Equation4023"}, + {"rhs": "Equation3914", "lhs": "Equation4024"}, + {"rhs": "Equation3917", "lhs": "Equation4026"}, + {"rhs": "Equation3918", "lhs": "Equation4027"}, + {"rhs": "Equation3917", "lhs": "Equation4028"}, + {"rhs": "Equation3914", "lhs": "Equation4030"}, + {"rhs": "Equation3915", "lhs": "Equation4031"}, + {"rhs": "Equation3914", "lhs": "Equation4032"}, + {"rhs": "Equation4067", "lhs": "Equation4069"}, + {"rhs": "Equation4070", "lhs": "Equation4072"}, + {"rhs": "Equation4073", "lhs": "Equation4075"}, + {"rhs": "Equation4070", "lhs": "Equation4076"}, + {"rhs": "Equation4071", "lhs": "Equation4077"}, + {"rhs": "Equation4070", "lhs": "Equation4078"}, + {"rhs": "Equation4080", "lhs": "Equation4082"}, + {"rhs": "Equation4083", "lhs": "Equation4085"}, + {"rhs": "Equation4080", "lhs": "Equation4086"}, + {"rhs": "Equation4081", "lhs": "Equation4087"}, + {"rhs": "Equation4080", "lhs": "Equation4088"}, + {"rhs": "Equation4090", "lhs": "Equation4092"}, + {"rhs": "Equation4093", "lhs": "Equation4095"}, + {"rhs": "Equation4090", "lhs": "Equation4096"}, + {"rhs": "Equation4091", "lhs": "Equation4097"}, + {"rhs": "Equation4090", "lhs": "Equation4098"}, + {"rhs": "Equation4080", "lhs": "Equation4100"}, + {"rhs": "Equation4081", "lhs": "Equation4101"}, + {"rhs": "Equation4080", "lhs": "Equation4102"}, + {"rhs": "Equation4083", "lhs": "Equation4104"}, + {"rhs": "Equation4084", "lhs": "Equation4105"}, + {"rhs": "Equation4083", "lhs": "Equation4106"}, + {"rhs": "Equation4080", "lhs": "Equation4108"}, + {"rhs": "Equation4081", "lhs": "Equation4109"}, + {"rhs": "Equation4080", "lhs": "Equation4110"}, + {"rhs": "Equation4117", "lhs": "Equation4119"}, + {"rhs": "Equation4120", "lhs": "Equation4122"}, + {"rhs": "Equation4117", "lhs": "Equation4123"}, + {"rhs": "Equation4118", "lhs": "Equation4124"}, + {"rhs": "Equation4117", "lhs": "Equation4125"}, + {"rhs": "Equation4127", "lhs": "Equation4129"}, + {"rhs": "Equation4130", "lhs": "Equation4132"}, + {"rhs": "Equation4127", "lhs": "Equation4133"}, + {"rhs": "Equation4128", "lhs": "Equation4134"}, + {"rhs": "Equation4127", "lhs": "Equation4135"}, + {"rhs": "Equation4117", "lhs": "Equation4137"}, + {"rhs": "Equation4118", "lhs": "Equation4138"}, + {"rhs": "Equation4117", "lhs": "Equation4139"}, + {"rhs": "Equation4120", "lhs": "Equation4141"}, + {"rhs": "Equation4121", "lhs": "Equation4142"}, + {"rhs": "Equation4120", "lhs": "Equation4143"}, + {"rhs": "Equation4117", "lhs": "Equation4145"}, + {"rhs": "Equation4118", "lhs": "Equation4146"}, + {"rhs": "Equation4117", "lhs": "Equation4147"}, + {"rhs": "Equation4154", "lhs": "Equation4156"}, + {"rhs": "Equation4157", "lhs": "Equation4159"}, + {"rhs": "Equation4154", "lhs": "Equation4160"}, + {"rhs": "Equation4155", "lhs": "Equation4161"}, + {"rhs": "Equation4154", "lhs": "Equation4162"}, + {"rhs": "Equation4164", "lhs": "Equation4166"}, + {"rhs": "Equation4167", "lhs": "Equation4169"}, + {"rhs": "Equation4164", "lhs": "Equation4170"}, + {"rhs": "Equation4165", "lhs": "Equation4171"}, + {"rhs": "Equation4164", "lhs": "Equation4172"}, + {"rhs": "Equation4154", "lhs": "Equation4174"}, + {"rhs": "Equation4155", "lhs": "Equation4175"}, + {"rhs": "Equation4154", "lhs": "Equation4176"}, + {"rhs": "Equation4157", "lhs": "Equation4178"}, + {"rhs": "Equation4158", "lhs": "Equation4179"}, + {"rhs": "Equation4157", "lhs": "Equation4180"}, + {"rhs": "Equation4154", "lhs": "Equation4182"}, + {"rhs": "Equation4155", "lhs": "Equation4183"}, + {"rhs": "Equation4154", "lhs": "Equation4184"}, + {"rhs": "Equation4117", "lhs": "Equation4191"}, + {"rhs": "Equation4118", "lhs": "Equation4192"}, + {"rhs": "Equation4117", "lhs": "Equation4193"}, + {"rhs": "Equation4120", "lhs": "Equation4195"}, + {"rhs": "Equation4121", "lhs": "Equation4196"}, + {"rhs": "Equation4120", "lhs": "Equation4197"}, + {"rhs": "Equation4117", "lhs": "Equation4199"}, + {"rhs": "Equation4118", "lhs": "Equation4200"}, + {"rhs": "Equation4117", "lhs": "Equation4201"}, + {"rhs": "Equation4127", "lhs": "Equation4208"}, + {"rhs": "Equation4128", "lhs": "Equation4209"}, + {"rhs": "Equation4127", "lhs": "Equation4210"}, + {"rhs": "Equation4130", "lhs": "Equation4212"}, + {"rhs": "Equation4131", "lhs": "Equation4213"}, + {"rhs": "Equation4130", "lhs": "Equation4214"}, + {"rhs": "Equation4127", "lhs": "Equation4216"}, + {"rhs": "Equation4128", "lhs": "Equation4217"}, + {"rhs": "Equation4127", "lhs": "Equation4218"}, + {"rhs": "Equation4117", "lhs": "Equation4225"}, + {"rhs": "Equation4118", "lhs": "Equation4226"}, + {"rhs": "Equation4117", "lhs": "Equation4227"}, + {"rhs": "Equation4120", "lhs": "Equation4229"}, + {"rhs": "Equation4121", "lhs": "Equation4230"}, + {"rhs": "Equation4120", "lhs": "Equation4231"}, + {"rhs": "Equation4117", "lhs": "Equation4233"}, + {"rhs": "Equation4118", "lhs": "Equation4234"}, + {"rhs": "Equation4117", "lhs": "Equation4235"}, + {"rhs": "Equation4269", "lhs": "Equation4271"}, + {"rhs": "Equation4272", "lhs": "Equation4274"}, + {"rhs": "Equation4275", "lhs": "Equation4277"}, + {"rhs": "Equation4272", "lhs": "Equation4278"}, + {"rhs": "Equation4273", "lhs": "Equation4279"}, + {"rhs": "Equation4272", "lhs": "Equation4280"}, + {"rhs": "Equation4283", "lhs": "Equation4285"}, + {"rhs": "Equation4290", "lhs": "Equation4292"}, + {"rhs": "Equation4293", "lhs": "Equation4294"}, + {"rhs": "Equation4290", "lhs": "Equation4295"}, + {"rhs": "Equation4291", "lhs": "Equation4296"}, + {"rhs": "Equation4290", "lhs": "Equation4297"}, + {"rhs": "Equation4283", "lhs": "Equation4303"}, + {"rhs": "Equation4284", "lhs": "Equation4304"}, + {"rhs": "Equation4283", "lhs": "Equation4305"}, + {"rhs": "Equation4320", "lhs": "Equation4322"}, + {"rhs": "Equation4320", "lhs": "Equation4323"}, + {"rhs": "Equation4321", "lhs": "Equation4324"}, + {"rhs": "Equation4320", "lhs": "Equation4325"}, + {"rhs": "Equation4314", "lhs": "Equation4331"}, + {"rhs": "Equation4343", "lhs": "Equation4344"}, + {"rhs": "Equation4343", "lhs": "Equation4345"}, + {"rhs": "Equation4343", "lhs": "Equation4346"}, + {"rhs": "Equation4320", "lhs": "Equation4362"}, + {"rhs": "Equation4320", "lhs": "Equation4364"}, + {"rhs": "Equation4382", "lhs": "Equation4384"}, + {"rhs": "Equation4385", "lhs": "Equation4387"}, + {"rhs": "Equation4388", "lhs": "Equation4390"}, + {"rhs": "Equation4385", "lhs": "Equation4391"}, + {"rhs": "Equation4386", "lhs": "Equation4392"}, + {"rhs": "Equation4385", "lhs": "Equation4393"}, + {"rhs": "Equation4395", "lhs": "Equation4397"}, + {"rhs": "Equation4398", "lhs": "Equation4400"}, + {"rhs": "Equation4395", "lhs": "Equation4401"}, + {"rhs": "Equation4396", "lhs": "Equation4402"}, + {"rhs": "Equation4395", "lhs": "Equation4403"}, + {"rhs": "Equation4405", "lhs": "Equation4407"}, + {"rhs": "Equation4408", "lhs": "Equation4410"}, + {"rhs": "Equation4405", "lhs": "Equation4411"}, + {"rhs": "Equation4406", "lhs": "Equation4412"}, + {"rhs": "Equation4405", "lhs": "Equation4413"}, + {"rhs": "Equation4395", "lhs": "Equation4415"}, + {"rhs": "Equation4396", "lhs": "Equation4416"}, + {"rhs": "Equation4395", "lhs": "Equation4417"}, + {"rhs": "Equation4398", "lhs": "Equation4419"}, + {"rhs": "Equation4399", "lhs": "Equation4420"}, + {"rhs": "Equation4398", "lhs": "Equation4421"}, + {"rhs": "Equation4395", "lhs": "Equation4423"}, + {"rhs": "Equation4396", "lhs": "Equation4424"}, + {"rhs": "Equation4395", "lhs": "Equation4425"}, + {"rhs": "Equation4432", "lhs": "Equation4434"}, + {"rhs": "Equation4435", "lhs": "Equation4437"}, + {"rhs": "Equation4432", "lhs": "Equation4438"}, + {"rhs": "Equation4433", "lhs": "Equation4439"}, + {"rhs": "Equation4432", "lhs": "Equation4440"}, + {"rhs": "Equation4442", "lhs": "Equation4444"}, + {"rhs": "Equation4445", "lhs": "Equation4447"}, + {"rhs": "Equation4442", "lhs": "Equation4448"}, + {"rhs": "Equation4443", "lhs": "Equation4449"}, + {"rhs": "Equation4442", "lhs": "Equation4450"}, + {"rhs": "Equation4432", "lhs": "Equation4452"}, + {"rhs": "Equation4433", "lhs": "Equation4453"}, + {"rhs": "Equation4432", "lhs": "Equation4454"}, + {"rhs": "Equation4435", "lhs": "Equation4456"}, + {"rhs": "Equation4436", "lhs": "Equation4457"}, + {"rhs": "Equation4435", "lhs": "Equation4458"}, + {"rhs": "Equation4432", "lhs": "Equation4460"}, + {"rhs": "Equation4433", "lhs": "Equation4461"}, + {"rhs": "Equation4432", "lhs": "Equation4462"}, + {"rhs": "Equation4469", "lhs": "Equation4471"}, + {"rhs": "Equation4472", "lhs": "Equation4474"}, + {"rhs": "Equation4469", "lhs": "Equation4475"}, + {"rhs": "Equation4470", "lhs": "Equation4476"}, + {"rhs": "Equation4469", "lhs": "Equation4477"}, + {"rhs": "Equation4479", "lhs": "Equation4481"}, + {"rhs": "Equation4482", "lhs": "Equation4484"}, + {"rhs": "Equation4479", "lhs": "Equation4485"}, + {"rhs": "Equation4480", "lhs": "Equation4486"}, + {"rhs": "Equation4479", "lhs": "Equation4487"}, + {"rhs": "Equation4469", "lhs": "Equation4489"}, + {"rhs": "Equation4470", "lhs": "Equation4490"}, + {"rhs": "Equation4469", "lhs": "Equation4491"}, + {"rhs": "Equation4472", "lhs": "Equation4493"}, + {"rhs": "Equation4473", "lhs": "Equation4494"}, + {"rhs": "Equation4472", "lhs": "Equation4495"}, + {"rhs": "Equation4469", "lhs": "Equation4497"}, + {"rhs": "Equation4470", "lhs": "Equation4498"}, + {"rhs": "Equation4469", "lhs": "Equation4499"}, + {"rhs": "Equation4432", "lhs": "Equation4506"}, + {"rhs": "Equation4433", "lhs": "Equation4507"}, + {"rhs": "Equation4432", "lhs": "Equation4508"}, + {"rhs": "Equation4435", "lhs": "Equation4510"}, + {"rhs": "Equation4436", "lhs": "Equation4511"}, + {"rhs": "Equation4435", "lhs": "Equation4512"}, + {"rhs": "Equation4432", "lhs": "Equation4514"}, + {"rhs": "Equation4433", "lhs": "Equation4515"}, + {"rhs": "Equation4432", "lhs": "Equation4516"}, + {"rhs": "Equation4442", "lhs": "Equation4523"}, + {"rhs": "Equation4443", "lhs": "Equation4524"}, + {"rhs": "Equation4442", "lhs": "Equation4525"}, + {"rhs": "Equation4445", "lhs": "Equation4527"}, + {"rhs": "Equation4446", "lhs": "Equation4528"}, + {"rhs": "Equation4445", "lhs": "Equation4529"}, + {"rhs": "Equation4442", "lhs": "Equation4531"}, + {"rhs": "Equation4443", "lhs": "Equation4532"}, + {"rhs": "Equation4442", "lhs": "Equation4533"}, + {"rhs": "Equation4432", "lhs": "Equation4540"}, + {"rhs": "Equation4433", "lhs": "Equation4541"}, + {"rhs": "Equation4432", "lhs": "Equation4542"}, + {"rhs": "Equation4435", "lhs": "Equation4544"}, + {"rhs": "Equation4436", "lhs": "Equation4545"}, + {"rhs": "Equation4435", "lhs": "Equation4546"}, + {"rhs": "Equation4432", "lhs": "Equation4548"}, + {"rhs": "Equation4433", "lhs": "Equation4549"}, + {"rhs": "Equation4432", "lhs": "Equation4550"}, + {"rhs": "Equation4584", "lhs": "Equation4586"}, + {"rhs": "Equation4587", "lhs": "Equation4589"}, + {"rhs": "Equation4590", "lhs": "Equation4592"}, + {"rhs": "Equation4587", "lhs": "Equation4593"}, + {"rhs": "Equation4588", "lhs": "Equation4594"}, + {"rhs": "Equation4587", "lhs": "Equation4595"}, + {"rhs": "Equation4598", "lhs": "Equation4600"}, + {"rhs": "Equation4605", "lhs": "Equation4607"}, + {"rhs": "Equation4608", "lhs": "Equation4609"}, + {"rhs": "Equation4605", "lhs": "Equation4610"}, + {"rhs": "Equation4606", "lhs": "Equation4611"}, + {"rhs": "Equation4605", "lhs": "Equation4612"}, + {"rhs": "Equation4598", "lhs": "Equation4618"}, + {"rhs": "Equation4599", "lhs": "Equation4619"}, + {"rhs": "Equation4598", "lhs": "Equation4620"}, + {"rhs": "Equation4635", "lhs": "Equation4637"}, + {"rhs": "Equation4635", "lhs": "Equation4638"}, + {"rhs": "Equation4636", "lhs": "Equation4639"}, + {"rhs": "Equation4635", "lhs": "Equation4640"}, + {"rhs": "Equation4629", "lhs": "Equation4646"}, + {"rhs": "Equation4658", "lhs": "Equation4659"}, + {"rhs": "Equation4658", "lhs": "Equation4660"}, + {"rhs": "Equation4658", "lhs": "Equation4661"}, + {"rhs": "Equation4635", "lhs": "Equation4677"}, + {"rhs": "Equation4635", "lhs": "Equation4679"}, + {"rhs": "Equation6", "lhs": "Equation7"}, + {"rhs": "Equation11", "lhs": "Equation12"}, + {"rhs": "Equation14", "lhs": "Equation15"}, + {"rhs": "Equation17", "lhs": "Equation18"}, + {"rhs": "Equation16", "lhs": "Equation19"}, + {"rhs": "Equation17", "lhs": "Equation20"}, + {"rhs": "Equation17", "lhs": "Equation21"}, + {"rhs": "Equation26", "lhs": "Equation27"}, + {"rhs": "Equation29", "lhs": "Equation30"}, + {"rhs": "Equation32", "lhs": "Equation33"}, + {"rhs": "Equation31", "lhs": "Equation34"}, + {"rhs": "Equation32", "lhs": "Equation35"}, + {"rhs": "Equation32", "lhs": "Equation36"}, + {"rhs": "Equation40", "lhs": "Equation41"}, + {"rhs": "Equation50", "lhs": "Equation51"}, + {"rhs": "Equation53", "lhs": "Equation54"}, + {"rhs": "Equation56", "lhs": "Equation57"}, + {"rhs": "Equation55", "lhs": "Equation58"}, + {"rhs": "Equation56", "lhs": "Equation59"}, + {"rhs": "Equation56", "lhs": "Equation60"}, + {"rhs": "Equation63", "lhs": "Equation64"}, + {"rhs": "Equation66", "lhs": "Equation67"}, + {"rhs": "Equation65", "lhs": "Equation68"}, + {"rhs": "Equation66", "lhs": "Equation69"}, + {"rhs": "Equation66", "lhs": "Equation70"}, + {"rhs": "Equation73", "lhs": "Equation74"}, + {"rhs": "Equation76", "lhs": "Equation77"}, + {"rhs": "Equation75", "lhs": "Equation78"}, + {"rhs": "Equation76", "lhs": "Equation79"}, + {"rhs": "Equation76", "lhs": "Equation80"}, + {"rhs": "Equation72", "lhs": "Equation82"}, + {"rhs": "Equation73", "lhs": "Equation83"}, + {"rhs": "Equation73", "lhs": "Equation84"}, + {"rhs": "Equation75", "lhs": "Equation86"}, + {"rhs": "Equation76", "lhs": "Equation87"}, + {"rhs": "Equation76", "lhs": "Equation88"}, + {"rhs": "Equation75", "lhs": "Equation90"}, + {"rhs": "Equation76", "lhs": "Equation91"}, + {"rhs": "Equation76", "lhs": "Equation92"}, + {"rhs": "Equation102", "lhs": "Equation103"}, + {"rhs": "Equation105", "lhs": "Equation106"}, + {"rhs": "Equation108", "lhs": "Equation109"}, + {"rhs": "Equation107", "lhs": "Equation110"}, + {"rhs": "Equation108", "lhs": "Equation111"}, + {"rhs": "Equation108", "lhs": "Equation112"}, + {"rhs": "Equation115", "lhs": "Equation116"}, + {"rhs": "Equation118", "lhs": "Equation119"}, + {"rhs": "Equation117", "lhs": "Equation120"}, + {"rhs": "Equation118", "lhs": "Equation121"}, + {"rhs": "Equation118", "lhs": "Equation122"}, + {"rhs": "Equation125", "lhs": "Equation126"}, + {"rhs": "Equation128", "lhs": "Equation129"}, + {"rhs": "Equation127", "lhs": "Equation130"}, + {"rhs": "Equation128", "lhs": "Equation131"}, + {"rhs": "Equation128", "lhs": "Equation132"}, + {"rhs": "Equation124", "lhs": "Equation134"}, + {"rhs": "Equation125", "lhs": "Equation135"}, + {"rhs": "Equation125", "lhs": "Equation136"}, + {"rhs": "Equation127", "lhs": "Equation138"}, + {"rhs": "Equation128", "lhs": "Equation139"}, + {"rhs": "Equation128", "lhs": "Equation140"}, + {"rhs": "Equation127", "lhs": "Equation142"}, + {"rhs": "Equation128", "lhs": "Equation143"}, + {"rhs": "Equation128", "lhs": "Equation144"}, + {"rhs": "Equation154", "lhs": "Equation155"}, + {"rhs": "Equation157", "lhs": "Equation158"}, + {"rhs": "Equation160", "lhs": "Equation161"}, + {"rhs": "Equation159", "lhs": "Equation162"}, + {"rhs": "Equation160", "lhs": "Equation163"}, + {"rhs": "Equation160", "lhs": "Equation164"}, + {"rhs": "Equation167", "lhs": "Equation168"}, + {"rhs": "Equation170", "lhs": "Equation171"}, + {"rhs": "Equation169", "lhs": "Equation172"}, + {"rhs": "Equation170", "lhs": "Equation173"}, + {"rhs": "Equation170", "lhs": "Equation174"}, + {"rhs": "Equation177", "lhs": "Equation178"}, + {"rhs": "Equation180", "lhs": "Equation181"}, + {"rhs": "Equation179", "lhs": "Equation182"}, + {"rhs": "Equation180", "lhs": "Equation183"}, + {"rhs": "Equation180", "lhs": "Equation184"}, + {"rhs": "Equation176", "lhs": "Equation186"}, + {"rhs": "Equation177", "lhs": "Equation187"}, + {"rhs": "Equation177", "lhs": "Equation188"}, + {"rhs": "Equation179", "lhs": "Equation190"}, + {"rhs": "Equation180", "lhs": "Equation191"}, + {"rhs": "Equation180", "lhs": "Equation192"}, + {"rhs": "Equation179", "lhs": "Equation194"}, + {"rhs": "Equation180", "lhs": "Equation195"}, + {"rhs": "Equation180", "lhs": "Equation196"}, + {"rhs": "Equation206", "lhs": "Equation207"}, + {"rhs": "Equation209", "lhs": "Equation210"}, + {"rhs": "Equation212", "lhs": "Equation213"}, + {"rhs": "Equation211", "lhs": "Equation214"}, + {"rhs": "Equation212", "lhs": "Equation215"}, + {"rhs": "Equation212", "lhs": "Equation216"}, + {"rhs": "Equation219", "lhs": "Equation220"}, + {"rhs": "Equation222", "lhs": "Equation223"}, + {"rhs": "Equation221", "lhs": "Equation224"}, + {"rhs": "Equation222", "lhs": "Equation225"}, + {"rhs": "Equation222", "lhs": "Equation226"}, + {"rhs": "Equation229", "lhs": "Equation230"}, + {"rhs": "Equation232", "lhs": "Equation233"}, + {"rhs": "Equation231", "lhs": "Equation234"}, + {"rhs": "Equation232", "lhs": "Equation235"}, + {"rhs": "Equation232", "lhs": "Equation236"}, + {"rhs": "Equation228", "lhs": "Equation238"}, + {"rhs": "Equation229", "lhs": "Equation239"}, + {"rhs": "Equation229", "lhs": "Equation240"}, + {"rhs": "Equation231", "lhs": "Equation242"}, + {"rhs": "Equation232", "lhs": "Equation243"}, + {"rhs": "Equation232", "lhs": "Equation244"}, + {"rhs": "Equation231", "lhs": "Equation246"}, + {"rhs": "Equation232", "lhs": "Equation247"}, + {"rhs": "Equation232", "lhs": "Equation248"}, + {"rhs": "Equation258", "lhs": "Equation259"}, + {"rhs": "Equation261", "lhs": "Equation262"}, + {"rhs": "Equation264", "lhs": "Equation265"}, + {"rhs": "Equation263", "lhs": "Equation266"}, + {"rhs": "Equation264", "lhs": "Equation267"}, + {"rhs": "Equation264", "lhs": "Equation268"}, + {"rhs": "Equation271", "lhs": "Equation272"}, + {"rhs": "Equation274", "lhs": "Equation275"}, + {"rhs": "Equation273", "lhs": "Equation276"}, + {"rhs": "Equation274", "lhs": "Equation277"}, + {"rhs": "Equation274", "lhs": "Equation278"}, + {"rhs": "Equation281", "lhs": "Equation282"}, + {"rhs": "Equation284", "lhs": "Equation285"}, + {"rhs": "Equation283", "lhs": "Equation286"}, + {"rhs": "Equation284", "lhs": "Equation287"}, + {"rhs": "Equation284", "lhs": "Equation288"}, + {"rhs": "Equation280", "lhs": "Equation290"}, + {"rhs": "Equation281", "lhs": "Equation291"}, + {"rhs": "Equation281", "lhs": "Equation292"}, + {"rhs": "Equation283", "lhs": "Equation294"}, + {"rhs": "Equation284", "lhs": "Equation295"}, + {"rhs": "Equation284", "lhs": "Equation296"}, + {"rhs": "Equation283", "lhs": "Equation298"}, + {"rhs": "Equation284", "lhs": "Equation299"}, + {"rhs": "Equation284", "lhs": "Equation300"}, + {"rhs": "Equation310", "lhs": "Equation311"}, + {"rhs": "Equation313", "lhs": "Equation314"}, + {"rhs": "Equation316", "lhs": "Equation317"}, + {"rhs": "Equation315", "lhs": "Equation318"}, + {"rhs": "Equation316", "lhs": "Equation319"}, + {"rhs": "Equation316", "lhs": "Equation320"}, + {"rhs": "Equation323", "lhs": "Equation324"}, + {"rhs": "Equation326", "lhs": "Equation327"}, + {"rhs": "Equation325", "lhs": "Equation328"}, + {"rhs": "Equation326", "lhs": "Equation329"}, + {"rhs": "Equation326", "lhs": "Equation330"}, + {"rhs": "Equation333", "lhs": "Equation334"}, + {"rhs": "Equation336", "lhs": "Equation337"}, + {"rhs": "Equation335", "lhs": "Equation338"}, + {"rhs": "Equation336", "lhs": "Equation339"}, + {"rhs": "Equation336", "lhs": "Equation340"}, + {"rhs": "Equation332", "lhs": "Equation342"}, + {"rhs": "Equation333", "lhs": "Equation343"}, + {"rhs": "Equation333", "lhs": "Equation344"}, + {"rhs": "Equation335", "lhs": "Equation346"}, + {"rhs": "Equation336", "lhs": "Equation347"}, + {"rhs": "Equation336", "lhs": "Equation348"}, + {"rhs": "Equation335", "lhs": "Equation350"}, + {"rhs": "Equation336", "lhs": "Equation351"}, + {"rhs": "Equation336", "lhs": "Equation352"}, + {"rhs": "Equation362", "lhs": "Equation363"}, + {"rhs": "Equation365", "lhs": "Equation366"}, + {"rhs": "Equation368", "lhs": "Equation369"}, + {"rhs": "Equation367", "lhs": "Equation370"}, + {"rhs": "Equation368", "lhs": "Equation371"}, + {"rhs": "Equation368", "lhs": "Equation372"}, + {"rhs": "Equation375", "lhs": "Equation376"}, + {"rhs": "Equation378", "lhs": "Equation379"}, + {"rhs": "Equation377", "lhs": "Equation380"}, + {"rhs": "Equation378", "lhs": "Equation381"}, + {"rhs": "Equation378", "lhs": "Equation382"}, + {"rhs": "Equation385", "lhs": "Equation386"}, + {"rhs": "Equation388", "lhs": "Equation389"}, + {"rhs": "Equation387", "lhs": "Equation390"}, + {"rhs": "Equation388", "lhs": "Equation391"}, + {"rhs": "Equation388", "lhs": "Equation392"}, + {"rhs": "Equation384", "lhs": "Equation394"}, + {"rhs": "Equation385", "lhs": "Equation395"}, + {"rhs": "Equation385", "lhs": "Equation396"}, + {"rhs": "Equation387", "lhs": "Equation398"}, + {"rhs": "Equation388", "lhs": "Equation399"}, + {"rhs": "Equation388", "lhs": "Equation400"}, + {"rhs": "Equation387", "lhs": "Equation402"}, + {"rhs": "Equation388", "lhs": "Equation403"}, + {"rhs": "Equation388", "lhs": "Equation404"}, + {"rhs": "Equation414", "lhs": "Equation415"}, + {"rhs": "Equation417", "lhs": "Equation418"}, + {"rhs": "Equation420", "lhs": "Equation421"}, + {"rhs": "Equation419", "lhs": "Equation422"}, + {"rhs": "Equation420", "lhs": "Equation423"}, + {"rhs": "Equation420", "lhs": "Equation424"}, + {"rhs": "Equation427", "lhs": "Equation428"}, + {"rhs": "Equation430", "lhs": "Equation431"}, + {"rhs": "Equation429", "lhs": "Equation432"}, + {"rhs": "Equation430", "lhs": "Equation433"}, + {"rhs": "Equation430", "lhs": "Equation434"}, + {"rhs": "Equation437", "lhs": "Equation438"}, + {"rhs": "Equation440", "lhs": "Equation441"}, + {"rhs": "Equation439", "lhs": "Equation442"}, + {"rhs": "Equation440", "lhs": "Equation443"}, + {"rhs": "Equation440", "lhs": "Equation444"}, + {"rhs": "Equation436", "lhs": "Equation446"}, + {"rhs": "Equation437", "lhs": "Equation447"}, + {"rhs": "Equation437", "lhs": "Equation448"}, + {"rhs": "Equation439", "lhs": "Equation450"}, + {"rhs": "Equation440", "lhs": "Equation451"}, + {"rhs": "Equation440", "lhs": "Equation452"}, + {"rhs": "Equation439", "lhs": "Equation454"}, + {"rhs": "Equation440", "lhs": "Equation455"}, + {"rhs": "Equation440", "lhs": "Equation456"}, + {"rhs": "Equation464", "lhs": "Equation465"}, + {"rhs": "Equation467", "lhs": "Equation468"}, + {"rhs": "Equation466", "lhs": "Equation469"}, + {"rhs": "Equation467", "lhs": "Equation470"}, + {"rhs": "Equation467", "lhs": "Equation471"}, + {"rhs": "Equation474", "lhs": "Equation475"}, + {"rhs": "Equation477", "lhs": "Equation478"}, + {"rhs": "Equation476", "lhs": "Equation479"}, + {"rhs": "Equation477", "lhs": "Equation480"}, + {"rhs": "Equation477", "lhs": "Equation481"}, + {"rhs": "Equation473", "lhs": "Equation483"}, + {"rhs": "Equation474", "lhs": "Equation484"}, + {"rhs": "Equation474", "lhs": "Equation485"}, + {"rhs": "Equation476", "lhs": "Equation487"}, + {"rhs": "Equation477", "lhs": "Equation488"}, + {"rhs": "Equation477", "lhs": "Equation489"}, + {"rhs": "Equation476", "lhs": "Equation491"}, + {"rhs": "Equation477", "lhs": "Equation492"}, + {"rhs": "Equation477", "lhs": "Equation493"}, + {"rhs": "Equation501", "lhs": "Equation502"}, + {"rhs": "Equation504", "lhs": "Equation505"}, + {"rhs": "Equation503", "lhs": "Equation506"}, + {"rhs": "Equation504", "lhs": "Equation507"}, + {"rhs": "Equation504", "lhs": "Equation508"}, + {"rhs": "Equation511", "lhs": "Equation512"}, + {"rhs": "Equation514", "lhs": "Equation515"}, + {"rhs": "Equation513", "lhs": "Equation516"}, + {"rhs": "Equation514", "lhs": "Equation517"}, + {"rhs": "Equation514", "lhs": "Equation518"}, + {"rhs": "Equation510", "lhs": "Equation520"}, + {"rhs": "Equation511", "lhs": "Equation521"}, + {"rhs": "Equation511", "lhs": "Equation522"}, + {"rhs": "Equation513", "lhs": "Equation524"}, + {"rhs": "Equation514", "lhs": "Equation525"}, + {"rhs": "Equation514", "lhs": "Equation526"}, + {"rhs": "Equation513", "lhs": "Equation528"}, + {"rhs": "Equation514", "lhs": "Equation529"}, + {"rhs": "Equation514", "lhs": "Equation530"}, + {"rhs": "Equation500", "lhs": "Equation537"}, + {"rhs": "Equation501", "lhs": "Equation538"}, + {"rhs": "Equation501", "lhs": "Equation539"}, + {"rhs": "Equation503", "lhs": "Equation541"}, + {"rhs": "Equation504", "lhs": "Equation542"}, + {"rhs": "Equation504", "lhs": "Equation543"}, + {"rhs": "Equation503", "lhs": "Equation545"}, + {"rhs": "Equation504", "lhs": "Equation546"}, + {"rhs": "Equation504", "lhs": "Equation547"}, + {"rhs": "Equation510", "lhs": "Equation554"}, + {"rhs": "Equation511", "lhs": "Equation555"}, + {"rhs": "Equation511", "lhs": "Equation556"}, + {"rhs": "Equation513", "lhs": "Equation558"}, + {"rhs": "Equation514", "lhs": "Equation559"}, + {"rhs": "Equation514", "lhs": "Equation560"}, + {"rhs": "Equation513", "lhs": "Equation562"}, + {"rhs": "Equation514", "lhs": "Equation563"}, + {"rhs": "Equation514", "lhs": "Equation564"}, + {"rhs": "Equation510", "lhs": "Equation571"}, + {"rhs": "Equation511", "lhs": "Equation572"}, + {"rhs": "Equation511", "lhs": "Equation573"}, + {"rhs": "Equation513", "lhs": "Equation575"}, + {"rhs": "Equation514", "lhs": "Equation576"}, + {"rhs": "Equation514", "lhs": "Equation577"}, + {"rhs": "Equation513", "lhs": "Equation579"}, + {"rhs": "Equation514", "lhs": "Equation580"}, + {"rhs": "Equation514", "lhs": "Equation581"}, + {"rhs": "Equation617", "lhs": "Equation618"}, + {"rhs": "Equation620", "lhs": "Equation621"}, + {"rhs": "Equation623", "lhs": "Equation624"}, + {"rhs": "Equation622", "lhs": "Equation625"}, + {"rhs": "Equation623", "lhs": "Equation626"}, + {"rhs": "Equation623", "lhs": "Equation627"}, + {"rhs": "Equation630", "lhs": "Equation631"}, + {"rhs": "Equation633", "lhs": "Equation634"}, + {"rhs": "Equation632", "lhs": "Equation635"}, + {"rhs": "Equation633", "lhs": "Equation636"}, + {"rhs": "Equation633", "lhs": "Equation637"}, + {"rhs": "Equation640", "lhs": "Equation641"}, + {"rhs": "Equation643", "lhs": "Equation644"}, + {"rhs": "Equation642", "lhs": "Equation645"}, + {"rhs": "Equation643", "lhs": "Equation646"}, + {"rhs": "Equation643", "lhs": "Equation647"}, + {"rhs": "Equation639", "lhs": "Equation649"}, + {"rhs": "Equation640", "lhs": "Equation650"}, + {"rhs": "Equation640", "lhs": "Equation651"}, + {"rhs": "Equation642", "lhs": "Equation653"}, + {"rhs": "Equation643", "lhs": "Equation654"}, + {"rhs": "Equation643", "lhs": "Equation655"}, + {"rhs": "Equation642", "lhs": "Equation657"}, + {"rhs": "Equation643", "lhs": "Equation658"}, + {"rhs": "Equation643", "lhs": "Equation659"}, + {"rhs": "Equation667", "lhs": "Equation668"}, + {"rhs": "Equation670", "lhs": "Equation671"}, + {"rhs": "Equation669", "lhs": "Equation672"}, + {"rhs": "Equation670", "lhs": "Equation673"}, + {"rhs": "Equation670", "lhs": "Equation674"}, + {"rhs": "Equation677", "lhs": "Equation678"}, + {"rhs": "Equation680", "lhs": "Equation681"}, + {"rhs": "Equation679", "lhs": "Equation682"}, + {"rhs": "Equation680", "lhs": "Equation683"}, + {"rhs": "Equation680", "lhs": "Equation684"}, + {"rhs": "Equation676", "lhs": "Equation686"}, + {"rhs": "Equation677", "lhs": "Equation687"}, + {"rhs": "Equation677", "lhs": "Equation688"}, + {"rhs": "Equation679", "lhs": "Equation690"}, + {"rhs": "Equation680", "lhs": "Equation691"}, + {"rhs": "Equation680", "lhs": "Equation692"}, + {"rhs": "Equation679", "lhs": "Equation694"}, + {"rhs": "Equation680", "lhs": "Equation695"}, + {"rhs": "Equation680", "lhs": "Equation696"}, + {"rhs": "Equation704", "lhs": "Equation705"}, + {"rhs": "Equation707", "lhs": "Equation708"}, + {"rhs": "Equation706", "lhs": "Equation709"}, + {"rhs": "Equation707", "lhs": "Equation710"}, + {"rhs": "Equation707", "lhs": "Equation711"}, + {"rhs": "Equation714", "lhs": "Equation715"}, + {"rhs": "Equation717", "lhs": "Equation718"}, + {"rhs": "Equation716", "lhs": "Equation719"}, + {"rhs": "Equation717", "lhs": "Equation720"}, + {"rhs": "Equation717", "lhs": "Equation721"}, + {"rhs": "Equation713", "lhs": "Equation723"}, + {"rhs": "Equation714", "lhs": "Equation724"}, + {"rhs": "Equation714", "lhs": "Equation725"}, + {"rhs": "Equation716", "lhs": "Equation727"}, + {"rhs": "Equation717", "lhs": "Equation728"}, + {"rhs": "Equation717", "lhs": "Equation729"}, + {"rhs": "Equation716", "lhs": "Equation731"}, + {"rhs": "Equation717", "lhs": "Equation732"}, + {"rhs": "Equation717", "lhs": "Equation733"}, + {"rhs": "Equation703", "lhs": "Equation740"}, + {"rhs": "Equation704", "lhs": "Equation741"}, + {"rhs": "Equation704", "lhs": "Equation742"}, + {"rhs": "Equation706", "lhs": "Equation744"}, + {"rhs": "Equation707", "lhs": "Equation745"}, + {"rhs": "Equation707", "lhs": "Equation746"}, + {"rhs": "Equation706", "lhs": "Equation748"}, + {"rhs": "Equation707", "lhs": "Equation749"}, + {"rhs": "Equation707", "lhs": "Equation750"}, + {"rhs": "Equation713", "lhs": "Equation757"}, + {"rhs": "Equation714", "lhs": "Equation758"}, + {"rhs": "Equation714", "lhs": "Equation759"}, + {"rhs": "Equation716", "lhs": "Equation761"}, + {"rhs": "Equation717", "lhs": "Equation762"}, + {"rhs": "Equation717", "lhs": "Equation763"}, + {"rhs": "Equation716", "lhs": "Equation765"}, + {"rhs": "Equation717", "lhs": "Equation766"}, + {"rhs": "Equation717", "lhs": "Equation767"}, + {"rhs": "Equation713", "lhs": "Equation774"}, + {"rhs": "Equation714", "lhs": "Equation775"}, + {"rhs": "Equation714", "lhs": "Equation776"}, + {"rhs": "Equation716", "lhs": "Equation778"}, + {"rhs": "Equation717", "lhs": "Equation779"}, + {"rhs": "Equation717", "lhs": "Equation780"}, + {"rhs": "Equation716", "lhs": "Equation782"}, + {"rhs": "Equation717", "lhs": "Equation783"}, + {"rhs": "Equation717", "lhs": "Equation784"}, + {"rhs": "Equation820", "lhs": "Equation821"}, + {"rhs": "Equation823", "lhs": "Equation824"}, + {"rhs": "Equation826", "lhs": "Equation827"}, + {"rhs": "Equation825", "lhs": "Equation828"}, + {"rhs": "Equation826", "lhs": "Equation829"}, + {"rhs": "Equation826", "lhs": "Equation830"}, + {"rhs": "Equation833", "lhs": "Equation834"}, + {"rhs": "Equation836", "lhs": "Equation837"}, + {"rhs": "Equation835", "lhs": "Equation838"}, + {"rhs": "Equation836", "lhs": "Equation839"}, + {"rhs": "Equation836", "lhs": "Equation840"}, + {"rhs": "Equation843", "lhs": "Equation844"}, + {"rhs": "Equation846", "lhs": "Equation847"}, + {"rhs": "Equation845", "lhs": "Equation848"}, + {"rhs": "Equation846", "lhs": "Equation849"}, + {"rhs": "Equation846", "lhs": "Equation850"}, + {"rhs": "Equation842", "lhs": "Equation852"}, + {"rhs": "Equation843", "lhs": "Equation853"}, + {"rhs": "Equation843", "lhs": "Equation854"}, + {"rhs": "Equation845", "lhs": "Equation856"}, + {"rhs": "Equation846", "lhs": "Equation857"}, + {"rhs": "Equation846", "lhs": "Equation858"}, + {"rhs": "Equation845", "lhs": "Equation860"}, + {"rhs": "Equation846", "lhs": "Equation861"}, + {"rhs": "Equation846", "lhs": "Equation862"}, + {"rhs": "Equation870", "lhs": "Equation871"}, + {"rhs": "Equation873", "lhs": "Equation874"}, + {"rhs": "Equation872", "lhs": "Equation875"}, + {"rhs": "Equation873", "lhs": "Equation876"}, + {"rhs": "Equation873", "lhs": "Equation877"}, + {"rhs": "Equation880", "lhs": "Equation881"}, + {"rhs": "Equation883", "lhs": "Equation884"}, + {"rhs": "Equation882", "lhs": "Equation885"}, + {"rhs": "Equation883", "lhs": "Equation886"}, + {"rhs": "Equation883", "lhs": "Equation887"}, + {"rhs": "Equation879", "lhs": "Equation889"}, + {"rhs": "Equation880", "lhs": "Equation890"}, + {"rhs": "Equation880", "lhs": "Equation891"}, + {"rhs": "Equation882", "lhs": "Equation893"}, + {"rhs": "Equation883", "lhs": "Equation894"}, + {"rhs": "Equation883", "lhs": "Equation895"}, + {"rhs": "Equation882", "lhs": "Equation897"}, + {"rhs": "Equation883", "lhs": "Equation898"}, + {"rhs": "Equation883", "lhs": "Equation899"}, + {"rhs": "Equation907", "lhs": "Equation908"}, + {"rhs": "Equation910", "lhs": "Equation911"}, + {"rhs": "Equation909", "lhs": "Equation912"}, + {"rhs": "Equation910", "lhs": "Equation913"}, + {"rhs": "Equation910", "lhs": "Equation914"}, + {"rhs": "Equation917", "lhs": "Equation918"}, + {"rhs": "Equation920", "lhs": "Equation921"}, + {"rhs": "Equation919", "lhs": "Equation922"}, + {"rhs": "Equation920", "lhs": "Equation923"}, + {"rhs": "Equation920", "lhs": "Equation924"}, + {"rhs": "Equation916", "lhs": "Equation926"}, + {"rhs": "Equation917", "lhs": "Equation927"}, + {"rhs": "Equation917", "lhs": "Equation928"}, + {"rhs": "Equation919", "lhs": "Equation930"}, + {"rhs": "Equation920", "lhs": "Equation931"}, + {"rhs": "Equation920", "lhs": "Equation932"}, + {"rhs": "Equation919", "lhs": "Equation934"}, + {"rhs": "Equation920", "lhs": "Equation935"}, + {"rhs": "Equation920", "lhs": "Equation936"}, + {"rhs": "Equation906", "lhs": "Equation943"}, + {"rhs": "Equation907", "lhs": "Equation944"}, + {"rhs": "Equation907", "lhs": "Equation945"}, + {"rhs": "Equation909", "lhs": "Equation947"}, + {"rhs": "Equation910", "lhs": "Equation948"}, + {"rhs": "Equation910", "lhs": "Equation949"}, + {"rhs": "Equation909", "lhs": "Equation951"}, + {"rhs": "Equation910", "lhs": "Equation952"}, + {"rhs": "Equation910", "lhs": "Equation953"}, + {"rhs": "Equation916", "lhs": "Equation960"}, + {"rhs": "Equation917", "lhs": "Equation961"}, + {"rhs": "Equation917", "lhs": "Equation962"}, + {"rhs": "Equation919", "lhs": "Equation964"}, + {"rhs": "Equation920", "lhs": "Equation965"}, + {"rhs": "Equation920", "lhs": "Equation966"}, + {"rhs": "Equation919", "lhs": "Equation968"}, + {"rhs": "Equation920", "lhs": "Equation969"}, + {"rhs": "Equation920", "lhs": "Equation970"}, + {"rhs": "Equation916", "lhs": "Equation977"}, + {"rhs": "Equation917", "lhs": "Equation978"}, + {"rhs": "Equation917", "lhs": "Equation979"}, + {"rhs": "Equation919", "lhs": "Equation981"}, + {"rhs": "Equation920", "lhs": "Equation982"}, + {"rhs": "Equation920", "lhs": "Equation983"}, + {"rhs": "Equation919", "lhs": "Equation985"}, + {"rhs": "Equation920", "lhs": "Equation986"}, + {"rhs": "Equation920", "lhs": "Equation987"}, + {"rhs": "Equation1023", "lhs": "Equation1024"}, + {"rhs": "Equation1026", "lhs": "Equation1027"}, + {"rhs": "Equation1029", "lhs": "Equation1030"}, + {"rhs": "Equation1028", "lhs": "Equation1031"}, + {"rhs": "Equation1029", "lhs": "Equation1032"}, + {"rhs": "Equation1029", "lhs": "Equation1033"}, + {"rhs": "Equation1036", "lhs": "Equation1037"}, + {"rhs": "Equation1039", "lhs": "Equation1040"}, + {"rhs": "Equation1038", "lhs": "Equation1041"}, + {"rhs": "Equation1039", "lhs": "Equation1042"}, + {"rhs": "Equation1039", "lhs": "Equation1043"}, + {"rhs": "Equation1046", "lhs": "Equation1047"}, + {"rhs": "Equation1049", "lhs": "Equation1050"}, + {"rhs": "Equation1048", "lhs": "Equation1051"}, + {"rhs": "Equation1049", "lhs": "Equation1052"}, + {"rhs": "Equation1049", "lhs": "Equation1053"}, + {"rhs": "Equation1045", "lhs": "Equation1055"}, + {"rhs": "Equation1046", "lhs": "Equation1056"}, + {"rhs": "Equation1046", "lhs": "Equation1057"}, + {"rhs": "Equation1048", "lhs": "Equation1059"}, + {"rhs": "Equation1049", "lhs": "Equation1060"}, + {"rhs": "Equation1049", "lhs": "Equation1061"}, + {"rhs": "Equation1048", "lhs": "Equation1063"}, + {"rhs": "Equation1049", "lhs": "Equation1064"}, + {"rhs": "Equation1049", "lhs": "Equation1065"}, + {"rhs": "Equation1073", "lhs": "Equation1074"}, + {"rhs": "Equation1076", "lhs": "Equation1077"}, + {"rhs": "Equation1075", "lhs": "Equation1078"}, + {"rhs": "Equation1076", "lhs": "Equation1079"}, + {"rhs": "Equation1076", "lhs": "Equation1080"}, + {"rhs": "Equation1083", "lhs": "Equation1084"}, + {"rhs": "Equation1086", "lhs": "Equation1087"}, + {"rhs": "Equation1085", "lhs": "Equation1088"}, + {"rhs": "Equation1086", "lhs": "Equation1089"}, + {"rhs": "Equation1086", "lhs": "Equation1090"}, + {"rhs": "Equation1082", "lhs": "Equation1092"}, + {"rhs": "Equation1083", "lhs": "Equation1093"}, + {"rhs": "Equation1083", "lhs": "Equation1094"}, + {"rhs": "Equation1085", "lhs": "Equation1096"}, + {"rhs": "Equation1086", "lhs": "Equation1097"}, + {"rhs": "Equation1086", "lhs": "Equation1098"}, + {"rhs": "Equation1085", "lhs": "Equation1100"}, + {"rhs": "Equation1086", "lhs": "Equation1101"}, + {"rhs": "Equation1086", "lhs": "Equation1102"}, + {"rhs": "Equation1110", "lhs": "Equation1111"}, + {"rhs": "Equation1113", "lhs": "Equation1114"}, + {"rhs": "Equation1112", "lhs": "Equation1115"}, + {"rhs": "Equation1113", "lhs": "Equation1116"}, + {"rhs": "Equation1113", "lhs": "Equation1117"}, + {"rhs": "Equation1120", "lhs": "Equation1121"}, + {"rhs": "Equation1123", "lhs": "Equation1124"}, + {"rhs": "Equation1122", "lhs": "Equation1125"}, + {"rhs": "Equation1123", "lhs": "Equation1126"}, + {"rhs": "Equation1123", "lhs": "Equation1127"}, + {"rhs": "Equation1119", "lhs": "Equation1129"}, + {"rhs": "Equation1120", "lhs": "Equation1130"}, + {"rhs": "Equation1120", "lhs": "Equation1131"}, + {"rhs": "Equation1122", "lhs": "Equation1133"}, + {"rhs": "Equation1123", "lhs": "Equation1134"}, + {"rhs": "Equation1123", 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"lhs": "Equation1984"}, + {"rhs": "Equation1935", "lhs": "Equation1985"}, + {"rhs": "Equation1931", "lhs": "Equation1992"}, + {"rhs": "Equation1932", "lhs": "Equation1993"}, + {"rhs": "Equation1932", "lhs": "Equation1994"}, + {"rhs": "Equation1934", "lhs": "Equation1996"}, + {"rhs": "Equation1935", "lhs": "Equation1997"}, + {"rhs": "Equation1935", "lhs": "Equation1998"}, + {"rhs": "Equation1934", "lhs": "Equation2000"}, + {"rhs": "Equation1935", "lhs": "Equation2001"}, + {"rhs": "Equation1935", "lhs": "Equation2002"}, + {"rhs": "Equation2038", "lhs": "Equation2039"}, + {"rhs": "Equation2041", "lhs": "Equation2042"}, + {"rhs": "Equation2044", "lhs": "Equation2045"}, + {"rhs": "Equation2043", "lhs": "Equation2046"}, + {"rhs": "Equation2044", "lhs": "Equation2047"}, + {"rhs": "Equation2044", "lhs": "Equation2048"}, + {"rhs": "Equation2051", "lhs": "Equation2052"}, + {"rhs": "Equation2054", "lhs": "Equation2055"}, + {"rhs": "Equation2053", "lhs": "Equation2056"}, + {"rhs": "Equation2054", "lhs": "Equation2057"}, + {"rhs": "Equation2054", "lhs": "Equation2058"}, + {"rhs": "Equation2061", "lhs": "Equation2062"}, + {"rhs": "Equation2064", "lhs": "Equation2065"}, + {"rhs": "Equation2063", "lhs": "Equation2066"}, + {"rhs": "Equation2064", "lhs": "Equation2067"}, + {"rhs": "Equation2064", "lhs": "Equation2068"}, + {"rhs": "Equation2060", "lhs": "Equation2070"}, + {"rhs": "Equation2061", "lhs": "Equation2071"}, + {"rhs": "Equation2061", "lhs": "Equation2072"}, + {"rhs": "Equation2063", "lhs": "Equation2074"}, + {"rhs": "Equation2064", "lhs": "Equation2075"}, + {"rhs": "Equation2064", "lhs": "Equation2076"}, + {"rhs": "Equation2063", "lhs": "Equation2078"}, + {"rhs": "Equation2064", "lhs": "Equation2079"}, + {"rhs": "Equation2064", "lhs": "Equation2080"}, + {"rhs": "Equation2088", "lhs": "Equation2089"}, + {"rhs": "Equation2091", "lhs": "Equation2092"}, + {"rhs": "Equation2090", "lhs": "Equation2093"}, + {"rhs": "Equation2091", "lhs": "Equation2094"}, + {"rhs": "Equation2091", "lhs": "Equation2095"}, + {"rhs": "Equation2098", "lhs": "Equation2099"}, + {"rhs": "Equation2101", "lhs": "Equation2102"}, + {"rhs": "Equation2100", "lhs": "Equation2103"}, + {"rhs": "Equation2101", "lhs": "Equation2104"}, + {"rhs": "Equation2101", "lhs": "Equation2105"}, + {"rhs": "Equation2097", "lhs": "Equation2107"}, + {"rhs": "Equation2098", "lhs": "Equation2108"}, + {"rhs": "Equation2098", "lhs": "Equation2109"}, + {"rhs": "Equation2100", "lhs": "Equation2111"}, + {"rhs": "Equation2101", "lhs": "Equation2112"}, + {"rhs": "Equation2101", "lhs": "Equation2113"}, + {"rhs": "Equation2100", "lhs": "Equation2115"}, + {"rhs": "Equation2101", "lhs": "Equation2116"}, + {"rhs": "Equation2101", "lhs": "Equation2117"}, + {"rhs": "Equation2125", "lhs": "Equation2126"}, + {"rhs": "Equation2128", "lhs": "Equation2129"}, + {"rhs": "Equation2127", "lhs": "Equation2130"}, + {"rhs": "Equation2128", "lhs": "Equation2131"}, + {"rhs": "Equation2128", "lhs": "Equation2132"}, + {"rhs": "Equation2135", "lhs": "Equation2136"}, + {"rhs": "Equation2138", "lhs": "Equation2139"}, + {"rhs": "Equation2137", "lhs": "Equation2140"}, + {"rhs": "Equation2138", "lhs": "Equation2141"}, + {"rhs": "Equation2138", "lhs": "Equation2142"}, + {"rhs": "Equation2134", "lhs": "Equation2144"}, + {"rhs": "Equation2135", "lhs": "Equation2145"}, + {"rhs": "Equation2135", "lhs": "Equation2146"}, + {"rhs": "Equation2137", "lhs": "Equation2148"}, + {"rhs": "Equation2138", "lhs": "Equation2149"}, + {"rhs": "Equation2138", "lhs": "Equation2150"}, + {"rhs": "Equation2137", "lhs": "Equation2152"}, + {"rhs": "Equation2138", "lhs": "Equation2153"}, + {"rhs": "Equation2138", "lhs": "Equation2154"}, + {"rhs": "Equation2124", "lhs": "Equation2161"}, + {"rhs": "Equation2125", "lhs": "Equation2162"}, + {"rhs": "Equation2125", "lhs": "Equation2163"}, + {"rhs": "Equation2127", "lhs": "Equation2165"}, + {"rhs": "Equation2128", "lhs": "Equation2166"}, + {"rhs": "Equation2128", "lhs": "Equation2167"}, + {"rhs": "Equation2127", "lhs": "Equation2169"}, + {"rhs": "Equation2128", "lhs": "Equation2170"}, + {"rhs": "Equation2128", "lhs": "Equation2171"}, + {"rhs": "Equation2134", "lhs": "Equation2178"}, + {"rhs": "Equation2135", "lhs": "Equation2179"}, + {"rhs": "Equation2135", "lhs": "Equation2180"}, + {"rhs": "Equation2137", "lhs": "Equation2182"}, + {"rhs": "Equation2138", "lhs": "Equation2183"}, + {"rhs": "Equation2138", "lhs": "Equation2184"}, + {"rhs": "Equation2137", "lhs": "Equation2186"}, + {"rhs": "Equation2138", "lhs": "Equation2187"}, + {"rhs": "Equation2138", "lhs": "Equation2188"}, + {"rhs": "Equation2134", "lhs": "Equation2195"}, + {"rhs": "Equation2135", "lhs": "Equation2196"}, + {"rhs": "Equation2135", "lhs": "Equation2197"}, + {"rhs": "Equation2137", "lhs": "Equation2199"}, + {"rhs": "Equation2138", "lhs": "Equation2200"}, + {"rhs": "Equation2138", "lhs": "Equation2201"}, + {"rhs": "Equation2137", "lhs": "Equation2203"}, + {"rhs": "Equation2138", "lhs": "Equation2204"}, + {"rhs": "Equation2138", "lhs": "Equation2205"}, + {"rhs": "Equation2241", "lhs": "Equation2242"}, + {"rhs": "Equation2244", "lhs": "Equation2245"}, + {"rhs": "Equation2247", "lhs": "Equation2248"}, + {"rhs": "Equation2246", "lhs": "Equation2249"}, + {"rhs": "Equation2247", "lhs": "Equation2250"}, + {"rhs": "Equation2247", "lhs": "Equation2251"}, + {"rhs": "Equation2254", "lhs": "Equation2255"}, + {"rhs": "Equation2257", "lhs": "Equation2258"}, + {"rhs": "Equation2256", "lhs": "Equation2259"}, + {"rhs": "Equation2257", "lhs": "Equation2260"}, + {"rhs": "Equation2257", "lhs": "Equation2261"}, + {"rhs": "Equation2264", "lhs": "Equation2265"}, + {"rhs": "Equation2267", "lhs": "Equation2268"}, + {"rhs": "Equation2266", "lhs": "Equation2269"}, + {"rhs": "Equation2267", "lhs": "Equation2270"}, + {"rhs": "Equation2267", "lhs": "Equation2271"}, + {"rhs": "Equation2263", "lhs": "Equation2273"}, + {"rhs": "Equation2264", "lhs": "Equation2274"}, + {"rhs": "Equation2264", "lhs": "Equation2275"}, + {"rhs": "Equation2266", "lhs": "Equation2277"}, + {"rhs": "Equation2267", "lhs": "Equation2278"}, + {"rhs": "Equation2267", "lhs": "Equation2279"}, + {"rhs": "Equation2266", "lhs": "Equation2281"}, + {"rhs": "Equation2267", "lhs": "Equation2282"}, + {"rhs": "Equation2267", "lhs": "Equation2283"}, + {"rhs": "Equation2291", "lhs": "Equation2292"}, + {"rhs": "Equation2294", "lhs": "Equation2295"}, + {"rhs": "Equation2293", "lhs": "Equation2296"}, + {"rhs": "Equation2294", "lhs": "Equation2297"}, + {"rhs": "Equation2294", "lhs": "Equation2298"}, + {"rhs": "Equation2301", "lhs": "Equation2302"}, + {"rhs": "Equation2304", "lhs": "Equation2305"}, + {"rhs": "Equation2303", "lhs": "Equation2306"}, + {"rhs": "Equation2304", "lhs": "Equation2307"}, + {"rhs": "Equation2304", "lhs": "Equation2308"}, + {"rhs": "Equation2300", "lhs": "Equation2310"}, + {"rhs": "Equation2301", "lhs": "Equation2311"}, + {"rhs": "Equation2301", "lhs": "Equation2312"}, + {"rhs": "Equation2303", "lhs": "Equation2314"}, + {"rhs": "Equation2304", "lhs": "Equation2315"}, + {"rhs": "Equation2304", "lhs": "Equation2316"}, + {"rhs": "Equation2303", "lhs": "Equation2318"}, + {"rhs": "Equation2304", "lhs": "Equation2319"}, + {"rhs": "Equation2304", "lhs": "Equation2320"}, + {"rhs": "Equation2328", "lhs": "Equation2329"}, + {"rhs": "Equation2331", "lhs": "Equation2332"}, + {"rhs": "Equation2330", "lhs": "Equation2333"}, + {"rhs": "Equation2331", "lhs": "Equation2334"}, + {"rhs": "Equation2331", "lhs": "Equation2335"}, + {"rhs": "Equation2338", "lhs": "Equation2339"}, + {"rhs": "Equation2341", "lhs": "Equation2342"}, + {"rhs": "Equation2340", "lhs": "Equation2343"}, + {"rhs": "Equation2341", "lhs": "Equation2344"}, + {"rhs": "Equation2341", "lhs": "Equation2345"}, + {"rhs": "Equation2337", "lhs": "Equation2347"}, + {"rhs": "Equation2338", "lhs": "Equation2348"}, + {"rhs": "Equation2338", "lhs": "Equation2349"}, + {"rhs": "Equation2340", "lhs": "Equation2351"}, + {"rhs": "Equation2341", "lhs": "Equation2352"}, + {"rhs": "Equation2341", "lhs": "Equation2353"}, + {"rhs": "Equation2340", "lhs": "Equation2355"}, + {"rhs": "Equation2341", "lhs": "Equation2356"}, + {"rhs": "Equation2341", "lhs": "Equation2357"}, + {"rhs": "Equation2327", "lhs": "Equation2364"}, + {"rhs": "Equation2328", "lhs": "Equation2365"}, + {"rhs": "Equation2328", "lhs": "Equation2366"}, + {"rhs": "Equation2330", "lhs": "Equation2368"}, + {"rhs": "Equation2331", "lhs": "Equation2369"}, + {"rhs": "Equation2331", "lhs": "Equation2370"}, + {"rhs": "Equation2330", "lhs": "Equation2372"}, + {"rhs": "Equation2331", "lhs": "Equation2373"}, + {"rhs": "Equation2331", "lhs": "Equation2374"}, + {"rhs": "Equation2337", "lhs": "Equation2381"}, + {"rhs": "Equation2338", "lhs": "Equation2382"}, + {"rhs": "Equation2338", "lhs": "Equation2383"}, + {"rhs": "Equation2340", "lhs": "Equation2385"}, + {"rhs": "Equation2341", "lhs": "Equation2386"}, + {"rhs": "Equation2341", "lhs": "Equation2387"}, + {"rhs": "Equation2340", "lhs": "Equation2389"}, + {"rhs": "Equation2341", "lhs": "Equation2390"}, + {"rhs": "Equation2341", "lhs": "Equation2391"}, + {"rhs": "Equation2337", "lhs": "Equation2398"}, + {"rhs": "Equation2338", "lhs": "Equation2399"}, + {"rhs": "Equation2338", "lhs": "Equation2400"}, + {"rhs": "Equation2340", "lhs": "Equation2402"}, + {"rhs": "Equation2341", "lhs": "Equation2403"}, + {"rhs": "Equation2341", "lhs": "Equation2404"}, + {"rhs": "Equation2340", "lhs": "Equation2406"}, + {"rhs": "Equation2341", "lhs": "Equation2407"}, + {"rhs": "Equation2341", "lhs": "Equation2408"}, + {"rhs": "Equation2444", "lhs": "Equation2445"}, + {"rhs": "Equation2447", "lhs": "Equation2448"}, + {"rhs": "Equation2450", "lhs": "Equation2451"}, + {"rhs": "Equation2449", "lhs": "Equation2452"}, + {"rhs": "Equation2450", "lhs": "Equation2453"}, + {"rhs": "Equation2450", "lhs": "Equation2454"}, + {"rhs": "Equation2457", "lhs": "Equation2458"}, + {"rhs": "Equation2460", "lhs": "Equation2461"}, + {"rhs": "Equation2459", "lhs": "Equation2462"}, + {"rhs": "Equation2460", "lhs": "Equation2463"}, + {"rhs": "Equation2460", "lhs": "Equation2464"}, + {"rhs": "Equation2467", "lhs": "Equation2468"}, + {"rhs": "Equation2470", "lhs": "Equation2471"}, + {"rhs": "Equation2469", "lhs": "Equation2472"}, + {"rhs": "Equation2470", "lhs": "Equation2473"}, + {"rhs": "Equation2470", "lhs": "Equation2474"}, + {"rhs": "Equation2466", "lhs": "Equation2476"}, + {"rhs": "Equation2467", "lhs": "Equation2477"}, + {"rhs": "Equation2467", "lhs": "Equation2478"}, + {"rhs": "Equation2469", "lhs": "Equation2480"}, + {"rhs": "Equation2470", "lhs": "Equation2481"}, + {"rhs": "Equation2470", "lhs": "Equation2482"}, + {"rhs": "Equation2469", "lhs": "Equation2484"}, + {"rhs": "Equation2470", "lhs": "Equation2485"}, + {"rhs": "Equation2470", "lhs": "Equation2486"}, + {"rhs": "Equation2494", "lhs": "Equation2495"}, + {"rhs": "Equation2497", "lhs": "Equation2498"}, + {"rhs": "Equation2496", "lhs": "Equation2499"}, + {"rhs": "Equation2497", "lhs": "Equation2500"}, + {"rhs": "Equation2497", "lhs": "Equation2501"}, + {"rhs": "Equation2504", "lhs": "Equation2505"}, + {"rhs": "Equation2507", "lhs": "Equation2508"}, + {"rhs": "Equation2506", "lhs": "Equation2509"}, + {"rhs": "Equation2507", "lhs": "Equation2510"}, + {"rhs": "Equation2507", "lhs": "Equation2511"}, + {"rhs": "Equation2503", "lhs": "Equation2513"}, + {"rhs": "Equation2504", "lhs": "Equation2514"}, + {"rhs": "Equation2504", "lhs": "Equation2515"}, + {"rhs": "Equation2506", "lhs": "Equation2517"}, + {"rhs": "Equation2507", "lhs": "Equation2518"}, + {"rhs": "Equation2507", "lhs": "Equation2519"}, + {"rhs": "Equation2506", "lhs": "Equation2521"}, + {"rhs": "Equation2507", "lhs": "Equation2522"}, + {"rhs": "Equation2507", "lhs": "Equation2523"}, + {"rhs": "Equation2531", "lhs": "Equation2532"}, + {"rhs": "Equation2534", "lhs": "Equation2535"}, + {"rhs": "Equation2533", "lhs": "Equation2536"}, + {"rhs": "Equation2534", "lhs": "Equation2537"}, + {"rhs": "Equation2534", "lhs": "Equation2538"}, + {"rhs": "Equation2541", "lhs": "Equation2542"}, + {"rhs": "Equation2544", "lhs": "Equation2545"}, + {"rhs": "Equation2543", "lhs": "Equation2546"}, + {"rhs": "Equation2544", "lhs": "Equation2547"}, + {"rhs": "Equation2544", "lhs": "Equation2548"}, + {"rhs": "Equation2540", "lhs": "Equation2550"}, + {"rhs": "Equation2541", "lhs": "Equation2551"}, + {"rhs": "Equation2541", "lhs": "Equation2552"}, + {"rhs": "Equation2543", "lhs": "Equation2554"}, + {"rhs": "Equation2544", "lhs": "Equation2555"}, + {"rhs": "Equation2544", "lhs": "Equation2556"}, + {"rhs": "Equation2543", "lhs": "Equation2558"}, + {"rhs": "Equation2544", "lhs": "Equation2559"}, + {"rhs": "Equation2544", "lhs": "Equation2560"}, + {"rhs": "Equation2530", "lhs": "Equation2567"}, + {"rhs": "Equation2531", "lhs": "Equation2568"}, + {"rhs": "Equation2531", "lhs": "Equation2569"}, + {"rhs": "Equation2533", "lhs": "Equation2571"}, + {"rhs": "Equation2534", "lhs": "Equation2572"}, + {"rhs": "Equation2534", "lhs": "Equation2573"}, + {"rhs": "Equation2533", "lhs": "Equation2575"}, + {"rhs": "Equation2534", "lhs": "Equation2576"}, + {"rhs": "Equation2534", "lhs": "Equation2577"}, + {"rhs": "Equation2540", "lhs": "Equation2584"}, + {"rhs": "Equation2541", "lhs": "Equation2585"}, + {"rhs": "Equation2541", "lhs": "Equation2586"}, + {"rhs": "Equation2543", "lhs": "Equation2588"}, + {"rhs": "Equation2544", "lhs": "Equation2589"}, + {"rhs": "Equation2544", "lhs": "Equation2590"}, + {"rhs": "Equation2543", "lhs": "Equation2592"}, + {"rhs": "Equation2544", "lhs": "Equation2593"}, + {"rhs": "Equation2544", "lhs": "Equation2594"}, + {"rhs": "Equation2540", "lhs": "Equation2601"}, + {"rhs": "Equation2541", "lhs": "Equation2602"}, + {"rhs": "Equation2541", "lhs": "Equation2603"}, + {"rhs": "Equation2543", "lhs": "Equation2605"}, + {"rhs": "Equation2544", "lhs": "Equation2606"}, + {"rhs": "Equation2544", "lhs": "Equation2607"}, + {"rhs": "Equation2543", "lhs": "Equation2609"}, + {"rhs": "Equation2544", "lhs": "Equation2610"}, + {"rhs": "Equation2544", "lhs": "Equation2611"}, + {"rhs": "Equation2647", "lhs": "Equation2648"}, + {"rhs": "Equation2650", "lhs": "Equation2651"}, + {"rhs": "Equation2653", "lhs": "Equation2654"}, + {"rhs": "Equation2652", "lhs": "Equation2655"}, + {"rhs": "Equation2653", "lhs": "Equation2656"}, + {"rhs": "Equation2653", "lhs": "Equation2657"}, + {"rhs": "Equation2660", "lhs": "Equation2661"}, + {"rhs": "Equation2663", "lhs": "Equation2664"}, + {"rhs": "Equation2662", "lhs": "Equation2665"}, + {"rhs": "Equation2663", "lhs": "Equation2666"}, + {"rhs": "Equation2663", "lhs": "Equation2667"}, + {"rhs": "Equation2670", "lhs": "Equation2671"}, + {"rhs": "Equation2673", "lhs": "Equation2674"}, + {"rhs": "Equation2672", "lhs": "Equation2675"}, + {"rhs": "Equation2673", "lhs": "Equation2676"}, + {"rhs": "Equation2673", "lhs": "Equation2677"}, + {"rhs": "Equation2669", "lhs": "Equation2679"}, + {"rhs": "Equation2670", "lhs": "Equation2680"}, + {"rhs": "Equation2670", "lhs": "Equation2681"}, + {"rhs": "Equation2672", "lhs": "Equation2683"}, + {"rhs": "Equation2673", "lhs": "Equation2684"}, + {"rhs": "Equation2673", "lhs": "Equation2685"}, + {"rhs": "Equation2672", "lhs": "Equation2687"}, + {"rhs": "Equation2673", "lhs": "Equation2688"}, + {"rhs": "Equation2673", "lhs": "Equation2689"}, + {"rhs": "Equation2697", "lhs": "Equation2698"}, + {"rhs": "Equation2700", "lhs": "Equation2701"}, + {"rhs": "Equation2699", "lhs": "Equation2702"}, + {"rhs": "Equation2700", "lhs": "Equation2703"}, + {"rhs": "Equation2700", "lhs": "Equation2704"}, + {"rhs": "Equation2707", "lhs": "Equation2708"}, + {"rhs": "Equation2710", "lhs": "Equation2711"}, + {"rhs": "Equation2709", "lhs": "Equation2712"}, + {"rhs": "Equation2710", "lhs": "Equation2713"}, + {"rhs": "Equation2710", "lhs": "Equation2714"}, + {"rhs": "Equation2706", "lhs": "Equation2716"}, + {"rhs": "Equation2707", "lhs": "Equation2717"}, + {"rhs": "Equation2707", "lhs": "Equation2718"}, + {"rhs": "Equation2709", "lhs": "Equation2720"}, + {"rhs": "Equation2710", "lhs": "Equation2721"}, + {"rhs": "Equation2710", "lhs": "Equation2722"}, + {"rhs": "Equation2709", "lhs": "Equation2724"}, + {"rhs": "Equation2710", "lhs": "Equation2725"}, + {"rhs": "Equation2710", "lhs": "Equation2726"}, + {"rhs": "Equation2734", "lhs": "Equation2735"}, + {"rhs": "Equation2737", "lhs": "Equation2738"}, + {"rhs": "Equation2736", "lhs": "Equation2739"}, + {"rhs": "Equation2737", "lhs": "Equation2740"}, + {"rhs": "Equation2737", "lhs": "Equation2741"}, + {"rhs": "Equation2744", "lhs": "Equation2745"}, + {"rhs": "Equation2747", "lhs": "Equation2748"}, + {"rhs": "Equation2746", "lhs": "Equation2749"}, + {"rhs": "Equation2747", "lhs": "Equation2750"}, + {"rhs": "Equation2747", "lhs": "Equation2751"}, + {"rhs": "Equation2743", "lhs": "Equation2753"}, + {"rhs": "Equation2744", "lhs": "Equation2754"}, + {"rhs": "Equation2744", "lhs": "Equation2755"}, + {"rhs": "Equation2746", "lhs": "Equation2757"}, + {"rhs": "Equation2747", "lhs": "Equation2758"}, + {"rhs": "Equation2747", "lhs": "Equation2759"}, + {"rhs": "Equation2746", "lhs": "Equation2761"}, + {"rhs": "Equation2747", "lhs": "Equation2762"}, + {"rhs": "Equation2747", "lhs": "Equation2763"}, + {"rhs": "Equation2733", "lhs": "Equation2770"}, + {"rhs": "Equation2734", "lhs": "Equation2771"}, + {"rhs": "Equation2734", "lhs": "Equation2772"}, + {"rhs": "Equation2736", "lhs": "Equation2774"}, + {"rhs": "Equation2737", "lhs": "Equation2775"}, + {"rhs": "Equation2737", "lhs": "Equation2776"}, + {"rhs": "Equation2736", "lhs": "Equation2778"}, + {"rhs": "Equation2737", "lhs": "Equation2779"}, + {"rhs": "Equation2737", "lhs": "Equation2780"}, + {"rhs": "Equation2743", "lhs": "Equation2787"}, + {"rhs": "Equation2744", "lhs": "Equation2788"}, + {"rhs": "Equation2744", "lhs": "Equation2789"}, + {"rhs": "Equation2746", "lhs": "Equation2791"}, + {"rhs": "Equation2747", "lhs": "Equation2792"}, + {"rhs": "Equation2747", "lhs": "Equation2793"}, + {"rhs": "Equation2746", "lhs": "Equation2795"}, + {"rhs": "Equation2747", "lhs": "Equation2796"}, + {"rhs": "Equation2747", "lhs": "Equation2797"}, + {"rhs": "Equation2743", "lhs": "Equation2804"}, + {"rhs": "Equation2744", "lhs": "Equation2805"}, + {"rhs": "Equation2744", "lhs": "Equation2806"}, + {"rhs": "Equation2746", "lhs": "Equation2808"}, + {"rhs": "Equation2747", "lhs": "Equation2809"}, + {"rhs": "Equation2747", "lhs": "Equation2810"}, + {"rhs": "Equation2746", "lhs": "Equation2812"}, + {"rhs": "Equation2747", "lhs": "Equation2813"}, + {"rhs": "Equation2747", "lhs": "Equation2814"}, + {"rhs": "Equation2850", "lhs": "Equation2851"}, + {"rhs": "Equation2853", "lhs": "Equation2854"}, + {"rhs": "Equation2856", "lhs": "Equation2857"}, + {"rhs": "Equation2855", "lhs": "Equation2858"}, + {"rhs": "Equation2856", "lhs": "Equation2859"}, + {"rhs": "Equation2856", "lhs": "Equation2860"}, + {"rhs": "Equation2863", "lhs": "Equation2864"}, + {"rhs": "Equation2866", "lhs": "Equation2867"}, + {"rhs": "Equation2865", "lhs": "Equation2868"}, + {"rhs": "Equation2866", "lhs": "Equation2869"}, + {"rhs": "Equation2866", "lhs": "Equation2870"}, + {"rhs": "Equation2873", "lhs": "Equation2874"}, + {"rhs": "Equation2876", "lhs": "Equation2877"}, + {"rhs": "Equation2875", "lhs": "Equation2878"}, + {"rhs": "Equation2876", "lhs": "Equation2879"}, + {"rhs": "Equation2876", "lhs": "Equation2880"}, + {"rhs": "Equation2872", "lhs": "Equation2882"}, + {"rhs": "Equation2873", "lhs": "Equation2883"}, + {"rhs": "Equation2873", "lhs": "Equation2884"}, + {"rhs": "Equation2875", "lhs": "Equation2886"}, + {"rhs": "Equation2876", "lhs": "Equation2887"}, + {"rhs": "Equation2876", "lhs": "Equation2888"}, + {"rhs": "Equation2875", "lhs": "Equation2890"}, + {"rhs": "Equation2876", "lhs": "Equation2891"}, + {"rhs": "Equation2876", "lhs": "Equation2892"}, + {"rhs": "Equation2900", "lhs": "Equation2901"}, + {"rhs": "Equation2903", "lhs": "Equation2904"}, + {"rhs": "Equation2902", "lhs": "Equation2905"}, + {"rhs": "Equation2903", "lhs": "Equation2906"}, + {"rhs": "Equation2903", "lhs": "Equation2907"}, + {"rhs": "Equation2910", "lhs": "Equation2911"}, + {"rhs": "Equation2913", "lhs": "Equation2914"}, + {"rhs": "Equation2912", "lhs": "Equation2915"}, + {"rhs": "Equation2913", "lhs": "Equation2916"}, + {"rhs": "Equation2913", "lhs": "Equation2917"}, + {"rhs": "Equation2909", "lhs": "Equation2919"}, + {"rhs": "Equation2910", "lhs": "Equation2920"}, + {"rhs": "Equation2910", "lhs": "Equation2921"}, + {"rhs": "Equation2912", "lhs": "Equation2923"}, + {"rhs": "Equation2913", "lhs": "Equation2924"}, + {"rhs": "Equation2913", "lhs": "Equation2925"}, + {"rhs": "Equation2912", "lhs": "Equation2927"}, + {"rhs": "Equation2913", "lhs": "Equation2928"}, + {"rhs": "Equation2913", "lhs": "Equation2929"}, + {"rhs": "Equation2937", "lhs": "Equation2938"}, + {"rhs": "Equation2940", "lhs": "Equation2941"}, + {"rhs": "Equation2939", "lhs": "Equation2942"}, + {"rhs": "Equation2940", "lhs": "Equation2943"}, + {"rhs": "Equation2940", "lhs": "Equation2944"}, + {"rhs": "Equation2947", 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"Equation46", "lhs": "Equation3849"}, + {"rhs": "Equation46", "lhs": "Equation3850"}, + {"rhs": "Equation46", "lhs": "Equation3853"}, + {"rhs": "Equation46", "lhs": "Equation3854"}, + {"rhs": "Equation46", "lhs": "Equation3855"}, + {"rhs": "Equation46", "lhs": "Equation3858"}, + {"rhs": "Equation46", "lhs": "Equation3859"}, + {"rhs": "Equation46", "lhs": "Equation3860"}, + {"rhs": "Equation46", "lhs": "Equation3861"}, + {"rhs": "Equation46", "lhs": "Equation4032"}, + {"rhs": "Equation46", "lhs": "Equation4033"}, + {"rhs": "Equation46", "lhs": "Equation4036"}, + {"rhs": "Equation46", "lhs": "Equation4037"}, + {"rhs": "Equation46", "lhs": "Equation4038"}, + {"rhs": "Equation46", "lhs": "Equation4051"}, + {"rhs": "Equation46", "lhs": "Equation4052"}, + {"rhs": "Equation46", "lhs": "Equation4053"}, + {"rhs": "Equation46", "lhs": "Equation4056"}, + {"rhs": "Equation46", "lhs": "Equation4057"}, + {"rhs": "Equation46", "lhs": "Equation4058"}, + {"rhs": "Equation46", "lhs": "Equation4061"}, + {"rhs": "Equation46", "lhs": "Equation4062"}, + {"rhs": "Equation46", "lhs": "Equation4063"}, + {"rhs": "Equation46", "lhs": "Equation4064"}, + {"rhs": "Equation46", "lhs": "Equation4235"}, + {"rhs": "Equation46", "lhs": "Equation4236"}, + {"rhs": "Equation46", "lhs": "Equation4239"}, + {"rhs": "Equation46", "lhs": "Equation4240"}, + {"rhs": "Equation46", "lhs": "Equation4241"}, + {"rhs": "Equation46", "lhs": "Equation4254"}, + {"rhs": "Equation46", "lhs": "Equation4255"}, + {"rhs": "Equation46", "lhs": "Equation4256"}, + {"rhs": "Equation46", "lhs": "Equation4259"}, + {"rhs": "Equation46", "lhs": "Equation4260"}, + {"rhs": "Equation46", "lhs": "Equation4261"}, + {"rhs": "Equation46", "lhs": "Equation4264"}, + {"rhs": "Equation46", "lhs": "Equation4265"}, + {"rhs": "Equation46", "lhs": "Equation4266"}, + {"rhs": "Equation46", "lhs": "Equation4267"}, + {"rhs": "Equation2", "lhs": "Equation6"}, + {"rhs": "Equation2", "lhs": "Equation7"}, + {"rhs": "Equation2", "lhs": "Equation17"}, + {"rhs": "Equation2", "lhs": "Equation18"}, + {"rhs": "Equation2", "lhs": "Equation20"}, + {"rhs": "Equation2", "lhs": "Equation21"}, + {"rhs": "Equation2", "lhs": "Equation22"}, + {"rhs": "Equation2", "lhs": "Equation32"}, + {"rhs": "Equation2", "lhs": "Equation33"}, + {"rhs": "Equation2", "lhs": "Equation35"}, + {"rhs": "Equation2", "lhs": "Equation36"}, + {"rhs": "Equation2", "lhs": "Equation37"}, + {"rhs": "Equation2", "lhs": "Equation76"}, + {"rhs": "Equation2", "lhs": "Equation77"}, + {"rhs": "Equation2", "lhs": "Equation79"}, + {"rhs": "Equation2", "lhs": "Equation80"}, + {"rhs": "Equation2", "lhs": "Equation81"}, + {"rhs": "Equation2", "lhs": "Equation87"}, + {"rhs": "Equation2", "lhs": "Equation88"}, + {"rhs": "Equation2", "lhs": "Equation89"}, + {"rhs": "Equation2", "lhs": "Equation91"}, + {"rhs": "Equation2", "lhs": "Equation92"}, + {"rhs": "Equation2", "lhs": "Equation93"}, + {"rhs": "Equation2", "lhs": "Equation95"}, + {"rhs": "Equation2", "lhs": "Equation96"}, + {"rhs": 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"Equation2", "lhs": "Equation518"}, + {"rhs": "Equation2", "lhs": "Equation519"}, + {"rhs": "Equation2", "lhs": "Equation525"}, + {"rhs": "Equation2", "lhs": "Equation526"}, + {"rhs": "Equation2", "lhs": "Equation527"}, + {"rhs": "Equation2", "lhs": "Equation529"}, + {"rhs": "Equation2", "lhs": "Equation530"}, + {"rhs": "Equation2", "lhs": "Equation531"}, + {"rhs": "Equation2", "lhs": "Equation533"}, + {"rhs": "Equation2", "lhs": "Equation534"}, + {"rhs": "Equation2", "lhs": "Equation535"}, + {"rhs": "Equation2", "lhs": "Equation536"}, + {"rhs": "Equation2", "lhs": "Equation559"}, + {"rhs": "Equation2", "lhs": "Equation560"}, + {"rhs": "Equation2", "lhs": "Equation561"}, + {"rhs": "Equation2", "lhs": "Equation563"}, + {"rhs": "Equation2", "lhs": "Equation564"}, + {"rhs": "Equation2", "lhs": "Equation565"}, + {"rhs": "Equation2", "lhs": "Equation567"}, + {"rhs": "Equation2", "lhs": "Equation568"}, + {"rhs": "Equation2", "lhs": "Equation569"}, + {"rhs": "Equation2", "lhs": "Equation570"}, + {"rhs": "Equation2", "lhs": "Equation576"}, + {"rhs": "Equation2", "lhs": "Equation577"}, + {"rhs": "Equation2", "lhs": "Equation578"}, + {"rhs": "Equation2", "lhs": "Equation580"}, + {"rhs": "Equation2", "lhs": "Equation581"}, + {"rhs": "Equation2", "lhs": "Equation582"}, + {"rhs": "Equation2", "lhs": "Equation584"}, + {"rhs": "Equation2", "lhs": "Equation585"}, + {"rhs": "Equation2", "lhs": "Equation586"}, + {"rhs": "Equation2", "lhs": "Equation587"}, + {"rhs": "Equation2", "lhs": "Equation594"}, + {"rhs": "Equation2", "lhs": "Equation595"}, + {"rhs": "Equation2", "lhs": "Equation596"}, + {"rhs": "Equation2", "lhs": "Equation597"}, + {"rhs": "Equation2", "lhs": "Equation599"}, + {"rhs": "Equation2", "lhs": "Equation600"}, + {"rhs": "Equation2", "lhs": "Equation601"}, + {"rhs": "Equation2", "lhs": "Equation602"}, + {"rhs": "Equation2", "lhs": "Equation604"}, + {"rhs": "Equation2", "lhs": "Equation605"}, + {"rhs": "Equation2", "lhs": "Equation606"}, + {"rhs": 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"Equation11"}, + {"rhs": "Equation858", "lhs": "Equation11"}, + {"rhs": "Equation101", "lhs": "Equation110"}, + {"rhs": "Equation104", "lhs": "Equation110"}, + {"rhs": "Equation1067", "lhs": "Equation110"}, + {"rhs": "Equation107", "lhs": "Equation110"}, + {"rhs": "Equation1270", "lhs": "Equation110"}, + {"rhs": "Equation1028", "lhs": "Equation1100"}, + {"rhs": "Equation1072", "lhs": "Equation1100"}, + {"rhs": "Equation1085", "lhs": "Equation1100"}, + {"rhs": "Equation1028", "lhs": "Equation1101"}, + {"rhs": "Equation1073", "lhs": "Equation1101"}, + {"rhs": "Equation1086", "lhs": "Equation1101"}, + {"rhs": "Equation1029", "lhs": "Equation1102"}, + {"rhs": "Equation1072", "lhs": "Equation1102"}, + {"rhs": "Equation1086", "lhs": "Equation1102"}, + {"rhs": "Equation1030", "lhs": "Equation1103"}, + {"rhs": "Equation1074", "lhs": "Equation1103"}, + {"rhs": "Equation1087", "lhs": "Equation1103"}, + {"rhs": "Equation1100", "lhs": "Equation1103"}, + {"rhs": "Equation1101", "lhs": 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"Equation1107"}, + {"rhs": "Equation1080", "lhs": "Equation1107"}, + {"rhs": "Equation1090", "lhs": "Equation1107"}, + {"rhs": "Equation1092", "lhs": "Equation1107"}, + {"rhs": "Equation1097", "lhs": "Equation1107"}, + {"rhs": "Equation1102", "lhs": "Equation1107"}, + {"rhs": "Equation1034", "lhs": "Equation1108"}, + {"rhs": "Equation1081", "lhs": "Equation1108"}, + {"rhs": "Equation1091", "lhs": "Equation1108"}, + {"rhs": "Equation1095", "lhs": "Equation1108"}, + {"rhs": "Equation1099", "lhs": "Equation1108"}, + {"rhs": "Equation1103", "lhs": "Equation1108"}, + {"rhs": "Equation1104", "lhs": "Equation1108"}, + {"rhs": "Equation1105", "lhs": "Equation1108"}, + {"rhs": "Equation1106", "lhs": "Equation1108"}, + {"rhs": "Equation1107", "lhs": "Equation1108"}, + {"rhs": "Equation1020", "lhs": "Equation1109"}, + {"rhs": "Equation101", "lhs": "Equation111"}, + {"rhs": "Equation105", "lhs": "Equation111"}, + {"rhs": "Equation1068", "lhs": "Equation111"}, + {"rhs": "Equation108", "lhs": "Equation111"}, + {"rhs": "Equation1020", "lhs": "Equation1110"}, + {"rhs": "Equation1021", "lhs": "Equation1111"}, + {"rhs": "Equation1109", "lhs": "Equation1111"}, + {"rhs": "Equation1110", "lhs": "Equation1111"}, + {"rhs": "Equation1020", "lhs": "Equation1112"}, + {"rhs": "Equation1020", "lhs": "Equation1113"}, + {"rhs": "Equation1021", "lhs": "Equation1114"}, + {"rhs": "Equation1112", "lhs": "Equation1114"}, + {"rhs": "Equation1113", "lhs": "Equation1114"}, + {"rhs": "Equation1022", "lhs": "Equation1115"}, + {"rhs": "Equation1109", "lhs": "Equation1115"}, + {"rhs": "Equation1112", "lhs": "Equation1115"}, + {"rhs": "Equation1022", "lhs": "Equation1116"}, + {"rhs": "Equation1110", "lhs": "Equation1116"}, + {"rhs": "Equation1113", "lhs": "Equation1116"}, + {"rhs": "Equation1023", "lhs": "Equation1117"}, + {"rhs": "Equation1109", "lhs": "Equation1117"}, + {"rhs": "Equation1113", "lhs": "Equation1117"}, + {"rhs": "Equation1024", "lhs": "Equation1118"}, + {"rhs": "Equation1111", "lhs": "Equation1118"}, + {"rhs": "Equation1114", "lhs": "Equation1118"}, + {"rhs": "Equation1115", "lhs": "Equation1118"}, + {"rhs": "Equation1116", "lhs": "Equation1118"}, + {"rhs": "Equation1117", "lhs": "Equation1118"}, + {"rhs": "Equation1020", "lhs": "Equation1119"}, + {"rhs": "Equation102", "lhs": "Equation112"}, + {"rhs": "Equation104", "lhs": "Equation112"}, + {"rhs": "Equation108", "lhs": "Equation112"}, + {"rhs": "Equation1273", "lhs": "Equation112"}, + {"rhs": "Equation1020", "lhs": "Equation1120"}, + {"rhs": "Equation1021", "lhs": "Equation1121"}, + {"rhs": "Equation1119", "lhs": "Equation1121"}, + {"rhs": "Equation1120", "lhs": "Equation1121"}, + {"rhs": "Equation1020", "lhs": "Equation1122"}, + {"rhs": "Equation1123", "lhs": "Equation1124"}, + {"rhs": "Equation1022", "lhs": "Equation1125"}, + {"rhs": "Equation1119", "lhs": "Equation1125"}, + {"rhs": "Equation1122", "lhs": "Equation1125"}, + {"rhs": "Equation1127", "lhs": "Equation1128"}, + {"rhs": "Equation1025", "lhs": "Equation1129"}, + {"rhs": "Equation1109", "lhs": "Equation1129"}, + {"rhs": "Equation1119", "lhs": "Equation1129"}, + {"rhs": "Equation103", "lhs": "Equation113"}, + {"rhs": "Equation106", "lhs": "Equation113"}, + {"rhs": "Equation1071", "lhs": "Equation113"}, + {"rhs": "Equation109", "lhs": "Equation113"}, + {"rhs": "Equation110", "lhs": "Equation113"}, + {"rhs": "Equation111", "lhs": "Equation113"}, + {"rhs": "Equation112", "lhs": "Equation113"}, + {"rhs": "Equation1274", "lhs": "Equation113"}, + {"rhs": "Equation868", "lhs": "Equation113"}, + {"rhs": "Equation1025", "lhs": "Equation1130"}, + {"rhs": "Equation1110", "lhs": "Equation1130"}, + {"rhs": "Equation1120", "lhs": "Equation1130"}, + {"rhs": "Equation1026", "lhs": "Equation1131"}, + {"rhs": "Equation1109", "lhs": "Equation1131"}, + {"rhs": "Equation1120", "lhs": "Equation1131"}, + {"rhs": "Equation1027", "lhs": "Equation1132"}, + {"rhs": "Equation1111", "lhs": "Equation1132"}, + {"rhs": "Equation1121", "lhs": "Equation1132"}, + {"rhs": "Equation1129", "lhs": "Equation1132"}, + {"rhs": "Equation1130", "lhs": "Equation1132"}, + {"rhs": "Equation1131", "lhs": "Equation1132"}, + {"rhs": "Equation1025", "lhs": "Equation1133"}, + {"rhs": "Equation1112", "lhs": "Equation1133"}, + {"rhs": "Equation1122", "lhs": "Equation1133"}, + {"rhs": "Equation1135", "lhs": "Equation1136"}, + {"rhs": "Equation1028", "lhs": "Equation1137"}, + {"rhs": "Equation1109", "lhs": "Equation1137"}, + {"rhs": "Equation1122", "lhs": "Equation1137"}, + {"rhs": "Equation1755", "lhs": "Equation114"}, + {"rhs": "Equation99", "lhs": "Equation114"}, + {"rhs": "Equation1139", "lhs": "Equation1140"}, + {"rhs": "Equation1031", "lhs": "Equation1141"}, + {"rhs": "Equation1115", "lhs": "Equation1141"}, + {"rhs": "Equation1125", "lhs": "Equation1141"}, + {"rhs": "Equation1129", "lhs": "Equation1141"}, + {"rhs": "Equation1133", "lhs": "Equation1141"}, + {"rhs": "Equation1137", "lhs": "Equation1141"}, + {"rhs": "Equation1144", "lhs": "Equation1145"}, + {"rhs": "Equation1035", "lhs": "Equation1146"}, + {"rhs": "Equation1072", "lhs": "Equation1146"}, + {"rhs": "Equation1109", "lhs": "Equation1146"}, + {"rhs": "Equation1035", "lhs": "Equation1147"}, + {"rhs": "Equation1073", "lhs": "Equation1147"}, + {"rhs": "Equation1110", "lhs": "Equation1147"}, + {"rhs": "Equation1036", "lhs": "Equation1148"}, + {"rhs": "Equation1072", "lhs": "Equation1148"}, + {"rhs": "Equation1110", "lhs": "Equation1148"}, + {"rhs": "Equation1037", "lhs": "Equation1149"}, + {"rhs": "Equation1074", "lhs": "Equation1149"}, + {"rhs": "Equation1111", "lhs": "Equation1149"}, + {"rhs": "Equation1146", "lhs": "Equation1149"}, + {"rhs": "Equation1147", "lhs": "Equation1149"}, + {"rhs": "Equation1148", "lhs": "Equation1149"}, + {"rhs": "Equation99", "lhs": "Equation115"}, + {"rhs": "Equation1035", "lhs": "Equation1150"}, + {"rhs": "Equation1075", "lhs": "Equation1150"}, + {"rhs": "Equation1112", "lhs": "Equation1150"}, + {"rhs": "Equation1035", "lhs": "Equation1151"}, + {"rhs": "Equation1076", "lhs": "Equation1151"}, + {"rhs": "Equation1113", "lhs": "Equation1151"}, + {"rhs": "Equation1036", "lhs": "Equation1152"}, + {"rhs": "Equation1075", "lhs": "Equation1152"}, + {"rhs": "Equation1113", "lhs": "Equation1152"}, + {"rhs": "Equation1037", "lhs": "Equation1153"}, + {"rhs": "Equation1077", "lhs": "Equation1153"}, + {"rhs": "Equation1114", "lhs": "Equation1153"}, + {"rhs": "Equation1150", "lhs": "Equation1153"}, + {"rhs": "Equation1151", "lhs": "Equation1153"}, + {"rhs": "Equation1152", "lhs": "Equation1153"}, + {"rhs": "Equation1038", "lhs": "Equation1154"}, + {"rhs": "Equation1072", "lhs": "Equation1154"}, + {"rhs": "Equation1112", "lhs": "Equation1154"}, + {"rhs": "Equation1038", "lhs": "Equation1155"}, + {"rhs": "Equation1073", "lhs": "Equation1155"}, + {"rhs": "Equation1113", "lhs": "Equation1155"}, + {"rhs": "Equation1039", "lhs": "Equation1156"}, + {"rhs": "Equation1072", "lhs": "Equation1156"}, + {"rhs": "Equation1113", "lhs": "Equation1156"}, + {"rhs": "Equation1040", "lhs": "Equation1157"}, + {"rhs": "Equation1074", "lhs": "Equation1157"}, + {"rhs": "Equation1114", "lhs": "Equation1157"}, + {"rhs": "Equation1154", "lhs": "Equation1157"}, + {"rhs": "Equation1155", "lhs": "Equation1157"}, + {"rhs": "Equation1156", "lhs": "Equation1157"}, + {"rhs": "Equation1041", "lhs": "Equation1158"}, + {"rhs": "Equation1078", "lhs": "Equation1158"}, + {"rhs": "Equation1115", "lhs": "Equation1158"}, + {"rhs": "Equation1146", "lhs": "Equation1158"}, + {"rhs": "Equation1150", "lhs": "Equation1158"}, + {"rhs": "Equation1154", "lhs": "Equation1158"}, + {"rhs": "Equation1041", "lhs": "Equation1159"}, + {"rhs": "Equation1079", "lhs": "Equation1159"}, + {"rhs": "Equation1116", "lhs": "Equation1159"}, + {"rhs": "Equation1147", "lhs": "Equation1159"}, + {"rhs": "Equation1151", "lhs": "Equation1159"}, + {"rhs": "Equation1155", "lhs": "Equation1159"}, + {"rhs": "Equation100", "lhs": "Equation116"}, + {"rhs": "Equation114", "lhs": "Equation116"}, + {"rhs": "Equation115", "lhs": "Equation116"}, + {"rhs": "Equation1758", "lhs": "Equation116"}, + {"rhs": "Equation878", "lhs": "Equation116"}, + {"rhs": "Equation1042", "lhs": "Equation1160"}, + {"rhs": "Equation1078", "lhs": "Equation1160"}, + {"rhs": "Equation1116", "lhs": "Equation1160"}, + {"rhs": "Equation1148", "lhs": "Equation1160"}, + {"rhs": "Equation1152", "lhs": "Equation1160"}, + {"rhs": "Equation1156", "lhs": "Equation1160"}, + {"rhs": "Equation1043", "lhs": "Equation1161"}, + {"rhs": "Equation1080", "lhs": "Equation1161"}, + {"rhs": "Equation1117", "lhs": "Equation1161"}, + {"rhs": "Equation1146", "lhs": "Equation1161"}, + {"rhs": "Equation1151", "lhs": "Equation1161"}, + {"rhs": "Equation1156", "lhs": "Equation1161"}, + {"rhs": "Equation1044", "lhs": "Equation1162"}, + {"rhs": "Equation1081", "lhs": "Equation1162"}, + {"rhs": "Equation1118", "lhs": "Equation1162"}, + {"rhs": "Equation1149", "lhs": "Equation1162"}, + {"rhs": "Equation1153", "lhs": "Equation1162"}, + {"rhs": "Equation1157", "lhs": "Equation1162"}, + {"rhs": "Equation1158", "lhs": "Equation1162"}, + {"rhs": "Equation1159", "lhs": "Equation1162"}, + {"rhs": "Equation1160", "lhs": "Equation1162"}, + {"rhs": "Equation1161", "lhs": "Equation1162"}, + {"rhs": "Equation1035", "lhs": "Equation1163"}, + {"rhs": "Equation1082", "lhs": "Equation1163"}, + {"rhs": "Equation1119", "lhs": "Equation1163"}, + {"rhs": "Equation1035", "lhs": "Equation1164"}, + {"rhs": "Equation1083", "lhs": "Equation1164"}, + {"rhs": "Equation1120", "lhs": "Equation1164"}, + {"rhs": "Equation1036", "lhs": "Equation1165"}, + {"rhs": "Equation1082", "lhs": "Equation1165"}, + {"rhs": "Equation1120", "lhs": "Equation1165"}, + {"rhs": "Equation1037", "lhs": "Equation1166"}, + {"rhs": "Equation1084", "lhs": "Equation1166"}, + {"rhs": "Equation1121", "lhs": "Equation1166"}, + {"rhs": "Equation1163", "lhs": "Equation1166"}, + {"rhs": "Equation1164", "lhs": "Equation1166"}, + {"rhs": "Equation1165", "lhs": "Equation1166"}, + {"rhs": "Equation1035", "lhs": "Equation1167"}, + {"rhs": "Equation1085", "lhs": "Equation1167"}, + {"rhs": "Equation1122", "lhs": "Equation1167"}, + {"rhs": "Equation99", "lhs": "Equation117"}, + {"rhs": "Equation1169", "lhs": "Equation1170"}, + {"rhs": "Equation1038", "lhs": "Equation1171"}, + {"rhs": "Equation1082", "lhs": "Equation1171"}, + {"rhs": "Equation1122", "lhs": "Equation1171"}, + {"rhs": "Equation1173", "lhs": "Equation1174"}, + {"rhs": "Equation1041", "lhs": "Equation1175"}, + {"rhs": "Equation1088", "lhs": "Equation1175"}, + {"rhs": "Equation1125", "lhs": "Equation1175"}, + {"rhs": "Equation1163", "lhs": "Equation1175"}, + {"rhs": "Equation1167", "lhs": "Equation1175"}, + {"rhs": "Equation1171", "lhs": "Equation1175"}, + {"rhs": "Equation1178", "lhs": "Equation1179"}, + {"rhs": "Equation99", "lhs": "Equation118"}, + {"rhs": "Equation1045", "lhs": "Equation1180"}, + {"rhs": "Equation1072", "lhs": "Equation1180"}, + {"rhs": "Equation1119", "lhs": "Equation1180"}, + {"rhs": "Equation1045", "lhs": "Equation1181"}, + {"rhs": "Equation1073", "lhs": "Equation1181"}, + {"rhs": "Equation1120", "lhs": "Equation1181"}, + {"rhs": "Equation1046", "lhs": "Equation1182"}, + {"rhs": "Equation1072", "lhs": "Equation1182"}, + {"rhs": "Equation1120", "lhs": "Equation1182"}, + {"rhs": "Equation1047", "lhs": "Equation1183"}, + {"rhs": "Equation1074", "lhs": "Equation1183"}, + {"rhs": "Equation1121", "lhs": "Equation1183"}, + {"rhs": "Equation1180", "lhs": "Equation1183"}, + {"rhs": "Equation1181", "lhs": "Equation1183"}, + {"rhs": "Equation1182", "lhs": "Equation1183"}, + {"rhs": "Equation1045", "lhs": "Equation1184"}, + {"rhs": "Equation1075", "lhs": "Equation1184"}, + {"rhs": "Equation1122", "lhs": "Equation1184"}, + {"rhs": "Equation1186", "lhs": "Equation1187"}, + {"rhs": "Equation1048", "lhs": "Equation1188"}, + {"rhs": "Equation1072", "lhs": "Equation1188"}, + {"rhs": "Equation1122", "lhs": "Equation1188"}, + {"rhs": "Equation100", "lhs": "Equation119"}, + {"rhs": "Equation117", "lhs": "Equation119"}, + {"rhs": "Equation118", "lhs": "Equation119"}, + {"rhs": "Equation888", "lhs": "Equation119"}, + {"rhs": "Equation1190", "lhs": "Equation1191"}, + {"rhs": "Equation1051", "lhs": "Equation1192"}, + {"rhs": "Equation1078", "lhs": "Equation1192"}, + {"rhs": "Equation1125", "lhs": "Equation1192"}, + {"rhs": "Equation1180", "lhs": "Equation1192"}, + {"rhs": "Equation1184", "lhs": "Equation1192"}, + {"rhs": "Equation1188", "lhs": "Equation1192"}, + {"rhs": "Equation1195", "lhs": "Equation1196"}, + {"rhs": "Equation1055", "lhs": "Equation1197"}, + {"rhs": "Equation1092", "lhs": "Equation1197"}, + {"rhs": "Equation1129", "lhs": "Equation1197"}, + {"rhs": "Equation1146", "lhs": "Equation1197"}, + {"rhs": "Equation1163", "lhs": "Equation1197"}, + {"rhs": "Equation1180", "lhs": "Equation1197"}, + {"rhs": "Equation1055", "lhs": "Equation1198"}, + {"rhs": "Equation1093", "lhs": "Equation1198"}, + {"rhs": "Equation1130", "lhs": "Equation1198"}, + {"rhs": "Equation1147", "lhs": "Equation1198"}, + {"rhs": "Equation1164", "lhs": "Equation1198"}, + {"rhs": "Equation1181", "lhs": "Equation1198"}, + {"rhs": "Equation1056", "lhs": "Equation1199"}, + {"rhs": "Equation1092", "lhs": "Equation1199"}, + {"rhs": "Equation1130", "lhs": "Equation1199"}, + {"rhs": "Equation1148", "lhs": "Equation1199"}, + {"rhs": "Equation1165", "lhs": "Equation1199"}, + {"rhs": "Equation1182", "lhs": "Equation1199"}, + {"rhs": "Equation10", "lhs": "Equation12"}, + {"rhs": "Equation11", "lhs": "Equation12"}, + {"rhs": "Equation113", "lhs": "Equation12"}, + {"rhs": "Equation3730", "lhs": "Equation12"}, + {"rhs": "Equation61", "lhs": "Equation12"}, + {"rhs": "Equation9", "lhs": "Equation12"}, + {"rhs": "Equation101", "lhs": "Equation120"}, + {"rhs": "Equation1104", "lhs": "Equation120"}, + {"rhs": "Equation114", "lhs": "Equation120"}, + {"rhs": "Equation117", "lhs": "Equation120"}, + {"rhs": "Equation1767", "lhs": "Equation120"}, + {"rhs": "Equation1057", "lhs": "Equation1200"}, + {"rhs": "Equation1094", "lhs": "Equation1200"}, + {"rhs": "Equation1131", "lhs": "Equation1200"}, + {"rhs": "Equation1146", "lhs": "Equation1200"}, + {"rhs": "Equation1164", "lhs": "Equation1200"}, + {"rhs": "Equation1182", "lhs": "Equation1200"}, + {"rhs": "Equation1058", "lhs": "Equation1201"}, + {"rhs": "Equation1095", "lhs": "Equation1201"}, + {"rhs": "Equation1132", "lhs": "Equation1201"}, + {"rhs": "Equation1149", "lhs": "Equation1201"}, + {"rhs": "Equation1166", "lhs": "Equation1201"}, + {"rhs": "Equation1183", "lhs": "Equation1201"}, + {"rhs": "Equation1197", "lhs": "Equation1201"}, + {"rhs": "Equation1198", "lhs": "Equation1201"}, + {"rhs": "Equation1199", "lhs": "Equation1201"}, + {"rhs": "Equation1200", "lhs": "Equation1201"}, + {"rhs": "Equation1055", "lhs": "Equation1202"}, + {"rhs": "Equation1096", "lhs": "Equation1202"}, + {"rhs": "Equation1133", "lhs": "Equation1202"}, + {"rhs": "Equation1150", "lhs": "Equation1202"}, + {"rhs": "Equation1167", "lhs": "Equation1202"}, + {"rhs": "Equation1184", "lhs": "Equation1202"}, + {"rhs": "Equation1205", "lhs": "Equation1206"}, + {"rhs": "Equation1059", "lhs": "Equation1207"}, + {"rhs": "Equation1092", "lhs": "Equation1207"}, + {"rhs": "Equation1133", "lhs": "Equation1207"}, + {"rhs": "Equation1154", "lhs": "Equation1207"}, + {"rhs": "Equation1171", "lhs": "Equation1207"}, + {"rhs": "Equation1188", "lhs": "Equation1207"}, + {"rhs": "Equation101", "lhs": "Equation121"}, + {"rhs": "Equation1105", "lhs": "Equation121"}, + {"rhs": "Equation115", "lhs": "Equation121"}, + {"rhs": "Equation118", "lhs": "Equation121"}, + {"rhs": "Equation1210", "lhs": "Equation1211"}, + {"rhs": "Equation1063", "lhs": "Equation1212"}, + {"rhs": "Equation1100", "lhs": "Equation1212"}, + {"rhs": "Equation1137", "lhs": "Equation1212"}, + {"rhs": "Equation1146", "lhs": "Equation1212"}, + {"rhs": "Equation1167", "lhs": "Equation1212"}, + {"rhs": "Equation1188", "lhs": "Equation1212"}, + {"rhs": "Equation1215", "lhs": "Equation1216"}, + {"rhs": "Equation1067", "lhs": "Equation1217"}, + {"rhs": "Equation1104", "lhs": "Equation1217"}, + {"rhs": "Equation1141", "lhs": "Equation1217"}, + {"rhs": "Equation1158", "lhs": "Equation1217"}, + {"rhs": "Equation1175", "lhs": "Equation1217"}, + {"rhs": "Equation1192", "lhs": "Equation1217"}, + {"rhs": "Equation1197", "lhs": "Equation1217"}, + {"rhs": "Equation1202", "lhs": "Equation1217"}, + {"rhs": "Equation1207", "lhs": "Equation1217"}, + {"rhs": "Equation1212", "lhs": "Equation1217"}, + {"rhs": "Equation102", "lhs": "Equation122"}, + {"rhs": "Equation114", "lhs": "Equation122"}, + {"rhs": "Equation118", "lhs": "Equation122"}, + {"rhs": "Equation1770", "lhs": "Equation122"}, + {"rhs": "Equation1221", "lhs": "Equation1222"}, + {"rhs": "Equation1223", "lhs": "Equation1224"}, + {"rhs": "Equation1223", "lhs": "Equation1225"}, + {"rhs": "Equation1223", "lhs": "Equation1226"}, + {"rhs": "Equation1224", "lhs": "Equation1227"}, + {"rhs": "Equation1225", "lhs": "Equation1227"}, + {"rhs": "Equation1226", "lhs": "Equation1227"}, + {"rhs": "Equation1223", "lhs": "Equation1228"}, + {"rhs": "Equation1223", "lhs": "Equation1229"}, + {"rhs": "Equation103", "lhs": "Equation123"}, + {"rhs": "Equation1108", "lhs": "Equation123"}, + {"rhs": "Equation116", "lhs": "Equation123"}, + {"rhs": "Equation119", "lhs": "Equation123"}, + {"rhs": "Equation120", "lhs": "Equation123"}, + {"rhs": "Equation121", "lhs": "Equation123"}, + {"rhs": "Equation122", "lhs": "Equation123"}, + {"rhs": "Equation1771", "lhs": "Equation123"}, + {"rhs": "Equation905", "lhs": "Equation123"}, + {"rhs": "Equation1224", "lhs": "Equation1230"}, + {"rhs": "Equation1228", "lhs": "Equation1230"}, + {"rhs": "Equation1229", "lhs": "Equation1230"}, + {"rhs": "Equation1223", "lhs": "Equation1231"}, + {"rhs": "Equation1223", "lhs": "Equation1232"}, + {"rhs": "Equation1224", "lhs": "Equation1233"}, + {"rhs": "Equation1231", "lhs": "Equation1233"}, + {"rhs": "Equation1232", "lhs": "Equation1233"}, + {"rhs": "Equation1225", "lhs": "Equation1234"}, + {"rhs": "Equation1228", "lhs": "Equation1234"}, + {"rhs": "Equation1231", "lhs": "Equation1234"}, + {"rhs": "Equation1225", "lhs": "Equation1235"}, + {"rhs": "Equation1229", "lhs": "Equation1235"}, + {"rhs": "Equation1232", "lhs": "Equation1235"}, + {"rhs": "Equation1226", "lhs": "Equation1236"}, + {"rhs": "Equation1228", "lhs": "Equation1236"}, + {"rhs": "Equation1232", "lhs": "Equation1236"}, + {"rhs": "Equation1227", "lhs": "Equation1237"}, + {"rhs": "Equation1230", "lhs": "Equation1237"}, + {"rhs": "Equation1233", "lhs": "Equation1237"}, + {"rhs": "Equation1234", "lhs": "Equation1237"}, + {"rhs": "Equation1235", "lhs": "Equation1237"}, + {"rhs": "Equation1236", "lhs": "Equation1237"}, + {"rhs": "Equation1223", "lhs": "Equation1238"}, + {"rhs": "Equation1223", "lhs": "Equation1239"}, + {"rhs": "Equation99", "lhs": "Equation124"}, + {"rhs": "Equation1224", "lhs": "Equation1240"}, + {"rhs": "Equation1238", "lhs": "Equation1240"}, + {"rhs": "Equation1239", "lhs": "Equation1240"}, + {"rhs": "Equation1223", "lhs": "Equation1241"}, + {"rhs": "Equation1223", "lhs": "Equation1242"}, + {"rhs": "Equation1224", "lhs": "Equation1243"}, + {"rhs": "Equation1241", "lhs": "Equation1243"}, + {"rhs": "Equation1242", "lhs": "Equation1243"}, + {"rhs": "Equation1225", "lhs": "Equation1244"}, + {"rhs": "Equation1238", "lhs": "Equation1244"}, + {"rhs": "Equation1241", "lhs": "Equation1244"}, + {"rhs": "Equation1225", "lhs": "Equation1245"}, + {"rhs": "Equation1239", "lhs": "Equation1245"}, + {"rhs": "Equation1242", "lhs": "Equation1245"}, + {"rhs": "Equation1226", "lhs": "Equation1246"}, + {"rhs": "Equation1238", "lhs": "Equation1246"}, + {"rhs": "Equation1242", "lhs": "Equation1246"}, + {"rhs": "Equation1227", "lhs": "Equation1247"}, + {"rhs": "Equation1240", "lhs": "Equation1247"}, + {"rhs": "Equation1243", "lhs": "Equation1247"}, + {"rhs": "Equation1244", "lhs": "Equation1247"}, + {"rhs": "Equation1245", "lhs": "Equation1247"}, + {"rhs": "Equation1246", "lhs": "Equation1247"}, + {"rhs": "Equation1223", "lhs": "Equation1248"}, + {"rhs": "Equation1223", "lhs": "Equation1249"}, + {"rhs": "Equation99", "lhs": "Equation125"}, + {"rhs": "Equation1224", "lhs": "Equation1250"}, + {"rhs": "Equation1248", "lhs": "Equation1250"}, + {"rhs": "Equation1249", "lhs": "Equation1250"}, + {"rhs": "Equation1223", "lhs": "Equation1251"}, + {"rhs": "Equation1223", "lhs": "Equation1252"}, + {"rhs": "Equation1224", "lhs": "Equation1253"}, + {"rhs": "Equation1251", "lhs": "Equation1253"}, + {"rhs": "Equation1252", "lhs": "Equation1253"}, + {"rhs": "Equation1225", "lhs": "Equation1254"}, + {"rhs": "Equation1248", "lhs": "Equation1254"}, + {"rhs": "Equation1251", "lhs": "Equation1254"}, + {"rhs": "Equation1225", "lhs": "Equation1255"}, + {"rhs": "Equation1249", "lhs": "Equation1255"}, + {"rhs": "Equation1252", "lhs": "Equation1255"}, + {"rhs": "Equation1226", "lhs": "Equation1256"}, + {"rhs": "Equation1248", "lhs": "Equation1256"}, + {"rhs": "Equation1252", "lhs": "Equation1256"}, + {"rhs": "Equation1227", "lhs": "Equation1257"}, + {"rhs": "Equation1250", "lhs": "Equation1257"}, + {"rhs": "Equation1253", "lhs": "Equation1257"}, + {"rhs": "Equation1254", "lhs": "Equation1257"}, + {"rhs": "Equation1255", "lhs": "Equation1257"}, + {"rhs": "Equation1256", "lhs": "Equation1257"}, + {"rhs": "Equation1228", "lhs": "Equation1258"}, + {"rhs": "Equation1238", "lhs": "Equation1258"}, + {"rhs": "Equation1248", "lhs": "Equation1258"}, + {"rhs": "Equation1228", "lhs": "Equation1259"}, + {"rhs": "Equation1239", "lhs": "Equation1259"}, + {"rhs": "Equation1249", "lhs": "Equation1259"}, + {"rhs": "Equation100", "lhs": "Equation126"}, + {"rhs": "Equation124", "lhs": "Equation126"}, + {"rhs": "Equation125", "lhs": "Equation126"}, + {"rhs": "Equation915", "lhs": "Equation126"}, + {"rhs": "Equation1229", "lhs": "Equation1260"}, + {"rhs": "Equation1238", "lhs": "Equation1260"}, + {"rhs": "Equation1249", "lhs": "Equation1260"}, + {"rhs": "Equation1230", "lhs": "Equation1261"}, + {"rhs": "Equation1240", "lhs": "Equation1261"}, + {"rhs": "Equation1250", "lhs": "Equation1261"}, + {"rhs": "Equation1258", "lhs": "Equation1261"}, + {"rhs": "Equation1259", "lhs": "Equation1261"}, + {"rhs": "Equation1260", "lhs": "Equation1261"}, + {"rhs": "Equation1228", "lhs": "Equation1262"}, + {"rhs": "Equation1241", "lhs": "Equation1262"}, + {"rhs": "Equation1251", "lhs": "Equation1262"}, + {"rhs": "Equation1228", "lhs": "Equation1263"}, + {"rhs": "Equation1242", "lhs": "Equation1263"}, + {"rhs": "Equation1252", "lhs": "Equation1263"}, + {"rhs": "Equation1229", "lhs": "Equation1264"}, + {"rhs": "Equation1241", "lhs": "Equation1264"}, + {"rhs": "Equation1252", "lhs": "Equation1264"}, + {"rhs": "Equation1230", "lhs": "Equation1265"}, + {"rhs": "Equation1243", "lhs": "Equation1265"}, + {"rhs": "Equation1253", "lhs": "Equation1265"}, + {"rhs": "Equation1262", "lhs": "Equation1265"}, + {"rhs": "Equation1263", "lhs": "Equation1265"}, + {"rhs": "Equation1264", "lhs": "Equation1265"}, + {"rhs": "Equation1231", "lhs": "Equation1266"}, + {"rhs": "Equation1238", "lhs": "Equation1266"}, + {"rhs": "Equation1251", "lhs": "Equation1266"}, + {"rhs": "Equation1231", "lhs": "Equation1267"}, + {"rhs": "Equation1239", "lhs": "Equation1267"}, + {"rhs": "Equation1252", "lhs": "Equation1267"}, + {"rhs": "Equation1232", "lhs": "Equation1268"}, + {"rhs": "Equation1238", "lhs": "Equation1268"}, + {"rhs": "Equation1252", "lhs": "Equation1268"}, + {"rhs": "Equation1233", "lhs": "Equation1269"}, + {"rhs": "Equation1240", "lhs": "Equation1269"}, + {"rhs": "Equation1253", "lhs": "Equation1269"}, + {"rhs": "Equation1266", "lhs": "Equation1269"}, + {"rhs": "Equation1267", "lhs": "Equation1269"}, + {"rhs": "Equation1268", "lhs": "Equation1269"}, + {"rhs": "Equation99", "lhs": "Equation127"}, + {"rhs": "Equation1234", "lhs": "Equation1270"}, + {"rhs": "Equation1244", "lhs": "Equation1270"}, + {"rhs": "Equation1254", "lhs": "Equation1270"}, + {"rhs": "Equation1258", "lhs": "Equation1270"}, + {"rhs": "Equation1262", "lhs": "Equation1270"}, + {"rhs": "Equation1266", "lhs": "Equation1270"}, + {"rhs": "Equation1234", "lhs": "Equation1271"}, + {"rhs": "Equation1245", "lhs": "Equation1271"}, + {"rhs": "Equation1255", "lhs": "Equation1271"}, + {"rhs": "Equation1259", "lhs": "Equation1271"}, + {"rhs": "Equation1263", "lhs": "Equation1271"}, + {"rhs": "Equation1267", "lhs": "Equation1271"}, + {"rhs": "Equation1235", "lhs": "Equation1272"}, + {"rhs": "Equation1244", "lhs": "Equation1272"}, + {"rhs": "Equation1255", "lhs": "Equation1272"}, + {"rhs": "Equation1260", "lhs": "Equation1272"}, + {"rhs": "Equation1264", "lhs": "Equation1272"}, + {"rhs": "Equation1268", "lhs": "Equation1272"}, + {"rhs": "Equation1236", "lhs": "Equation1273"}, + {"rhs": "Equation1246", "lhs": "Equation1273"}, + {"rhs": "Equation1256", "lhs": "Equation1273"}, + {"rhs": "Equation1258", "lhs": "Equation1273"}, + {"rhs": "Equation1263", "lhs": "Equation1273"}, + {"rhs": "Equation1268", "lhs": "Equation1273"}, + {"rhs": "Equation1237", "lhs": "Equation1274"}, + {"rhs": "Equation1247", "lhs": "Equation1274"}, + {"rhs": "Equation1257", "lhs": "Equation1274"}, + {"rhs": "Equation1261", "lhs": "Equation1274"}, + {"rhs": "Equation1265", "lhs": "Equation1274"}, + {"rhs": "Equation1269", "lhs": "Equation1274"}, + {"rhs": "Equation1270", "lhs": "Equation1274"}, + {"rhs": "Equation1271", "lhs": "Equation1274"}, + {"rhs": "Equation1272", "lhs": "Equation1274"}, + {"rhs": "Equation1273", "lhs": "Equation1274"}, + {"rhs": "Equation1223", "lhs": "Equation1275"}, + {"rhs": "Equation1223", "lhs": "Equation1276"}, + {"rhs": "Equation1224", "lhs": "Equation1277"}, + {"rhs": "Equation1275", "lhs": "Equation1277"}, + {"rhs": "Equation1276", "lhs": "Equation1277"}, + {"rhs": "Equation1223", "lhs": "Equation1278"}, + {"rhs": "Equation1223", "lhs": "Equation1279"}, + {"rhs": "Equation1224", "lhs": "Equation1280"}, + {"rhs": "Equation1278", "lhs": "Equation1280"}, + {"rhs": "Equation1279", "lhs": "Equation1280"}, + {"rhs": "Equation1225", "lhs": "Equation1281"}, + {"rhs": "Equation1275", "lhs": "Equation1281"}, + {"rhs": "Equation1278", "lhs": "Equation1281"}, + {"rhs": "Equation1225", "lhs": "Equation1282"}, + {"rhs": "Equation1276", "lhs": "Equation1282"}, + {"rhs": "Equation1279", "lhs": "Equation1282"}, + {"rhs": "Equation1226", "lhs": "Equation1283"}, + {"rhs": "Equation1275", "lhs": "Equation1283"}, + {"rhs": "Equation1279", "lhs": "Equation1283"}, + {"rhs": "Equation1227", "lhs": "Equation1284"}, + {"rhs": "Equation1277", "lhs": "Equation1284"}, + {"rhs": "Equation1280", "lhs": "Equation1284"}, + {"rhs": "Equation1281", "lhs": "Equation1284"}, + {"rhs": "Equation1282", "lhs": "Equation1284"}, + {"rhs": "Equation1283", "lhs": "Equation1284"}, + {"rhs": "Equation1223", "lhs": "Equation1285"}, + {"rhs": "Equation1223", "lhs": "Equation1286"}, + {"rhs": "Equation1224", "lhs": "Equation1287"}, + {"rhs": "Equation1285", "lhs": "Equation1287"}, + {"rhs": "Equation1286", "lhs": "Equation1287"}, + {"rhs": "Equation1223", "lhs": "Equation1288"}, + {"rhs": "Equation1223", "lhs": "Equation1289"}, + {"rhs": "Equation128", "lhs": "Equation129"}, + {"rhs": "Equation1224", "lhs": "Equation1290"}, + {"rhs": "Equation1288", "lhs": "Equation1290"}, + {"rhs": "Equation1289", "lhs": "Equation1290"}, + {"rhs": "Equation1225", "lhs": "Equation1291"}, + {"rhs": "Equation1285", "lhs": "Equation1291"}, + {"rhs": "Equation1288", "lhs": "Equation1291"}, + {"rhs": "Equation1225", "lhs": "Equation1292"}, + {"rhs": "Equation1286", "lhs": "Equation1292"}, + {"rhs": "Equation1289", "lhs": "Equation1292"}, + {"rhs": "Equation1226", "lhs": "Equation1293"}, + {"rhs": "Equation1285", "lhs": "Equation1293"}, + {"rhs": "Equation1289", "lhs": "Equation1293"}, + {"rhs": "Equation1227", "lhs": "Equation1294"}, + {"rhs": "Equation1287", "lhs": "Equation1294"}, + {"rhs": "Equation1290", "lhs": "Equation1294"}, + {"rhs": "Equation1291", "lhs": "Equation1294"}, + {"rhs": "Equation1292", "lhs": "Equation1294"}, + {"rhs": "Equation1293", "lhs": "Equation1294"}, + {"rhs": "Equation1228", "lhs": "Equation1295"}, + {"rhs": "Equation1275", "lhs": "Equation1295"}, + {"rhs": "Equation1285", "lhs": "Equation1295"}, + {"rhs": "Equation1228", "lhs": "Equation1296"}, + {"rhs": "Equation1276", "lhs": "Equation1296"}, + {"rhs": "Equation1286", "lhs": "Equation1296"}, + {"rhs": "Equation1229", "lhs": "Equation1297"}, + {"rhs": "Equation1275", "lhs": "Equation1297"}, + {"rhs": "Equation1286", "lhs": "Equation1297"}, + {"rhs": "Equation1230", "lhs": "Equation1298"}, + {"rhs": "Equation1277", "lhs": "Equation1298"}, + {"rhs": "Equation1287", "lhs": "Equation1298"}, + {"rhs": "Equation1295", "lhs": "Equation1298"}, + {"rhs": "Equation1296", "lhs": "Equation1298"}, + {"rhs": "Equation1297", "lhs": "Equation1298"}, + {"rhs": "Equation1228", "lhs": "Equation1299"}, + {"rhs": "Equation1278", "lhs": "Equation1299"}, + {"rhs": "Equation1288", "lhs": "Equation1299"}, + {"rhs": "Equation186", "lhs": "Equation13"}, + {"rhs": "Equation8", "lhs": "Equation13"}, + {"rhs": "Equation101", "lhs": "Equation130"}, + {"rhs": "Equation1141", "lhs": "Equation130"}, + {"rhs": "Equation124", "lhs": "Equation130"}, + {"rhs": "Equation127", "lhs": "Equation130"}, + {"rhs": "Equation1228", "lhs": "Equation1300"}, + {"rhs": "Equation1279", "lhs": "Equation1300"}, + {"rhs": "Equation1289", "lhs": "Equation1300"}, + {"rhs": "Equation1229", "lhs": "Equation1301"}, + {"rhs": "Equation1278", "lhs": "Equation1301"}, + {"rhs": "Equation1289", "lhs": "Equation1301"}, + {"rhs": "Equation1230", "lhs": "Equation1302"}, + {"rhs": "Equation1280", "lhs": "Equation1302"}, + {"rhs": "Equation1290", "lhs": "Equation1302"}, + {"rhs": "Equation1299", "lhs": "Equation1302"}, + {"rhs": "Equation1300", "lhs": "Equation1302"}, + {"rhs": "Equation1301", "lhs": "Equation1302"}, + {"rhs": "Equation1231", "lhs": "Equation1303"}, + {"rhs": "Equation1275", "lhs": "Equation1303"}, + {"rhs": "Equation1288", "lhs": "Equation1303"}, + {"rhs": "Equation1231", "lhs": "Equation1304"}, + {"rhs": "Equation1276", "lhs": "Equation1304"}, + {"rhs": "Equation1289", "lhs": "Equation1304"}, + {"rhs": "Equation1232", "lhs": "Equation1305"}, + {"rhs": "Equation1275", "lhs": "Equation1305"}, + {"rhs": "Equation1289", "lhs": "Equation1305"}, + {"rhs": "Equation1233", "lhs": "Equation1306"}, + {"rhs": "Equation1277", "lhs": "Equation1306"}, + {"rhs": "Equation1290", "lhs": "Equation1306"}, + {"rhs": "Equation1303", "lhs": "Equation1306"}, + {"rhs": "Equation1304", "lhs": "Equation1306"}, + {"rhs": "Equation1305", "lhs": "Equation1306"}, + {"rhs": "Equation1234", "lhs": "Equation1307"}, + {"rhs": "Equation1281", "lhs": "Equation1307"}, + {"rhs": "Equation1291", "lhs": "Equation1307"}, + {"rhs": "Equation1295", "lhs": "Equation1307"}, + {"rhs": "Equation1299", "lhs": "Equation1307"}, + {"rhs": "Equation1303", "lhs": "Equation1307"}, + {"rhs": "Equation1234", "lhs": "Equation1308"}, + {"rhs": "Equation1282", "lhs": "Equation1308"}, + {"rhs": "Equation1292", "lhs": "Equation1308"}, + {"rhs": "Equation1296", "lhs": "Equation1308"}, + {"rhs": "Equation1300", "lhs": "Equation1308"}, + {"rhs": "Equation1304", "lhs": "Equation1308"}, + {"rhs": "Equation1235", "lhs": "Equation1309"}, + {"rhs": "Equation1281", "lhs": "Equation1309"}, + {"rhs": "Equation1292", "lhs": "Equation1309"}, + {"rhs": "Equation1297", "lhs": "Equation1309"}, + {"rhs": "Equation1301", "lhs": "Equation1309"}, + {"rhs": "Equation1305", "lhs": "Equation1309"}, + {"rhs": "Equation1236", "lhs": "Equation1310"}, + {"rhs": "Equation1283", "lhs": "Equation1310"}, + {"rhs": "Equation1293", "lhs": "Equation1310"}, + {"rhs": "Equation1295", "lhs": "Equation1310"}, + {"rhs": "Equation1300", "lhs": "Equation1310"}, + {"rhs": "Equation1305", "lhs": "Equation1310"}, + {"rhs": "Equation1237", "lhs": "Equation1311"}, + {"rhs": "Equation1284", "lhs": "Equation1311"}, + {"rhs": "Equation1294", "lhs": "Equation1311"}, + {"rhs": "Equation1298", "lhs": "Equation1311"}, + {"rhs": "Equation1302", "lhs": "Equation1311"}, + {"rhs": "Equation1306", "lhs": "Equation1311"}, + {"rhs": "Equation1307", "lhs": "Equation1311"}, + {"rhs": "Equation1308", "lhs": "Equation1311"}, + {"rhs": "Equation1309", "lhs": "Equation1311"}, + {"rhs": "Equation1310", "lhs": "Equation1311"}, + {"rhs": "Equation1223", "lhs": "Equation1312"}, + {"rhs": "Equation1223", "lhs": "Equation1313"}, + {"rhs": "Equation1224", "lhs": "Equation1314"}, + {"rhs": "Equation1312", "lhs": "Equation1314"}, + {"rhs": "Equation1313", "lhs": "Equation1314"}, + {"rhs": "Equation1223", "lhs": "Equation1315"}, + {"rhs": "Equation1223", "lhs": "Equation1316"}, + {"rhs": "Equation1224", "lhs": "Equation1317"}, + {"rhs": "Equation1315", "lhs": "Equation1317"}, + {"rhs": "Equation1316", "lhs": "Equation1317"}, + {"rhs": "Equation1225", "lhs": "Equation1318"}, + {"rhs": "Equation1312", "lhs": "Equation1318"}, + {"rhs": "Equation1315", "lhs": "Equation1318"}, + {"rhs": "Equation1225", "lhs": "Equation1319"}, + {"rhs": "Equation1313", "lhs": "Equation1319"}, + {"rhs": "Equation1316", "lhs": "Equation1319"}, + {"rhs": "Equation1226", "lhs": "Equation1320"}, + {"rhs": "Equation1312", "lhs": "Equation1320"}, + {"rhs": "Equation1316", "lhs": "Equation1320"}, + {"rhs": "Equation1227", "lhs": "Equation1321"}, + {"rhs": "Equation1314", "lhs": "Equation1321"}, + {"rhs": "Equation1317", "lhs": "Equation1321"}, + {"rhs": "Equation1318", "lhs": "Equation1321"}, + {"rhs": "Equation1319", "lhs": "Equation1321"}, + {"rhs": "Equation1320", "lhs": "Equation1321"}, + {"rhs": "Equation1223", "lhs": "Equation1322"}, + {"rhs": "Equation1223", "lhs": "Equation1323"}, + {"rhs": "Equation1224", "lhs": "Equation1324"}, + {"rhs": "Equation1322", "lhs": "Equation1324"}, + {"rhs": "Equation1323", "lhs": "Equation1324"}, + {"rhs": "Equation1223", "lhs": "Equation1325"}, + {"rhs": "Equation1326", "lhs": "Equation1327"}, + {"rhs": "Equation1225", "lhs": "Equation1328"}, + {"rhs": "Equation1322", "lhs": "Equation1328"}, + {"rhs": "Equation1325", "lhs": "Equation1328"}, + {"rhs": "Equation1330", "lhs": "Equation1331"}, + {"rhs": "Equation1228", "lhs": "Equation1332"}, + {"rhs": "Equation1312", "lhs": "Equation1332"}, + {"rhs": "Equation1322", "lhs": "Equation1332"}, + {"rhs": "Equation1228", "lhs": "Equation1333"}, + {"rhs": "Equation1313", "lhs": "Equation1333"}, + {"rhs": "Equation1323", "lhs": "Equation1333"}, + {"rhs": "Equation1229", "lhs": "Equation1334"}, + {"rhs": "Equation1312", "lhs": "Equation1334"}, + {"rhs": "Equation1323", "lhs": "Equation1334"}, + {"rhs": "Equation1230", "lhs": "Equation1335"}, + {"rhs": "Equation1314", "lhs": "Equation1335"}, + {"rhs": "Equation1324", "lhs": "Equation1335"}, + {"rhs": "Equation1332", "lhs": "Equation1335"}, + {"rhs": "Equation1333", "lhs": "Equation1335"}, + {"rhs": "Equation1334", "lhs": "Equation1335"}, + {"rhs": "Equation1228", "lhs": "Equation1336"}, + {"rhs": "Equation1315", "lhs": "Equation1336"}, + {"rhs": "Equation1325", "lhs": "Equation1336"}, + {"rhs": "Equation1338", "lhs": "Equation1339"}, + {"rhs": "Equation104", "lhs": "Equation134"}, + {"rhs": "Equation114", "lhs": "Equation134"}, + {"rhs": "Equation124", "lhs": "Equation134"}, + {"rhs": "Equation1400", "lhs": "Equation134"}, + {"rhs": "Equation1806", "lhs": "Equation134"}, + {"rhs": "Equation1231", "lhs": "Equation1340"}, + {"rhs": "Equation1312", "lhs": "Equation1340"}, + {"rhs": "Equation1325", "lhs": "Equation1340"}, + {"rhs": "Equation1342", "lhs": "Equation1343"}, + {"rhs": "Equation1234", "lhs": "Equation1344"}, + {"rhs": "Equation1318", "lhs": "Equation1344"}, + {"rhs": "Equation1328", "lhs": "Equation1344"}, + {"rhs": "Equation1332", "lhs": "Equation1344"}, + {"rhs": "Equation1336", "lhs": "Equation1344"}, + {"rhs": "Equation1340", "lhs": "Equation1344"}, + {"rhs": "Equation1347", "lhs": "Equation1348"}, + {"rhs": "Equation1238", "lhs": "Equation1349"}, + {"rhs": "Equation1275", "lhs": "Equation1349"}, + {"rhs": "Equation1312", "lhs": "Equation1349"}, + {"rhs": "Equation104", "lhs": "Equation135"}, + {"rhs": "Equation115", "lhs": "Equation135"}, + {"rhs": "Equation125", "lhs": "Equation135"}, + {"rhs": "Equation1401", "lhs": "Equation135"}, + {"rhs": "Equation1238", "lhs": "Equation1350"}, + {"rhs": "Equation1276", "lhs": "Equation1350"}, + {"rhs": "Equation1313", "lhs": "Equation1350"}, + {"rhs": "Equation1239", "lhs": "Equation1351"}, + {"rhs": "Equation1275", "lhs": "Equation1351"}, + {"rhs": "Equation1313", "lhs": "Equation1351"}, + {"rhs": "Equation1240", "lhs": "Equation1352"}, + {"rhs": "Equation1277", "lhs": "Equation1352"}, + {"rhs": "Equation1314", "lhs": "Equation1352"}, + {"rhs": "Equation1349", "lhs": "Equation1352"}, + {"rhs": "Equation1350", "lhs": "Equation1352"}, + {"rhs": "Equation1351", "lhs": "Equation1352"}, + {"rhs": "Equation1238", "lhs": "Equation1353"}, + {"rhs": "Equation1278", "lhs": "Equation1353"}, + {"rhs": "Equation1315", "lhs": "Equation1353"}, + {"rhs": "Equation1238", "lhs": 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"Equation2355", "lhs": "Equation2359"}, + {"rhs": "Equation2362", "lhs": "Equation2363"}, + {"rhs": "Equation2253", "lhs": "Equation2364"}, + {"rhs": "Equation2290", "lhs": "Equation2364"}, + {"rhs": "Equation2327", "lhs": "Equation2364"}, + {"rhs": "Equation2253", "lhs": "Equation2365"}, + {"rhs": "Equation2291", "lhs": "Equation2365"}, + {"rhs": "Equation2328", "lhs": "Equation2365"}, + {"rhs": "Equation2254", "lhs": "Equation2366"}, + {"rhs": "Equation2290", "lhs": "Equation2366"}, + {"rhs": "Equation2328", "lhs": "Equation2366"}, + {"rhs": "Equation2255", "lhs": "Equation2367"}, + {"rhs": "Equation2292", "lhs": "Equation2367"}, + {"rhs": "Equation2329", "lhs": "Equation2367"}, + {"rhs": "Equation2364", "lhs": "Equation2367"}, + {"rhs": "Equation2365", "lhs": "Equation2367"}, + {"rhs": "Equation2366", "lhs": "Equation2367"}, + {"rhs": "Equation2253", "lhs": "Equation2368"}, + {"rhs": "Equation2293", "lhs": "Equation2368"}, + {"rhs": "Equation2330", "lhs": "Equation2368"}, + {"rhs": 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"Equation2290", "lhs": "Equation2374"}, + {"rhs": "Equation2331", "lhs": "Equation2374"}, + {"rhs": "Equation2258", "lhs": "Equation2375"}, + {"rhs": "Equation2292", "lhs": "Equation2375"}, + {"rhs": "Equation2332", "lhs": "Equation2375"}, + {"rhs": "Equation2372", "lhs": "Equation2375"}, + {"rhs": "Equation2373", "lhs": "Equation2375"}, + {"rhs": "Equation2374", "lhs": "Equation2375"}, + {"rhs": "Equation2259", "lhs": "Equation2376"}, + {"rhs": "Equation2296", "lhs": "Equation2376"}, + {"rhs": "Equation2333", "lhs": "Equation2376"}, + {"rhs": "Equation2364", "lhs": "Equation2376"}, + {"rhs": "Equation2368", "lhs": "Equation2376"}, + {"rhs": "Equation2372", "lhs": "Equation2376"}, + {"rhs": "Equation2259", "lhs": "Equation2377"}, + {"rhs": "Equation2297", "lhs": "Equation2377"}, + {"rhs": "Equation2334", "lhs": "Equation2377"}, + {"rhs": "Equation2365", "lhs": "Equation2377"}, + {"rhs": "Equation2369", "lhs": "Equation2377"}, + {"rhs": "Equation2373", "lhs": "Equation2377"}, + {"rhs": "Equation2260", "lhs": "Equation2378"}, + {"rhs": "Equation2296", "lhs": "Equation2378"}, + {"rhs": "Equation2334", "lhs": "Equation2378"}, + {"rhs": "Equation2366", "lhs": "Equation2378"}, + {"rhs": "Equation2370", "lhs": "Equation2378"}, + {"rhs": "Equation2374", "lhs": "Equation2378"}, + {"rhs": "Equation2261", "lhs": "Equation2379"}, + {"rhs": "Equation2298", "lhs": "Equation2379"}, + {"rhs": "Equation2335", "lhs": "Equation2379"}, + {"rhs": "Equation2364", "lhs": "Equation2379"}, + {"rhs": "Equation2369", "lhs": "Equation2379"}, + {"rhs": "Equation2374", "lhs": "Equation2379"}, + {"rhs": "Equation208", "lhs": "Equation238"}, + {"rhs": "Equation218", "lhs": "Equation238"}, + {"rhs": "Equation228", "lhs": "Equation238"}, + {"rhs": "Equation2618", "lhs": "Equation238"}, + {"rhs": "Equation2821", "lhs": "Equation238"}, + {"rhs": "Equation2262", "lhs": "Equation2380"}, + {"rhs": "Equation2299", "lhs": "Equation2380"}, + {"rhs": "Equation2336", "lhs": "Equation2380"}, + {"rhs": "Equation2367", "lhs": "Equation2380"}, + {"rhs": "Equation2371", "lhs": "Equation2380"}, + {"rhs": "Equation2375", "lhs": "Equation2380"}, + {"rhs": "Equation2376", "lhs": "Equation2380"}, + {"rhs": "Equation2377", "lhs": "Equation2380"}, + {"rhs": "Equation2378", "lhs": "Equation2380"}, + {"rhs": "Equation2379", "lhs": "Equation2380"}, + {"rhs": "Equation2253", "lhs": "Equation2381"}, + {"rhs": "Equation2300", "lhs": "Equation2381"}, + {"rhs": "Equation2337", "lhs": "Equation2381"}, + {"rhs": "Equation2253", "lhs": "Equation2382"}, + {"rhs": "Equation2301", "lhs": "Equation2382"}, + {"rhs": "Equation2338", "lhs": "Equation2382"}, + {"rhs": "Equation2254", "lhs": "Equation2383"}, + {"rhs": "Equation2300", "lhs": "Equation2383"}, + {"rhs": "Equation2338", "lhs": "Equation2383"}, + {"rhs": "Equation2255", "lhs": "Equation2384"}, + {"rhs": "Equation2302", "lhs": "Equation2384"}, + {"rhs": "Equation2339", "lhs": "Equation2384"}, + {"rhs": "Equation2381", "lhs": "Equation2384"}, + {"rhs": "Equation2382", "lhs": "Equation2384"}, + {"rhs": "Equation2383", "lhs": "Equation2384"}, + {"rhs": "Equation2253", "lhs": "Equation2385"}, + {"rhs": "Equation2303", "lhs": "Equation2385"}, + {"rhs": "Equation2340", "lhs": "Equation2385"}, + {"rhs": "Equation2387", "lhs": "Equation2388"}, + {"rhs": "Equation2256", "lhs": "Equation2389"}, + {"rhs": "Equation2300", "lhs": "Equation2389"}, + {"rhs": "Equation2340", "lhs": "Equation2389"}, + {"rhs": "Equation208", "lhs": "Equation239"}, + {"rhs": "Equation219", "lhs": "Equation239"}, + {"rhs": "Equation229", "lhs": "Equation239"}, + {"rhs": "Equation2619", "lhs": "Equation239"}, + {"rhs": "Equation2391", "lhs": "Equation2392"}, + {"rhs": "Equation2259", "lhs": "Equation2393"}, + {"rhs": "Equation2306", "lhs": "Equation2393"}, + {"rhs": "Equation2343", "lhs": "Equation2393"}, + {"rhs": "Equation2381", "lhs": "Equation2393"}, + {"rhs": "Equation2385", "lhs": "Equation2393"}, + {"rhs": "Equation2389", "lhs": "Equation2393"}, + {"rhs": "Equation2396", "lhs": "Equation2397"}, + {"rhs": "Equation2263", "lhs": "Equation2398"}, + {"rhs": "Equation2290", "lhs": "Equation2398"}, + {"rhs": "Equation2337", "lhs": "Equation2398"}, + {"rhs": "Equation2263", "lhs": "Equation2399"}, + {"rhs": "Equation2291", "lhs": "Equation2399"}, + {"rhs": "Equation2338", "lhs": "Equation2399"}, + {"rhs": "Equation155", "lhs": "Equation24"}, + {"rhs": "Equation23", "lhs": "Equation24"}, + {"rhs": "Equation209", "lhs": "Equation240"}, + {"rhs": "Equation218", "lhs": "Equation240"}, + {"rhs": "Equation229", "lhs": "Equation240"}, + {"rhs": "Equation2824", "lhs": "Equation240"}, + {"rhs": "Equation2264", "lhs": "Equation2400"}, + {"rhs": "Equation2290", "lhs": "Equation2400"}, + {"rhs": "Equation2338", "lhs": "Equation2400"}, + {"rhs": "Equation2265", "lhs": "Equation2401"}, + {"rhs": "Equation2292", "lhs": "Equation2401"}, + {"rhs": "Equation2339", "lhs": "Equation2401"}, + {"rhs": "Equation2398", "lhs": "Equation2401"}, + {"rhs": "Equation2399", "lhs": "Equation2401"}, + {"rhs": "Equation2400", "lhs": "Equation2401"}, + {"rhs": "Equation2263", "lhs": "Equation2402"}, + {"rhs": "Equation2293", "lhs": "Equation2402"}, + {"rhs": "Equation2340", "lhs": "Equation2402"}, + {"rhs": "Equation2404", "lhs": "Equation2405"}, + {"rhs": "Equation2266", "lhs": "Equation2406"}, + {"rhs": "Equation2290", "lhs": "Equation2406"}, + {"rhs": "Equation2340", "lhs": "Equation2406"}, + {"rhs": "Equation2408", "lhs": "Equation2409"}, + {"rhs": "Equation1974", "lhs": "Equation241"}, + {"rhs": "Equation210", "lhs": "Equation241"}, + {"rhs": "Equation220", "lhs": "Equation241"}, + {"rhs": "Equation230", "lhs": "Equation241"}, + {"rhs": "Equation238", "lhs": "Equation241"}, + {"rhs": "Equation239", "lhs": "Equation241"}, + {"rhs": "Equation240", "lhs": "Equation241"}, + {"rhs": "Equation2622", "lhs": "Equation241"}, + {"rhs": "Equation2825", "lhs": "Equation241"}, + {"rhs": "Equation2269", "lhs": "Equation2410"}, + {"rhs": "Equation2296", "lhs": "Equation2410"}, + {"rhs": "Equation2343", "lhs": "Equation2410"}, + {"rhs": "Equation2398", "lhs": "Equation2410"}, + {"rhs": "Equation2402", "lhs": "Equation2410"}, + {"rhs": "Equation2406", "lhs": "Equation2410"}, + {"rhs": "Equation2413", "lhs": "Equation2414"}, + {"rhs": "Equation2273", "lhs": "Equation2415"}, + {"rhs": "Equation2310", "lhs": "Equation2415"}, + {"rhs": "Equation2347", "lhs": "Equation2415"}, + {"rhs": "Equation2364", "lhs": "Equation2415"}, + {"rhs": "Equation2381", "lhs": "Equation2415"}, + {"rhs": "Equation2398", "lhs": "Equation2415"}, + {"rhs": "Equation2273", "lhs": "Equation2416"}, + {"rhs": "Equation2311", "lhs": "Equation2416"}, + {"rhs": "Equation2348", "lhs": "Equation2416"}, + {"rhs": "Equation2365", "lhs": "Equation2416"}, + {"rhs": "Equation2382", "lhs": "Equation2416"}, + {"rhs": "Equation2399", "lhs": "Equation2416"}, + {"rhs": "Equation2274", "lhs": "Equation2417"}, + {"rhs": "Equation2310", "lhs": "Equation2417"}, + {"rhs": "Equation2348", "lhs": "Equation2417"}, + {"rhs": "Equation2366", "lhs": "Equation2417"}, + {"rhs": "Equation2383", "lhs": "Equation2417"}, + {"rhs": "Equation2400", "lhs": "Equation2417"}, + {"rhs": "Equation2275", "lhs": "Equation2418"}, + {"rhs": "Equation2312", "lhs": "Equation2418"}, + {"rhs": "Equation2349", "lhs": "Equation2418"}, + {"rhs": "Equation2364", "lhs": "Equation2418"}, + {"rhs": "Equation2382", "lhs": "Equation2418"}, + {"rhs": "Equation2400", "lhs": "Equation2418"}, + {"rhs": "Equation2276", "lhs": "Equation2419"}, + {"rhs": "Equation2313", "lhs": "Equation2419"}, + {"rhs": "Equation2350", "lhs": "Equation2419"}, + {"rhs": "Equation2367", "lhs": "Equation2419"}, + {"rhs": "Equation2384", "lhs": "Equation2419"}, + {"rhs": "Equation2401", "lhs": "Equation2419"}, + {"rhs": "Equation2415", "lhs": "Equation2419"}, + {"rhs": "Equation2416", "lhs": "Equation2419"}, + {"rhs": "Equation2417", "lhs": "Equation2419"}, + {"rhs": "Equation2418", "lhs": "Equation2419"}, + {"rhs": "Equation208", "lhs": "Equation242"}, + {"rhs": "Equation221", "lhs": "Equation242"}, + {"rhs": "Equation231", "lhs": "Equation242"}, + {"rhs": "Equation2623", "lhs": "Equation242"}, + {"rhs": "Equation2273", "lhs": "Equation2420"}, + {"rhs": "Equation2314", "lhs": "Equation2420"}, + {"rhs": "Equation2351", "lhs": "Equation2420"}, + {"rhs": "Equation2368", "lhs": "Equation2420"}, + {"rhs": "Equation2385", "lhs": "Equation2420"}, + {"rhs": "Equation2402", "lhs": "Equation2420"}, + {"rhs": "Equation2423", "lhs": "Equation2424"}, + {"rhs": "Equation2277", "lhs": "Equation2425"}, + {"rhs": "Equation2310", "lhs": "Equation2425"}, + {"rhs": "Equation2351", "lhs": "Equation2425"}, + {"rhs": "Equation2372", "lhs": "Equation2425"}, + {"rhs": "Equation2389", "lhs": "Equation2425"}, + {"rhs": "Equation2406", "lhs": "Equation2425"}, + {"rhs": "Equation2428", "lhs": "Equation2429"}, + {"rhs": "Equation2281", "lhs": "Equation2430"}, + {"rhs": "Equation2318", "lhs": "Equation2430"}, + {"rhs": "Equation2355", "lhs": 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"Equation2455"}, + {"rhs": "Equation2448", "lhs": "Equation2455"}, + {"rhs": "Equation2451", "lhs": "Equation2455"}, + {"rhs": "Equation2452", "lhs": "Equation2455"}, + {"rhs": "Equation2453", "lhs": "Equation2455"}, + {"rhs": "Equation2454", "lhs": "Equation2455"}, + {"rhs": "Equation2441", "lhs": "Equation2456"}, + {"rhs": "Equation2441", "lhs": "Equation2457"}, + {"rhs": "Equation2442", "lhs": "Equation2458"}, + {"rhs": "Equation2456", "lhs": "Equation2458"}, + {"rhs": "Equation2457", "lhs": "Equation2458"}, + {"rhs": "Equation2441", "lhs": "Equation2459"}, + {"rhs": "Equation211", "lhs": "Equation246"}, + {"rhs": "Equation218", "lhs": "Equation246"}, + {"rhs": "Equation231", "lhs": "Equation246"}, + {"rhs": "Equation2836", "lhs": "Equation246"}, + {"rhs": "Equation2441", "lhs": "Equation2460"}, + {"rhs": "Equation2442", "lhs": "Equation2461"}, + {"rhs": "Equation2459", "lhs": "Equation2461"}, + {"rhs": "Equation2460", "lhs": "Equation2461"}, + {"rhs": "Equation2443", "lhs": "Equation2462"}, + {"rhs": "Equation2456", "lhs": "Equation2462"}, + {"rhs": "Equation2459", "lhs": "Equation2462"}, + {"rhs": "Equation2443", "lhs": "Equation2463"}, + {"rhs": "Equation2457", "lhs": "Equation2463"}, + {"rhs": "Equation2460", "lhs": "Equation2463"}, + {"rhs": "Equation2444", "lhs": "Equation2464"}, + {"rhs": "Equation2456", "lhs": "Equation2464"}, + {"rhs": "Equation2460", "lhs": "Equation2464"}, + {"rhs": "Equation2445", "lhs": "Equation2465"}, + {"rhs": "Equation2458", "lhs": "Equation2465"}, + {"rhs": "Equation2461", "lhs": "Equation2465"}, + {"rhs": "Equation2462", "lhs": "Equation2465"}, + {"rhs": "Equation2463", "lhs": "Equation2465"}, + {"rhs": "Equation2464", "lhs": "Equation2465"}, + {"rhs": "Equation2441", "lhs": "Equation2466"}, + {"rhs": "Equation2441", "lhs": "Equation2467"}, + {"rhs": "Equation2442", "lhs": "Equation2468"}, + {"rhs": "Equation2466", "lhs": "Equation2468"}, + {"rhs": "Equation2467", "lhs": "Equation2468"}, + {"rhs": "Equation2441", "lhs": "Equation2469"}, + {"rhs": "Equation2441", "lhs": "Equation2470"}, + {"rhs": "Equation2442", "lhs": "Equation2471"}, + {"rhs": "Equation2469", "lhs": "Equation2471"}, + {"rhs": "Equation2470", "lhs": "Equation2471"}, + {"rhs": "Equation2443", "lhs": "Equation2472"}, + {"rhs": "Equation2466", "lhs": "Equation2472"}, + {"rhs": "Equation2469", "lhs": "Equation2472"}, + {"rhs": "Equation2443", "lhs": "Equation2473"}, + {"rhs": "Equation2467", "lhs": "Equation2473"}, + {"rhs": "Equation2470", "lhs": "Equation2473"}, + {"rhs": "Equation2444", "lhs": "Equation2474"}, + {"rhs": "Equation2466", "lhs": "Equation2474"}, + {"rhs": "Equation2470", "lhs": "Equation2474"}, + {"rhs": "Equation2445", "lhs": "Equation2475"}, + {"rhs": "Equation2468", "lhs": "Equation2475"}, + {"rhs": "Equation2471", "lhs": "Equation2475"}, + {"rhs": "Equation2472", "lhs": "Equation2475"}, + {"rhs": "Equation2473", "lhs": "Equation2475"}, + {"rhs": "Equation2474", "lhs": "Equation2475"}, + {"rhs": "Equation2446", "lhs": "Equation2476"}, + {"rhs": "Equation2456", "lhs": "Equation2476"}, + {"rhs": "Equation2466", "lhs": "Equation2476"}, + {"rhs": "Equation2446", "lhs": "Equation2477"}, + {"rhs": "Equation2457", "lhs": "Equation2477"}, + {"rhs": "Equation2467", "lhs": "Equation2477"}, + {"rhs": "Equation2447", "lhs": "Equation2478"}, + {"rhs": "Equation2456", "lhs": "Equation2478"}, + {"rhs": "Equation2467", "lhs": "Equation2478"}, + {"rhs": "Equation2448", "lhs": "Equation2479"}, + {"rhs": "Equation2458", "lhs": "Equation2479"}, + {"rhs": "Equation2468", "lhs": "Equation2479"}, + {"rhs": "Equation2476", "lhs": "Equation2479"}, + {"rhs": "Equation2477", "lhs": "Equation2479"}, + {"rhs": "Equation2478", "lhs": "Equation2479"}, + {"rhs": "Equation2446", "lhs": "Equation2480"}, + {"rhs": "Equation2459", "lhs": "Equation2480"}, + {"rhs": "Equation2469", "lhs": "Equation2480"}, + {"rhs": "Equation2446", "lhs": "Equation2481"}, + {"rhs": "Equation2460", "lhs": "Equation2481"}, + {"rhs": "Equation2470", "lhs": "Equation2481"}, + {"rhs": "Equation2447", "lhs": "Equation2482"}, + {"rhs": "Equation2459", "lhs": "Equation2482"}, + {"rhs": "Equation2470", "lhs": "Equation2482"}, + {"rhs": "Equation2448", "lhs": "Equation2483"}, + {"rhs": "Equation2461", "lhs": "Equation2483"}, + {"rhs": "Equation2471", "lhs": "Equation2483"}, + {"rhs": "Equation2480", "lhs": "Equation2483"}, + {"rhs": "Equation2481", "lhs": "Equation2483"}, + {"rhs": "Equation2482", "lhs": "Equation2483"}, + {"rhs": "Equation2449", "lhs": "Equation2484"}, + {"rhs": "Equation2456", "lhs": "Equation2484"}, + {"rhs": "Equation2469", "lhs": "Equation2484"}, + {"rhs": "Equation2449", "lhs": "Equation2485"}, + {"rhs": "Equation2457", "lhs": "Equation2485"}, + {"rhs": "Equation2470", "lhs": "Equation2485"}, + {"rhs": "Equation2450", "lhs": "Equation2486"}, + {"rhs": "Equation2456", "lhs": "Equation2486"}, + {"rhs": "Equation2470", "lhs": "Equation2486"}, + {"rhs": "Equation2451", "lhs": "Equation2487"}, + {"rhs": "Equation2458", "lhs": "Equation2487"}, + {"rhs": "Equation2471", "lhs": "Equation2487"}, + {"rhs": "Equation2484", "lhs": "Equation2487"}, + {"rhs": "Equation2485", "lhs": "Equation2487"}, + {"rhs": "Equation2486", "lhs": "Equation2487"}, + {"rhs": "Equation2452", "lhs": "Equation2488"}, + {"rhs": "Equation2462", "lhs": "Equation2488"}, + {"rhs": "Equation2472", "lhs": "Equation2488"}, + {"rhs": "Equation2476", "lhs": "Equation2488"}, + {"rhs": "Equation2480", "lhs": "Equation2488"}, + {"rhs": "Equation2484", "lhs": "Equation2488"}, + {"rhs": "Equation2452", "lhs": "Equation2489"}, + {"rhs": "Equation2463", "lhs": "Equation2489"}, + {"rhs": "Equation2473", "lhs": "Equation2489"}, + {"rhs": "Equation2477", "lhs": "Equation2489"}, + {"rhs": "Equation2481", "lhs": "Equation2489"}, + {"rhs": "Equation2485", "lhs": "Equation2489"}, + {"rhs": "Equation248", "lhs": "Equation249"}, + {"rhs": "Equation2453", "lhs": "Equation2490"}, + {"rhs": "Equation2462", "lhs": "Equation2490"}, + {"rhs": "Equation2473", "lhs": "Equation2490"}, + {"rhs": "Equation2478", "lhs": "Equation2490"}, + {"rhs": "Equation2482", "lhs": "Equation2490"}, + {"rhs": "Equation2486", "lhs": "Equation2490"}, + {"rhs": "Equation2454", "lhs": "Equation2491"}, + {"rhs": "Equation2464", "lhs": "Equation2491"}, + {"rhs": "Equation2474", "lhs": "Equation2491"}, + {"rhs": "Equation2476", "lhs": "Equation2491"}, + {"rhs": "Equation2481", "lhs": "Equation2491"}, + {"rhs": "Equation2486", "lhs": "Equation2491"}, + {"rhs": "Equation2455", "lhs": "Equation2492"}, + {"rhs": "Equation2465", "lhs": "Equation2492"}, + {"rhs": "Equation2475", "lhs": "Equation2492"}, + {"rhs": "Equation2479", "lhs": "Equation2492"}, + {"rhs": "Equation2483", "lhs": "Equation2492"}, + {"rhs": "Equation2487", "lhs": "Equation2492"}, + {"rhs": "Equation2488", "lhs": "Equation2492"}, + {"rhs": "Equation2489", "lhs": "Equation2492"}, + {"rhs": "Equation2490", "lhs": "Equation2492"}, + {"rhs": "Equation2491", "lhs": "Equation2492"}, + {"rhs": "Equation2441", "lhs": "Equation2493"}, + {"rhs": "Equation2441", "lhs": "Equation2494"}, + {"rhs": "Equation2442", "lhs": "Equation2495"}, + {"rhs": "Equation2493", "lhs": "Equation2495"}, + {"rhs": "Equation2494", "lhs": "Equation2495"}, + {"rhs": "Equation2441", "lhs": "Equation2496"}, + {"rhs": "Equation2441", "lhs": "Equation2497"}, + {"rhs": "Equation2442", "lhs": "Equation2498"}, + {"rhs": "Equation2496", "lhs": "Equation2498"}, + {"rhs": "Equation2497", "lhs": "Equation2498"}, + {"rhs": "Equation2443", "lhs": "Equation2499"}, + {"rhs": "Equation2493", "lhs": "Equation2499"}, + {"rhs": "Equation2496", "lhs": "Equation2499"}, + {"rhs": "Equation214", "lhs": "Equation25"}, + {"rhs": "Equation23", "lhs": "Equation25"}, + {"rhs": "Equation214", "lhs": "Equation250"}, + {"rhs": "Equation224", "lhs": "Equation250"}, + {"rhs": "Equation234", "lhs": "Equation250"}, + {"rhs": "Equation238", "lhs": "Equation250"}, + {"rhs": "Equation242", "lhs": "Equation250"}, + {"rhs": "Equation2435", "lhs": "Equation250"}, + {"rhs": "Equation246", "lhs": "Equation250"}, + {"rhs": "Equation2638", "lhs": "Equation250"}, + {"rhs": "Equation2841", "lhs": "Equation250"}, + {"rhs": "Equation2443", "lhs": "Equation2500"}, + {"rhs": "Equation2494", "lhs": "Equation2500"}, + {"rhs": "Equation2497", "lhs": "Equation2500"}, + {"rhs": "Equation2444", "lhs": "Equation2501"}, + {"rhs": "Equation2493", "lhs": "Equation2501"}, + {"rhs": "Equation2497", "lhs": "Equation2501"}, + {"rhs": "Equation2445", "lhs": "Equation2502"}, + {"rhs": "Equation2495", "lhs": "Equation2502"}, + {"rhs": "Equation2498", "lhs": "Equation2502"}, + {"rhs": "Equation2499", "lhs": "Equation2502"}, + {"rhs": "Equation2500", "lhs": "Equation2502"}, + {"rhs": "Equation2501", "lhs": "Equation2502"}, + {"rhs": "Equation2441", "lhs": "Equation2503"}, + {"rhs": "Equation2441", "lhs": "Equation2504"}, + {"rhs": "Equation2442", "lhs": "Equation2505"}, + {"rhs": "Equation2503", "lhs": "Equation2505"}, + {"rhs": "Equation2504", "lhs": "Equation2505"}, + {"rhs": "Equation2441", "lhs": "Equation2506"}, + {"rhs": "Equation2441", "lhs": "Equation2507"}, + {"rhs": "Equation2442", "lhs": "Equation2508"}, + {"rhs": "Equation2506", "lhs": "Equation2508"}, + {"rhs": "Equation2507", "lhs": "Equation2508"}, + {"rhs": "Equation2443", "lhs": "Equation2509"}, + {"rhs": "Equation2503", "lhs": "Equation2509"}, + {"rhs": "Equation2506", "lhs": "Equation2509"}, + {"rhs": "Equation2443", "lhs": "Equation2510"}, + {"rhs": "Equation2504", "lhs": "Equation2510"}, + {"rhs": "Equation2507", "lhs": "Equation2510"}, + {"rhs": "Equation2444", "lhs": "Equation2511"}, + {"rhs": "Equation2503", "lhs": "Equation2511"}, + {"rhs": "Equation2507", "lhs": "Equation2511"}, + {"rhs": "Equation2445", "lhs": "Equation2512"}, + {"rhs": "Equation2505", "lhs": "Equation2512"}, + {"rhs": "Equation2508", "lhs": "Equation2512"}, + {"rhs": "Equation2509", "lhs": "Equation2512"}, + {"rhs": "Equation2510", "lhs": "Equation2512"}, + {"rhs": "Equation2511", "lhs": "Equation2512"}, + {"rhs": "Equation2446", "lhs": "Equation2513"}, + {"rhs": "Equation2493", "lhs": "Equation2513"}, + {"rhs": "Equation2503", "lhs": "Equation2513"}, + {"rhs": "Equation2446", "lhs": "Equation2514"}, + {"rhs": "Equation2494", "lhs": "Equation2514"}, + {"rhs": "Equation2504", "lhs": "Equation2514"}, + {"rhs": "Equation2447", "lhs": "Equation2515"}, + {"rhs": "Equation2493", "lhs": "Equation2515"}, + {"rhs": "Equation2504", "lhs": "Equation2515"}, + {"rhs": "Equation2448", "lhs": "Equation2516"}, + {"rhs": "Equation2495", "lhs": "Equation2516"}, + {"rhs": "Equation2505", "lhs": "Equation2516"}, + {"rhs": "Equation2513", "lhs": "Equation2516"}, + {"rhs": "Equation2514", "lhs": "Equation2516"}, + {"rhs": "Equation2515", "lhs": "Equation2516"}, + {"rhs": "Equation2446", "lhs": "Equation2517"}, + {"rhs": "Equation2496", "lhs": "Equation2517"}, + {"rhs": "Equation2506", "lhs": "Equation2517"}, + {"rhs": "Equation2446", "lhs": "Equation2518"}, + {"rhs": "Equation2497", "lhs": "Equation2518"}, + {"rhs": "Equation2507", "lhs": "Equation2518"}, + {"rhs": "Equation2447", "lhs": "Equation2519"}, + {"rhs": "Equation2496", "lhs": "Equation2519"}, + {"rhs": "Equation2507", "lhs": "Equation2519"}, + {"rhs": "Equation2448", "lhs": "Equation2520"}, + {"rhs": "Equation2498", "lhs": "Equation2520"}, + {"rhs": "Equation2508", "lhs": "Equation2520"}, + {"rhs": "Equation2517", "lhs": "Equation2520"}, + {"rhs": "Equation2518", "lhs": "Equation2520"}, + {"rhs": "Equation2519", "lhs": "Equation2520"}, + {"rhs": "Equation2449", "lhs": "Equation2521"}, + {"rhs": "Equation2493", "lhs": "Equation2521"}, + {"rhs": "Equation2506", "lhs": "Equation2521"}, + {"rhs": "Equation2449", "lhs": "Equation2522"}, + {"rhs": "Equation2494", "lhs": "Equation2522"}, + {"rhs": "Equation2507", "lhs": "Equation2522"}, + {"rhs": "Equation2450", "lhs": "Equation2523"}, + {"rhs": "Equation2493", "lhs": "Equation2523"}, + {"rhs": "Equation2507", "lhs": "Equation2523"}, + {"rhs": "Equation2451", "lhs": "Equation2524"}, + {"rhs": "Equation2495", "lhs": "Equation2524"}, + {"rhs": "Equation2508", "lhs": "Equation2524"}, + {"rhs": "Equation2521", "lhs": "Equation2524"}, + {"rhs": "Equation2522", "lhs": "Equation2524"}, + {"rhs": "Equation2523", "lhs": "Equation2524"}, + {"rhs": "Equation2452", "lhs": "Equation2525"}, + {"rhs": "Equation2499", "lhs": "Equation2525"}, + {"rhs": "Equation2509", "lhs": "Equation2525"}, + {"rhs": "Equation2513", "lhs": "Equation2525"}, + {"rhs": "Equation2517", "lhs": "Equation2525"}, + {"rhs": "Equation2521", "lhs": "Equation2525"}, + {"rhs": "Equation2452", "lhs": "Equation2526"}, + {"rhs": "Equation2500", "lhs": "Equation2526"}, + {"rhs": "Equation2510", "lhs": "Equation2526"}, + {"rhs": "Equation2514", "lhs": "Equation2526"}, + {"rhs": "Equation2518", "lhs": "Equation2526"}, + {"rhs": "Equation2522", "lhs": "Equation2526"}, + {"rhs": "Equation2453", "lhs": "Equation2527"}, + {"rhs": "Equation2499", "lhs": "Equation2527"}, + {"rhs": "Equation2510", "lhs": "Equation2527"}, + {"rhs": "Equation2515", "lhs": "Equation2527"}, + {"rhs": "Equation2519", "lhs": "Equation2527"}, + {"rhs": "Equation2523", "lhs": "Equation2527"}, + {"rhs": "Equation2454", "lhs": "Equation2528"}, + {"rhs": "Equation2501", "lhs": "Equation2528"}, + {"rhs": "Equation2511", "lhs": "Equation2528"}, + {"rhs": "Equation2513", "lhs": "Equation2528"}, + {"rhs": "Equation2518", "lhs": "Equation2528"}, + {"rhs": "Equation2523", "lhs": "Equation2528"}, + {"rhs": "Equation2455", "lhs": "Equation2529"}, + {"rhs": "Equation2502", "lhs": "Equation2529"}, + {"rhs": "Equation2512", "lhs": "Equation2529"}, + {"rhs": "Equation2516", "lhs": "Equation2529"}, + {"rhs": "Equation2520", "lhs": "Equation2529"}, + {"rhs": "Equation2524", "lhs": "Equation2529"}, + {"rhs": "Equation2525", "lhs": "Equation2529"}, + {"rhs": "Equation2526", "lhs": "Equation2529"}, + {"rhs": "Equation2527", "lhs": "Equation2529"}, + {"rhs": "Equation2528", "lhs": "Equation2529"}, + {"rhs": "Equation2441", "lhs": "Equation2530"}, + {"rhs": "Equation2441", "lhs": "Equation2531"}, + {"rhs": "Equation2442", "lhs": "Equation2532"}, + {"rhs": "Equation2530", "lhs": "Equation2532"}, + {"rhs": "Equation2531", "lhs": "Equation2532"}, + {"rhs": "Equation2441", "lhs": "Equation2533"}, + {"rhs": "Equation2441", "lhs": "Equation2534"}, + {"rhs": "Equation2442", "lhs": "Equation2535"}, + {"rhs": "Equation2533", "lhs": "Equation2535"}, + {"rhs": "Equation2534", "lhs": "Equation2535"}, + {"rhs": "Equation2443", "lhs": "Equation2536"}, + {"rhs": "Equation2530", "lhs": "Equation2536"}, + {"rhs": "Equation2533", "lhs": "Equation2536"}, + {"rhs": "Equation2443", "lhs": "Equation2537"}, + {"rhs": "Equation2531", "lhs": "Equation2537"}, + {"rhs": "Equation2534", "lhs": "Equation2537"}, + {"rhs": "Equation2444", "lhs": "Equation2538"}, + {"rhs": "Equation2530", "lhs": "Equation2538"}, + {"rhs": "Equation2534", "lhs": "Equation2538"}, + {"rhs": "Equation2445", "lhs": "Equation2539"}, + {"rhs": "Equation2532", "lhs": "Equation2539"}, + {"rhs": "Equation2535", "lhs": "Equation2539"}, + {"rhs": "Equation2536", "lhs": "Equation2539"}, + {"rhs": "Equation2537", "lhs": "Equation2539"}, + {"rhs": "Equation2538", "lhs": "Equation2539"}, + {"rhs": "Equation253", "lhs": "Equation254"}, + {"rhs": "Equation2441", "lhs": "Equation2540"}, + {"rhs": "Equation2441", "lhs": "Equation2541"}, + {"rhs": "Equation2442", "lhs": "Equation2542"}, + {"rhs": "Equation2540", "lhs": "Equation2542"}, + {"rhs": "Equation2541", "lhs": "Equation2542"}, + {"rhs": "Equation2441", "lhs": "Equation2543"}, + {"rhs": "Equation2544", "lhs": "Equation2545"}, + {"rhs": "Equation2443", "lhs": "Equation2546"}, + {"rhs": "Equation2540", "lhs": "Equation2546"}, + {"rhs": "Equation2543", "lhs": "Equation2546"}, + {"rhs": "Equation2548", "lhs": "Equation2549"}, + {"rhs": "Equation2446", "lhs": "Equation2550"}, + {"rhs": "Equation2530", "lhs": "Equation2550"}, + {"rhs": "Equation2540", "lhs": "Equation2550"}, + {"rhs": "Equation2446", "lhs": "Equation2551"}, + {"rhs": "Equation2531", "lhs": "Equation2551"}, + {"rhs": "Equation2541", "lhs": "Equation2551"}, + {"rhs": "Equation2447", "lhs": "Equation2552"}, + {"rhs": "Equation2530", "lhs": "Equation2552"}, + {"rhs": "Equation2541", "lhs": "Equation2552"}, + {"rhs": "Equation2448", "lhs": "Equation2553"}, + {"rhs": "Equation2532", "lhs": "Equation2553"}, + {"rhs": "Equation2542", "lhs": "Equation2553"}, + {"rhs": "Equation2550", "lhs": "Equation2553"}, + {"rhs": "Equation2551", "lhs": "Equation2553"}, + {"rhs": "Equation2552", "lhs": "Equation2553"}, + {"rhs": "Equation2446", "lhs": "Equation2554"}, + {"rhs": "Equation2533", "lhs": "Equation2554"}, + {"rhs": "Equation2543", "lhs": "Equation2554"}, + {"rhs": "Equation2556", "lhs": "Equation2557"}, + {"rhs": "Equation2449", "lhs": "Equation2558"}, + {"rhs": "Equation2530", "lhs": "Equation2558"}, + {"rhs": "Equation2543", "lhs": "Equation2558"}, + {"rhs": "Equation2039", "lhs": "Equation256"}, + {"rhs": "Equation255", "lhs": "Equation256"}, + {"rhs": "Equation2560", "lhs": "Equation2561"}, + {"rhs": "Equation2452", "lhs": "Equation2562"}, + {"rhs": "Equation2536", "lhs": "Equation2562"}, + {"rhs": "Equation2546", "lhs": "Equation2562"}, + {"rhs": "Equation2550", "lhs": "Equation2562"}, + {"rhs": "Equation2554", "lhs": "Equation2562"}, + {"rhs": "Equation2558", "lhs": "Equation2562"}, + {"rhs": "Equation2565", "lhs": "Equation2566"}, + {"rhs": "Equation2456", "lhs": "Equation2567"}, + {"rhs": "Equation2493", "lhs": "Equation2567"}, + {"rhs": "Equation2530", "lhs": "Equation2567"}, + {"rhs": "Equation2456", "lhs": "Equation2568"}, + {"rhs": "Equation2494", "lhs": "Equation2568"}, + {"rhs": "Equation2531", "lhs": "Equation2568"}, + {"rhs": "Equation2457", "lhs": "Equation2569"}, + {"rhs": "Equation2493", "lhs": "Equation2569"}, + {"rhs": "Equation2531", "lhs": "Equation2569"}, + {"rhs": "Equation255", "lhs": "Equation257"}, + {"rhs": "Equation2655", "lhs": "Equation257"}, + {"rhs": "Equation2458", "lhs": "Equation2570"}, + {"rhs": "Equation2495", "lhs": "Equation2570"}, + {"rhs": "Equation2532", "lhs": "Equation2570"}, + {"rhs": "Equation2567", "lhs": "Equation2570"}, + {"rhs": "Equation2568", "lhs": "Equation2570"}, + {"rhs": "Equation2569", "lhs": "Equation2570"}, + {"rhs": "Equation2456", "lhs": "Equation2571"}, + {"rhs": "Equation2496", "lhs": "Equation2571"}, + {"rhs": "Equation2533", "lhs": "Equation2571"}, + {"rhs": "Equation2456", "lhs": "Equation2572"}, + {"rhs": "Equation2497", "lhs": "Equation2572"}, + {"rhs": "Equation2534", "lhs": "Equation2572"}, + {"rhs": "Equation2457", "lhs": "Equation2573"}, + {"rhs": "Equation2496", "lhs": "Equation2573"}, + {"rhs": "Equation2534", "lhs": "Equation2573"}, + {"rhs": "Equation2458", "lhs": "Equation2574"}, + {"rhs": "Equation2498", "lhs": "Equation2574"}, + {"rhs": "Equation2535", "lhs": "Equation2574"}, + {"rhs": "Equation2571", "lhs": "Equation2574"}, + {"rhs": "Equation2572", "lhs": "Equation2574"}, + {"rhs": "Equation2573", "lhs": "Equation2574"}, + {"rhs": "Equation2459", "lhs": "Equation2575"}, + {"rhs": "Equation2493", "lhs": "Equation2575"}, + {"rhs": "Equation2533", "lhs": "Equation2575"}, + {"rhs": "Equation2459", "lhs": "Equation2576"}, + {"rhs": "Equation2494", "lhs": "Equation2576"}, + {"rhs": "Equation2534", "lhs": "Equation2576"}, + {"rhs": "Equation2460", "lhs": "Equation2577"}, + {"rhs": "Equation2493", "lhs": "Equation2577"}, + {"rhs": "Equation2534", "lhs": "Equation2577"}, + {"rhs": "Equation2461", "lhs": "Equation2578"}, + {"rhs": "Equation2495", "lhs": "Equation2578"}, + {"rhs": "Equation2535", "lhs": "Equation2578"}, + {"rhs": "Equation2575", "lhs": "Equation2578"}, + {"rhs": "Equation2576", "lhs": "Equation2578"}, + {"rhs": "Equation2577", "lhs": "Equation2578"}, + {"rhs": "Equation2462", "lhs": "Equation2579"}, + {"rhs": "Equation2499", "lhs": "Equation2579"}, + {"rhs": "Equation2536", "lhs": "Equation2579"}, + {"rhs": "Equation2567", "lhs": "Equation2579"}, + {"rhs": "Equation2571", "lhs": "Equation2579"}, + {"rhs": "Equation2575", "lhs": "Equation2579"}, + {"rhs": "Equation255", "lhs": "Equation258"}, + {"rhs": "Equation2462", "lhs": "Equation2580"}, + {"rhs": "Equation2500", "lhs": "Equation2580"}, + {"rhs": "Equation2537", "lhs": "Equation2580"}, + {"rhs": "Equation2568", "lhs": "Equation2580"}, + {"rhs": "Equation2572", "lhs": "Equation2580"}, + {"rhs": "Equation2576", "lhs": "Equation2580"}, + {"rhs": "Equation2463", "lhs": "Equation2581"}, + {"rhs": "Equation2499", "lhs": "Equation2581"}, + {"rhs": "Equation2537", "lhs": "Equation2581"}, + {"rhs": "Equation2569", "lhs": "Equation2581"}, + {"rhs": "Equation2573", "lhs": "Equation2581"}, + {"rhs": "Equation2577", "lhs": "Equation2581"}, + {"rhs": "Equation2464", "lhs": "Equation2582"}, + {"rhs": "Equation2501", "lhs": "Equation2582"}, + {"rhs": "Equation2538", "lhs": "Equation2582"}, + {"rhs": "Equation2567", "lhs": "Equation2582"}, + {"rhs": "Equation2572", "lhs": "Equation2582"}, + {"rhs": "Equation2577", "lhs": "Equation2582"}, + {"rhs": "Equation2465", "lhs": "Equation2583"}, + {"rhs": "Equation2502", "lhs": "Equation2583"}, + {"rhs": "Equation2539", "lhs": "Equation2583"}, + {"rhs": "Equation2570", "lhs": "Equation2583"}, + {"rhs": "Equation2574", "lhs": "Equation2583"}, + {"rhs": "Equation2578", "lhs": "Equation2583"}, + {"rhs": "Equation2579", "lhs": "Equation2583"}, + {"rhs": "Equation2580", "lhs": "Equation2583"}, + {"rhs": "Equation2581", "lhs": "Equation2583"}, + {"rhs": "Equation2582", "lhs": "Equation2583"}, + {"rhs": "Equation2456", "lhs": "Equation2584"}, + {"rhs": "Equation2503", "lhs": "Equation2584"}, + {"rhs": "Equation2540", "lhs": "Equation2584"}, + {"rhs": "Equation2456", "lhs": "Equation2585"}, + {"rhs": "Equation2504", "lhs": "Equation2585"}, + {"rhs": "Equation2541", "lhs": "Equation2585"}, + {"rhs": "Equation2457", "lhs": "Equation2586"}, + {"rhs": "Equation2503", "lhs": "Equation2586"}, + {"rhs": "Equation2541", "lhs": "Equation2586"}, + {"rhs": "Equation2458", "lhs": "Equation2587"}, + {"rhs": "Equation2505", "lhs": "Equation2587"}, + {"rhs": "Equation2542", "lhs": "Equation2587"}, + {"rhs": "Equation2584", "lhs": "Equation2587"}, + {"rhs": "Equation2585", "lhs": "Equation2587"}, + {"rhs": "Equation2586", "lhs": "Equation2587"}, + {"rhs": "Equation2456", "lhs": "Equation2588"}, + {"rhs": "Equation2506", "lhs": "Equation2588"}, + {"rhs": "Equation2543", "lhs": "Equation2588"}, + {"rhs": "Equation2049", "lhs": "Equation259"}, + {"rhs": "Equation256", "lhs": "Equation259"}, + {"rhs": "Equation257", "lhs": "Equation259"}, + {"rhs": "Equation258", "lhs": "Equation259"}, + {"rhs": "Equation2658", "lhs": "Equation259"}, + {"rhs": "Equation2590", "lhs": "Equation2591"}, + {"rhs": "Equation2459", "lhs": "Equation2592"}, + {"rhs": "Equation2503", "lhs": "Equation2592"}, + {"rhs": "Equation2543", "lhs": "Equation2592"}, + {"rhs": "Equation2594", "lhs": "Equation2595"}, + {"rhs": "Equation2462", "lhs": "Equation2596"}, + {"rhs": "Equation2509", "lhs": "Equation2596"}, + {"rhs": "Equation2546", "lhs": "Equation2596"}, + {"rhs": "Equation2584", "lhs": "Equation2596"}, + {"rhs": "Equation2588", "lhs": "Equation2596"}, + {"rhs": "Equation2592", "lhs": "Equation2596"}, + {"rhs": "Equation1873", "lhs": "Equation26"}, + {"rhs": "Equation23", "lhs": "Equation26"}, + {"rhs": "Equation4135", "lhs": "Equation26"}, + {"rhs": "Equation255", "lhs": "Equation260"}, + {"rhs": "Equation2882", "lhs": "Equation260"}, + {"rhs": "Equation2599", "lhs": "Equation2600"}, + {"rhs": "Equation2466", "lhs": "Equation2601"}, + {"rhs": "Equation2493", "lhs": "Equation2601"}, + {"rhs": "Equation2540", "lhs": "Equation2601"}, + {"rhs": "Equation2466", "lhs": "Equation2602"}, + {"rhs": "Equation2494", "lhs": "Equation2602"}, + {"rhs": "Equation2541", "lhs": "Equation2602"}, + {"rhs": "Equation2467", "lhs": "Equation2603"}, + {"rhs": "Equation2493", "lhs": "Equation2603"}, + {"rhs": "Equation2541", "lhs": "Equation2603"}, + {"rhs": "Equation2468", "lhs": "Equation2604"}, + {"rhs": "Equation2495", "lhs": "Equation2604"}, + {"rhs": "Equation2542", "lhs": "Equation2604"}, + {"rhs": "Equation2601", "lhs": "Equation2604"}, + {"rhs": "Equation2602", "lhs": "Equation2604"}, + {"rhs": "Equation2603", "lhs": "Equation2604"}, + {"rhs": "Equation2466", "lhs": "Equation2605"}, + {"rhs": "Equation2496", "lhs": "Equation2605"}, + {"rhs": "Equation2543", "lhs": "Equation2605"}, + {"rhs": "Equation2607", "lhs": "Equation2608"}, + {"rhs": "Equation2469", "lhs": "Equation2609"}, + {"rhs": "Equation2493", "lhs": "Equation2609"}, + {"rhs": "Equation2543", "lhs": "Equation2609"}, + {"rhs": "Equation255", "lhs": "Equation261"}, + {"rhs": "Equation2611", "lhs": "Equation2612"}, + {"rhs": "Equation2472", "lhs": "Equation2613"}, + {"rhs": "Equation2499", "lhs": "Equation2613"}, + {"rhs": "Equation2546", "lhs": "Equation2613"}, + {"rhs": "Equation2601", "lhs": "Equation2613"}, + {"rhs": "Equation2605", "lhs": "Equation2613"}, + {"rhs": "Equation2609", "lhs": "Equation2613"}, + {"rhs": "Equation2616", "lhs": "Equation2617"}, + {"rhs": "Equation2476", "lhs": "Equation2618"}, + {"rhs": "Equation2513", "lhs": "Equation2618"}, + {"rhs": "Equation2550", "lhs": "Equation2618"}, + {"rhs": "Equation2567", "lhs": "Equation2618"}, + {"rhs": "Equation2584", "lhs": "Equation2618"}, + {"rhs": "Equation2601", "lhs": "Equation2618"}, + {"rhs": "Equation2476", "lhs": "Equation2619"}, + {"rhs": "Equation2514", "lhs": "Equation2619"}, + {"rhs": "Equation2551", "lhs": "Equation2619"}, + {"rhs": "Equation2568", "lhs": "Equation2619"}, + {"rhs": "Equation2585", "lhs": "Equation2619"}, + {"rhs": "Equation2602", "lhs": "Equation2619"}, + {"rhs": "Equation2059", "lhs": "Equation262"}, + {"rhs": "Equation256", "lhs": "Equation262"}, + {"rhs": "Equation260", "lhs": "Equation262"}, + {"rhs": "Equation261", "lhs": "Equation262"}, + {"rhs": "Equation2885", "lhs": "Equation262"}, + {"rhs": "Equation2477", "lhs": "Equation2620"}, + {"rhs": "Equation2513", "lhs": "Equation2620"}, + {"rhs": "Equation2551", "lhs": "Equation2620"}, + {"rhs": "Equation2569", "lhs": "Equation2620"}, + {"rhs": "Equation2586", "lhs": "Equation2620"}, + {"rhs": "Equation2603", "lhs": "Equation2620"}, + {"rhs": "Equation2478", "lhs": "Equation2621"}, + {"rhs": "Equation2515", "lhs": "Equation2621"}, + {"rhs": "Equation2552", "lhs": "Equation2621"}, + {"rhs": "Equation2567", "lhs": "Equation2621"}, + {"rhs": "Equation2585", "lhs": "Equation2621"}, + {"rhs": "Equation2603", "lhs": "Equation2621"}, + {"rhs": "Equation2479", "lhs": "Equation2622"}, + {"rhs": "Equation2516", "lhs": "Equation2622"}, + {"rhs": "Equation2553", "lhs": "Equation2622"}, + {"rhs": "Equation2570", "lhs": "Equation2622"}, + {"rhs": "Equation2587", "lhs": "Equation2622"}, + {"rhs": "Equation2604", "lhs": "Equation2622"}, + {"rhs": "Equation2618", "lhs": "Equation2622"}, + {"rhs": "Equation2619", "lhs": "Equation2622"}, + {"rhs": "Equation2620", "lhs": "Equation2622"}, + {"rhs": "Equation2621", "lhs": "Equation2622"}, + {"rhs": "Equation2476", "lhs": "Equation2623"}, + {"rhs": "Equation2517", "lhs": "Equation2623"}, + {"rhs": "Equation2554", "lhs": "Equation2623"}, + {"rhs": "Equation2571", "lhs": "Equation2623"}, + {"rhs": "Equation2588", "lhs": "Equation2623"}, + {"rhs": "Equation2605", "lhs": "Equation2623"}, + {"rhs": "Equation2626", "lhs": "Equation2627"}, + {"rhs": "Equation2480", "lhs": "Equation2628"}, + {"rhs": "Equation2513", "lhs": "Equation2628"}, + {"rhs": "Equation2554", "lhs": "Equation2628"}, + {"rhs": "Equation2575", "lhs": "Equation2628"}, + {"rhs": "Equation2592", "lhs": "Equation2628"}, + {"rhs": "Equation2609", "lhs": "Equation2628"}, + {"rhs": "Equation255", "lhs": "Equation263"}, + {"rhs": "Equation2631", "lhs": "Equation2632"}, + {"rhs": "Equation2484", "lhs": "Equation2633"}, + {"rhs": "Equation2521", "lhs": "Equation2633"}, + {"rhs": "Equation2558", "lhs": "Equation2633"}, + {"rhs": "Equation2567", "lhs": "Equation2633"}, + {"rhs": "Equation2588", "lhs": "Equation2633"}, + {"rhs": "Equation2609", "lhs": "Equation2633"}, + {"rhs": "Equation2636", "lhs": "Equation2637"}, + {"rhs": "Equation2488", "lhs": "Equation2638"}, + {"rhs": "Equation2525", "lhs": "Equation2638"}, + {"rhs": "Equation2562", "lhs": "Equation2638"}, + {"rhs": "Equation2579", "lhs": "Equation2638"}, + {"rhs": "Equation2596", "lhs": "Equation2638"}, + {"rhs": "Equation2613", "lhs": "Equation2638"}, + {"rhs": "Equation2618", "lhs": "Equation2638"}, + {"rhs": "Equation2623", "lhs": "Equation2638"}, + {"rhs": "Equation2628", "lhs": "Equation2638"}, + {"rhs": "Equation2633", "lhs": "Equation2638"}, + {"rhs": "Equation255", "lhs": "Equation264"}, + {"rhs": "Equation2642", "lhs": "Equation2643"}, + {"rhs": "Equation2644", "lhs": "Equation2645"}, + {"rhs": "Equation2644", "lhs": "Equation2646"}, + {"rhs": "Equation2644", "lhs": "Equation2647"}, + {"rhs": "Equation2645", "lhs": "Equation2648"}, + {"rhs": "Equation2646", "lhs": "Equation2648"}, + {"rhs": "Equation2647", "lhs": "Equation2648"}, + {"rhs": "Equation2644", "lhs": "Equation2649"}, + {"rhs": "Equation2069", "lhs": "Equation265"}, + {"rhs": "Equation256", "lhs": "Equation265"}, + {"rhs": "Equation263", "lhs": "Equation265"}, + {"rhs": "Equation264", "lhs": "Equation265"}, + {"rhs": "Equation2644", "lhs": "Equation2650"}, + {"rhs": "Equation2645", "lhs": "Equation2651"}, + {"rhs": "Equation2649", "lhs": "Equation2651"}, + {"rhs": "Equation2650", "lhs": "Equation2651"}, + {"rhs": "Equation2644", "lhs": "Equation2652"}, + {"rhs": "Equation2644", "lhs": "Equation2653"}, + {"rhs": "Equation2645", "lhs": "Equation2654"}, + {"rhs": "Equation2652", "lhs": "Equation2654"}, + {"rhs": "Equation2653", "lhs": "Equation2654"}, + {"rhs": "Equation2646", "lhs": "Equation2655"}, + {"rhs": "Equation2649", "lhs": "Equation2655"}, + {"rhs": "Equation2652", "lhs": "Equation2655"}, + {"rhs": "Equation2646", "lhs": "Equation2656"}, + {"rhs": "Equation2650", "lhs": "Equation2656"}, + {"rhs": "Equation2653", "lhs": "Equation2656"}, + {"rhs": "Equation2647", "lhs": "Equation2657"}, + {"rhs": "Equation2649", "lhs": "Equation2657"}, + {"rhs": "Equation2653", "lhs": "Equation2657"}, + {"rhs": "Equation2648", "lhs": "Equation2658"}, + {"rhs": "Equation2651", "lhs": "Equation2658"}, + {"rhs": "Equation2654", "lhs": "Equation2658"}, + {"rhs": "Equation2655", "lhs": "Equation2658"}, + {"rhs": "Equation2656", "lhs": "Equation2658"}, + {"rhs": "Equation2657", "lhs": "Equation2658"}, + {"rhs": "Equation2644", "lhs": "Equation2659"}, + {"rhs": "Equation257", "lhs": "Equation266"}, + {"rhs": "Equation260", "lhs": "Equation266"}, + {"rhs": "Equation263", "lhs": "Equation266"}, + {"rhs": "Equation2691", "lhs": "Equation266"}, + {"rhs": "Equation2894", "lhs": "Equation266"}, + {"rhs": "Equation2644", "lhs": "Equation2660"}, + {"rhs": "Equation2645", "lhs": "Equation2661"}, + {"rhs": "Equation2659", "lhs": "Equation2661"}, + {"rhs": "Equation2660", "lhs": "Equation2661"}, + {"rhs": "Equation2644", "lhs": "Equation2662"}, + {"rhs": "Equation2644", "lhs": "Equation2663"}, + {"rhs": "Equation2645", "lhs": "Equation2664"}, + {"rhs": "Equation2662", "lhs": "Equation2664"}, + {"rhs": "Equation2663", "lhs": "Equation2664"}, + {"rhs": "Equation2646", "lhs": "Equation2665"}, + {"rhs": "Equation2659", "lhs": "Equation2665"}, + {"rhs": "Equation2662", "lhs": "Equation2665"}, + {"rhs": "Equation2646", "lhs": "Equation2666"}, + {"rhs": "Equation2660", "lhs": "Equation2666"}, + {"rhs": "Equation2663", "lhs": "Equation2666"}, + {"rhs": "Equation2647", "lhs": "Equation2667"}, + {"rhs": "Equation2659", "lhs": "Equation2667"}, + {"rhs": "Equation2663", "lhs": "Equation2667"}, + {"rhs": "Equation2648", "lhs": "Equation2668"}, + {"rhs": "Equation2661", "lhs": "Equation2668"}, + {"rhs": "Equation2664", "lhs": "Equation2668"}, + {"rhs": "Equation2665", "lhs": "Equation2668"}, + {"rhs": "Equation2666", "lhs": "Equation2668"}, + {"rhs": "Equation2667", "lhs": "Equation2668"}, + {"rhs": "Equation2644", "lhs": "Equation2669"}, + {"rhs": "Equation257", "lhs": "Equation267"}, + {"rhs": "Equation261", "lhs": "Equation267"}, + {"rhs": "Equation264", "lhs": "Equation267"}, + {"rhs": "Equation2692", "lhs": "Equation267"}, + {"rhs": "Equation2644", "lhs": "Equation2670"}, + {"rhs": "Equation2645", "lhs": "Equation2671"}, + {"rhs": "Equation2669", "lhs": "Equation2671"}, + {"rhs": "Equation2670", "lhs": "Equation2671"}, + {"rhs": "Equation2644", "lhs": "Equation2672"}, + {"rhs": "Equation2644", "lhs": "Equation2673"}, + {"rhs": "Equation2645", "lhs": "Equation2674"}, + {"rhs": "Equation2672", "lhs": "Equation2674"}, + {"rhs": "Equation2673", "lhs": "Equation2674"}, + {"rhs": "Equation2646", "lhs": "Equation2675"}, + {"rhs": "Equation2669", "lhs": "Equation2675"}, + {"rhs": "Equation2672", "lhs": "Equation2675"}, + {"rhs": "Equation2646", "lhs": "Equation2676"}, + {"rhs": "Equation2670", "lhs": "Equation2676"}, + {"rhs": "Equation2673", "lhs": "Equation2676"}, + {"rhs": "Equation2647", "lhs": "Equation2677"}, + {"rhs": "Equation2669", "lhs": "Equation2677"}, + {"rhs": "Equation2673", "lhs": "Equation2677"}, + {"rhs": "Equation2648", "lhs": "Equation2678"}, + {"rhs": "Equation2671", "lhs": "Equation2678"}, + {"rhs": "Equation2674", "lhs": "Equation2678"}, + {"rhs": "Equation2675", "lhs": "Equation2678"}, + {"rhs": "Equation2676", "lhs": "Equation2678"}, + {"rhs": "Equation2677", "lhs": "Equation2678"}, + {"rhs": "Equation2649", "lhs": "Equation2679"}, + {"rhs": "Equation2659", "lhs": "Equation2679"}, + {"rhs": "Equation2669", "lhs": "Equation2679"}, + {"rhs": "Equation258", "lhs": "Equation268"}, + {"rhs": "Equation260", "lhs": "Equation268"}, + {"rhs": "Equation264", "lhs": "Equation268"}, + {"rhs": "Equation2897", "lhs": "Equation268"}, + {"rhs": "Equation2649", "lhs": "Equation2680"}, + {"rhs": "Equation2660", "lhs": "Equation2680"}, + {"rhs": "Equation2670", "lhs": "Equation2680"}, + {"rhs": "Equation2650", "lhs": "Equation2681"}, + {"rhs": "Equation2659", "lhs": "Equation2681"}, + {"rhs": "Equation2670", "lhs": "Equation2681"}, + {"rhs": "Equation2651", "lhs": "Equation2682"}, + {"rhs": "Equation2661", "lhs": "Equation2682"}, + {"rhs": "Equation2671", "lhs": "Equation2682"}, + {"rhs": "Equation2679", "lhs": "Equation2682"}, + {"rhs": "Equation2680", "lhs": "Equation2682"}, + {"rhs": "Equation2681", "lhs": "Equation2682"}, + {"rhs": "Equation2649", "lhs": "Equation2683"}, + {"rhs": "Equation2662", "lhs": "Equation2683"}, + {"rhs": "Equation2672", "lhs": "Equation2683"}, + {"rhs": "Equation2649", "lhs": "Equation2684"}, + {"rhs": "Equation2663", "lhs": "Equation2684"}, + {"rhs": "Equation2673", "lhs": "Equation2684"}, + {"rhs": "Equation2650", "lhs": "Equation2685"}, + {"rhs": "Equation2662", "lhs": "Equation2685"}, + {"rhs": "Equation2673", "lhs": "Equation2685"}, + {"rhs": "Equation2651", "lhs": "Equation2686"}, + {"rhs": "Equation2664", "lhs": "Equation2686"}, + {"rhs": "Equation2674", "lhs": "Equation2686"}, + {"rhs": "Equation2683", "lhs": "Equation2686"}, + {"rhs": "Equation2684", "lhs": "Equation2686"}, + {"rhs": "Equation2685", "lhs": "Equation2686"}, + {"rhs": "Equation2652", "lhs": "Equation2687"}, + {"rhs": "Equation2659", "lhs": "Equation2687"}, + {"rhs": "Equation2672", "lhs": "Equation2687"}, + {"rhs": "Equation2652", "lhs": "Equation2688"}, + {"rhs": "Equation2660", "lhs": "Equation2688"}, + {"rhs": "Equation2673", "lhs": "Equation2688"}, + {"rhs": "Equation2653", "lhs": "Equation2689"}, + {"rhs": "Equation2659", "lhs": "Equation2689"}, + {"rhs": "Equation2673", "lhs": "Equation2689"}, + {"rhs": "Equation2086", "lhs": "Equation269"}, + {"rhs": "Equation259", "lhs": "Equation269"}, + {"rhs": "Equation262", "lhs": "Equation269"}, + {"rhs": "Equation265", "lhs": "Equation269"}, + {"rhs": "Equation266", "lhs": "Equation269"}, + {"rhs": "Equation267", "lhs": "Equation269"}, + {"rhs": "Equation268", "lhs": "Equation269"}, + {"rhs": "Equation2695", "lhs": "Equation269"}, + {"rhs": "Equation2898", "lhs": "Equation269"}, + {"rhs": "Equation2654", "lhs": "Equation2690"}, + {"rhs": "Equation2661", "lhs": "Equation2690"}, + {"rhs": "Equation2674", "lhs": "Equation2690"}, + {"rhs": "Equation2687", "lhs": "Equation2690"}, + {"rhs": "Equation2688", "lhs": "Equation2690"}, + {"rhs": "Equation2689", "lhs": "Equation2690"}, + {"rhs": "Equation2655", "lhs": "Equation2691"}, + {"rhs": "Equation2665", "lhs": "Equation2691"}, + {"rhs": "Equation2675", "lhs": "Equation2691"}, + {"rhs": "Equation2679", "lhs": "Equation2691"}, + {"rhs": "Equation2683", "lhs": "Equation2691"}, + {"rhs": "Equation2687", "lhs": "Equation2691"}, + {"rhs": "Equation2655", "lhs": "Equation2692"}, + {"rhs": "Equation2666", "lhs": "Equation2692"}, + {"rhs": "Equation2676", "lhs": "Equation2692"}, + {"rhs": "Equation2680", "lhs": "Equation2692"}, + {"rhs": "Equation2684", "lhs": "Equation2692"}, + {"rhs": "Equation2688", "lhs": "Equation2692"}, + {"rhs": "Equation2656", "lhs": "Equation2693"}, + {"rhs": "Equation2665", "lhs": "Equation2693"}, + {"rhs": "Equation2676", "lhs": "Equation2693"}, + {"rhs": "Equation2681", "lhs": "Equation2693"}, + {"rhs": "Equation2685", "lhs": "Equation2693"}, + {"rhs": "Equation2689", "lhs": "Equation2693"}, + {"rhs": "Equation2657", "lhs": "Equation2694"}, + {"rhs": "Equation2667", "lhs": "Equation2694"}, + {"rhs": "Equation2677", "lhs": "Equation2694"}, + {"rhs": "Equation2679", "lhs": "Equation2694"}, + {"rhs": "Equation2684", "lhs": "Equation2694"}, + {"rhs": "Equation2689", "lhs": "Equation2694"}, + {"rhs": "Equation2658", "lhs": "Equation2695"}, + {"rhs": "Equation2668", "lhs": "Equation2695"}, + {"rhs": "Equation2678", "lhs": "Equation2695"}, + {"rhs": "Equation2682", "lhs": "Equation2695"}, + {"rhs": "Equation2686", "lhs": "Equation2695"}, + {"rhs": "Equation2690", "lhs": "Equation2695"}, + {"rhs": "Equation2691", "lhs": "Equation2695"}, + {"rhs": "Equation2692", "lhs": "Equation2695"}, + {"rhs": "Equation2693", "lhs": "Equation2695"}, + {"rhs": "Equation2694", "lhs": "Equation2695"}, + {"rhs": "Equation2644", "lhs": "Equation2696"}, + {"rhs": "Equation2644", "lhs": "Equation2697"}, + {"rhs": "Equation2645", "lhs": "Equation2698"}, + {"rhs": "Equation2696", "lhs": "Equation2698"}, + {"rhs": "Equation2697", "lhs": "Equation2698"}, + {"rhs": "Equation2644", "lhs": "Equation2699"}, + {"rhs": "Equation165", "lhs": "Equation27"}, + {"rhs": "Equation217", "lhs": "Equation27"}, + {"rhs": "Equation24", "lhs": "Equation27"}, + {"rhs": "Equation25", "lhs": "Equation27"}, + {"rhs": "Equation26", "lhs": "Equation27"}, + {"rhs": "Equation4136", "lhs": "Equation27"}, + {"rhs": "Equation255", "lhs": "Equation270"}, + {"rhs": "Equation3176", "lhs": "Equation270"}, + {"rhs": "Equation2644", "lhs": "Equation2700"}, + {"rhs": "Equation2645", "lhs": "Equation2701"}, + {"rhs": "Equation2699", "lhs": "Equation2701"}, + {"rhs": "Equation2700", "lhs": "Equation2701"}, + {"rhs": "Equation2646", "lhs": "Equation2702"}, + {"rhs": "Equation2696", "lhs": "Equation2702"}, + {"rhs": "Equation2699", "lhs": "Equation2702"}, + {"rhs": "Equation2646", "lhs": "Equation2703"}, + {"rhs": "Equation2697", "lhs": "Equation2703"}, + {"rhs": "Equation2700", "lhs": "Equation2703"}, + {"rhs": "Equation2647", "lhs": "Equation2704"}, + {"rhs": "Equation2696", "lhs": "Equation2704"}, + {"rhs": "Equation2700", "lhs": "Equation2704"}, + {"rhs": "Equation2648", "lhs": "Equation2705"}, + {"rhs": "Equation2698", "lhs": "Equation2705"}, + {"rhs": "Equation2701", "lhs": "Equation2705"}, + {"rhs": "Equation2702", "lhs": "Equation2705"}, + {"rhs": "Equation2703", "lhs": "Equation2705"}, + {"rhs": "Equation2704", "lhs": "Equation2705"}, + {"rhs": "Equation2644", "lhs": "Equation2706"}, + {"rhs": "Equation2644", "lhs": "Equation2707"}, + {"rhs": "Equation2645", "lhs": "Equation2708"}, + {"rhs": "Equation2706", "lhs": "Equation2708"}, + {"rhs": "Equation2707", "lhs": "Equation2708"}, + {"rhs": "Equation2644", "lhs": "Equation2709"}, + {"rhs": "Equation255", "lhs": "Equation271"}, + {"rhs": "Equation2644", "lhs": "Equation2710"}, + {"rhs": "Equation2645", "lhs": "Equation2711"}, + {"rhs": "Equation2709", "lhs": "Equation2711"}, + {"rhs": "Equation2710", "lhs": "Equation2711"}, + {"rhs": "Equation2646", "lhs": "Equation2712"}, + {"rhs": "Equation2706", "lhs": "Equation2712"}, + {"rhs": "Equation2709", "lhs": "Equation2712"}, + {"rhs": "Equation2646", "lhs": "Equation2713"}, + {"rhs": "Equation2707", "lhs": "Equation2713"}, + {"rhs": "Equation2710", "lhs": "Equation2713"}, + {"rhs": "Equation2647", "lhs": "Equation2714"}, + {"rhs": "Equation2706", "lhs": "Equation2714"}, + {"rhs": "Equation2710", "lhs": "Equation2714"}, + {"rhs": "Equation2648", "lhs": "Equation2715"}, + {"rhs": "Equation2708", "lhs": "Equation2715"}, + {"rhs": "Equation2711", "lhs": "Equation2715"}, + {"rhs": "Equation2712", "lhs": "Equation2715"}, + {"rhs": "Equation2713", "lhs": "Equation2715"}, + {"rhs": "Equation2714", "lhs": "Equation2715"}, + {"rhs": "Equation2649", "lhs": "Equation2716"}, + {"rhs": "Equation2696", "lhs": "Equation2716"}, + {"rhs": "Equation2706", "lhs": "Equation2716"}, + {"rhs": "Equation2649", "lhs": "Equation2717"}, + {"rhs": "Equation2697", "lhs": "Equation2717"}, + {"rhs": "Equation2707", "lhs": "Equation2717"}, + {"rhs": "Equation2650", "lhs": "Equation2718"}, + {"rhs": "Equation2696", "lhs": "Equation2718"}, + {"rhs": "Equation2707", "lhs": "Equation2718"}, + {"rhs": "Equation2651", "lhs": "Equation2719"}, + {"rhs": "Equation2698", "lhs": "Equation2719"}, + {"rhs": "Equation2708", "lhs": "Equation2719"}, + {"rhs": "Equation2716", "lhs": "Equation2719"}, + {"rhs": "Equation2717", "lhs": "Equation2719"}, + {"rhs": "Equation2718", "lhs": "Equation2719"}, + {"rhs": "Equation2096", "lhs": "Equation272"}, + {"rhs": "Equation256", "lhs": "Equation272"}, + {"rhs": "Equation270", "lhs": "Equation272"}, + {"rhs": "Equation271", "lhs": "Equation272"}, + {"rhs": "Equation3179", "lhs": "Equation272"}, + {"rhs": "Equation2649", "lhs": "Equation2720"}, + {"rhs": "Equation2699", "lhs": "Equation2720"}, + {"rhs": "Equation2709", "lhs": "Equation2720"}, + {"rhs": "Equation2649", "lhs": "Equation2721"}, + {"rhs": "Equation2700", "lhs": "Equation2721"}, + {"rhs": "Equation2710", "lhs": "Equation2721"}, + {"rhs": "Equation2650", "lhs": "Equation2722"}, + {"rhs": "Equation2699", "lhs": "Equation2722"}, + {"rhs": "Equation2710", "lhs": "Equation2722"}, + {"rhs": "Equation2651", "lhs": "Equation2723"}, + {"rhs": "Equation2701", "lhs": "Equation2723"}, + {"rhs": "Equation2711", "lhs": "Equation2723"}, + {"rhs": "Equation2720", "lhs": "Equation2723"}, + {"rhs": "Equation2721", "lhs": "Equation2723"}, + {"rhs": "Equation2722", "lhs": "Equation2723"}, + {"rhs": "Equation2652", "lhs": "Equation2724"}, + {"rhs": "Equation2696", "lhs": "Equation2724"}, + {"rhs": "Equation2709", "lhs": "Equation2724"}, + {"rhs": "Equation2652", "lhs": "Equation2725"}, + {"rhs": "Equation2697", "lhs": "Equation2725"}, + {"rhs": "Equation2710", "lhs": "Equation2725"}, + {"rhs": "Equation2653", "lhs": "Equation2726"}, + {"rhs": "Equation2696", "lhs": "Equation2726"}, + {"rhs": "Equation2710", "lhs": "Equation2726"}, + {"rhs": "Equation2654", "lhs": "Equation2727"}, + {"rhs": "Equation2698", "lhs": "Equation2727"}, + {"rhs": "Equation2711", "lhs": "Equation2727"}, + {"rhs": "Equation2724", "lhs": "Equation2727"}, + {"rhs": "Equation2725", "lhs": "Equation2727"}, + {"rhs": "Equation2726", "lhs": "Equation2727"}, + {"rhs": "Equation2655", "lhs": "Equation2728"}, + {"rhs": "Equation2702", "lhs": "Equation2728"}, + {"rhs": "Equation2712", "lhs": "Equation2728"}, + {"rhs": "Equation2716", "lhs": "Equation2728"}, + {"rhs": "Equation2720", "lhs": "Equation2728"}, + {"rhs": "Equation2724", "lhs": "Equation2728"}, + {"rhs": "Equation2655", "lhs": "Equation2729"}, + {"rhs": "Equation2703", "lhs": "Equation2729"}, + {"rhs": "Equation2713", "lhs": "Equation2729"}, + {"rhs": "Equation2717", "lhs": "Equation2729"}, + {"rhs": "Equation2721", "lhs": "Equation2729"}, + {"rhs": "Equation2725", "lhs": "Equation2729"}, + {"rhs": "Equation255", "lhs": "Equation273"}, + {"rhs": "Equation2656", "lhs": "Equation2730"}, + {"rhs": "Equation2702", "lhs": "Equation2730"}, + {"rhs": "Equation2713", "lhs": "Equation2730"}, + {"rhs": "Equation2718", "lhs": "Equation2730"}, + {"rhs": "Equation2722", "lhs": "Equation2730"}, + {"rhs": "Equation2726", "lhs": "Equation2730"}, + {"rhs": "Equation2657", "lhs": "Equation2731"}, + {"rhs": "Equation2704", "lhs": "Equation2731"}, + {"rhs": "Equation2714", "lhs": "Equation2731"}, + {"rhs": "Equation2716", "lhs": "Equation2731"}, + {"rhs": "Equation2721", "lhs": "Equation2731"}, + {"rhs": "Equation2726", "lhs": "Equation2731"}, + {"rhs": "Equation2658", "lhs": "Equation2732"}, + {"rhs": "Equation2705", "lhs": "Equation2732"}, + {"rhs": "Equation2715", "lhs": "Equation2732"}, + {"rhs": "Equation2719", "lhs": "Equation2732"}, + {"rhs": "Equation2723", "lhs": "Equation2732"}, + {"rhs": "Equation2727", "lhs": "Equation2732"}, + {"rhs": "Equation2728", "lhs": "Equation2732"}, + {"rhs": "Equation2729", "lhs": "Equation2732"}, + {"rhs": "Equation2730", "lhs": "Equation2732"}, + {"rhs": "Equation2731", "lhs": "Equation2732"}, + {"rhs": "Equation2644", "lhs": "Equation2733"}, + {"rhs": "Equation2644", "lhs": "Equation2734"}, + {"rhs": "Equation2645", "lhs": "Equation2735"}, + {"rhs": "Equation2733", "lhs": "Equation2735"}, + {"rhs": "Equation2734", "lhs": "Equation2735"}, + {"rhs": "Equation2644", "lhs": "Equation2736"}, + {"rhs": "Equation2644", "lhs": "Equation2737"}, + {"rhs": "Equation2645", "lhs": "Equation2738"}, + {"rhs": "Equation2736", "lhs": "Equation2738"}, + {"rhs": "Equation2737", "lhs": "Equation2738"}, + {"rhs": "Equation2646", "lhs": "Equation2739"}, + {"rhs": "Equation2733", "lhs": "Equation2739"}, + {"rhs": "Equation2736", "lhs": "Equation2739"}, + {"rhs": "Equation255", "lhs": "Equation274"}, + {"rhs": "Equation2646", "lhs": "Equation2740"}, + {"rhs": "Equation2734", "lhs": "Equation2740"}, + {"rhs": "Equation2737", "lhs": "Equation2740"}, + {"rhs": 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"Equation4240"}, + {"rhs": "Equation4126", "lhs": "Equation4241"}, + {"rhs": "Equation4173", "lhs": "Equation4241"}, + {"rhs": "Equation4228", "lhs": "Equation4241"}, + {"rhs": "Equation4232", "lhs": "Equation4241"}, + {"rhs": "Equation4237", "lhs": "Equation4241"}, + {"rhs": "Equation4100", "lhs": "Equation4242"}, + {"rhs": "Equation4137", "lhs": "Equation4242"}, + {"rhs": "Equation4174", "lhs": "Equation4242"}, + {"rhs": "Equation4191", "lhs": "Equation4242"}, + {"rhs": "Equation4208", "lhs": "Equation4242"}, + {"rhs": "Equation4225", "lhs": "Equation4242"}, + {"rhs": "Equation4100", "lhs": "Equation4243"}, + {"rhs": "Equation4138", "lhs": "Equation4243"}, + {"rhs": "Equation4175", "lhs": "Equation4243"}, + {"rhs": "Equation4192", "lhs": "Equation4243"}, + {"rhs": "Equation4209", "lhs": "Equation4243"}, + {"rhs": "Equation4226", "lhs": "Equation4243"}, + {"rhs": "Equation4101", "lhs": "Equation4244"}, + {"rhs": "Equation4137", "lhs": "Equation4244"}, + {"rhs": "Equation4175", "lhs": "Equation4244"}, + {"rhs": "Equation4193", "lhs": "Equation4244"}, + {"rhs": "Equation4210", "lhs": "Equation4244"}, + {"rhs": "Equation4227", "lhs": "Equation4244"}, + {"rhs": "Equation4102", "lhs": "Equation4245"}, + {"rhs": "Equation4139", "lhs": "Equation4245"}, + {"rhs": "Equation4176", "lhs": "Equation4245"}, + {"rhs": "Equation4191", "lhs": "Equation4245"}, + {"rhs": "Equation4209", "lhs": "Equation4245"}, + {"rhs": "Equation4227", "lhs": "Equation4245"}, + {"rhs": "Equation4103", "lhs": "Equation4246"}, + {"rhs": "Equation4140", "lhs": "Equation4246"}, + {"rhs": "Equation4177", "lhs": "Equation4246"}, + {"rhs": "Equation4194", "lhs": "Equation4246"}, + {"rhs": "Equation4211", "lhs": "Equation4246"}, + {"rhs": "Equation4228", "lhs": "Equation4246"}, + {"rhs": "Equation4242", "lhs": "Equation4246"}, + {"rhs": "Equation4243", "lhs": "Equation4246"}, + {"rhs": "Equation4244", "lhs": "Equation4246"}, + {"rhs": "Equation4245", "lhs": "Equation4246"}, + {"rhs": "Equation4100", "lhs": "Equation4247"}, + {"rhs": "Equation4141", "lhs": "Equation4247"}, + {"rhs": "Equation4178", "lhs": "Equation4247"}, + {"rhs": "Equation4195", "lhs": "Equation4247"}, + {"rhs": "Equation4212", "lhs": "Equation4247"}, + {"rhs": "Equation4229", "lhs": "Equation4247"}, + {"rhs": "Equation4230", "lhs": "Equation4248"}, + {"rhs": "Equation4141", "lhs": "Equation4249"}, + {"rhs": "Equation4197", "lhs": "Equation4249"}, + {"rhs": "Equation4214", "lhs": "Equation4249"}, + {"rhs": "Equation4231", "lhs": "Equation4249"}, + {"rhs": "Equation415", "lhs": "Equation425"}, + {"rhs": "Equation418", "lhs": "Equation425"}, + {"rhs": "Equation421", "lhs": "Equation425"}, + {"rhs": "Equation422", "lhs": "Equation425"}, + {"rhs": "Equation423", "lhs": "Equation425"}, + {"rhs": "Equation424", "lhs": "Equation425"}, + {"rhs": "Equation4143", "lhs": "Equation4250"}, + {"rhs": "Equation4180", "lhs": "Equation4250"}, + {"rhs": "Equation4195", "lhs": "Equation4250"}, + {"rhs": "Equation4231", "lhs": 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"Equation4255"}, + {"rhs": "Equation4180", "lhs": "Equation4255"}, + {"rhs": "Equation4199", "lhs": "Equation4255"}, + {"rhs": "Equation4235", "lhs": "Equation4255"}, + {"rhs": "Equation4140", "lhs": "Equation4256"}, + {"rhs": "Equation4181", "lhs": "Equation4256"}, + {"rhs": "Equation4202", "lhs": "Equation4256"}, + {"rhs": "Equation4219", "lhs": "Equation4256"}, + {"rhs": "Equation4252", "lhs": "Equation4256"}, + {"rhs": "Equation4108", "lhs": "Equation4257"}, + {"rhs": "Equation4145", "lhs": "Equation4257"}, + {"rhs": "Equation4182", "lhs": "Equation4257"}, + {"rhs": "Equation4191", "lhs": "Equation4257"}, + {"rhs": "Equation4212", "lhs": "Equation4257"}, + {"rhs": "Equation4233", "lhs": "Equation4257"}, + {"rhs": "Equation4145", "lhs": "Equation4259"}, + {"rhs": "Equation4193", "lhs": "Equation4259"}, + {"rhs": "Equation4214", "lhs": "Equation4259"}, + {"rhs": "Equation4235", "lhs": "Equation4259"}, + {"rhs": "Equation411", "lhs": "Equation426"}, + {"rhs": "Equation4147", "lhs": "Equation4260"}, + {"rhs": "Equation4184", "lhs": "Equation4260"}, + {"rhs": "Equation4191", "lhs": "Equation4260"}, + {"rhs": "Equation4235", "lhs": "Equation4260"}, + {"rhs": "Equation4148", "lhs": "Equation4261"}, + {"rhs": "Equation4185", "lhs": "Equation4261"}, + {"rhs": "Equation4194", "lhs": "Equation4261"}, + {"rhs": "Equation4215", "lhs": "Equation4261"}, + {"rhs": "Equation4257", "lhs": "Equation4261"}, + {"rhs": "Equation4112", "lhs": "Equation4262"}, + {"rhs": "Equation4149", "lhs": "Equation4262"}, + {"rhs": "Equation4186", "lhs": "Equation4262"}, + {"rhs": "Equation4203", "lhs": "Equation4262"}, + {"rhs": "Equation4220", "lhs": "Equation4262"}, + {"rhs": "Equation4237", "lhs": "Equation4262"}, + {"rhs": "Equation4242", "lhs": "Equation4262"}, + {"rhs": "Equation4247", "lhs": "Equation4262"}, + {"rhs": "Equation4252", "lhs": "Equation4262"}, + {"rhs": "Equation4257", "lhs": "Equation4262"}, + {"rhs": "Equation4258", "lhs": "Equation4263"}, + {"rhs": "Equation4149", "lhs": 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"Equation4338"}, + {"rhs": "Equation4319", "lhs": "Equation4338"}, + {"rhs": "Equation4322", "lhs": "Equation4338"}, + {"rhs": "Equation4328", "lhs": "Equation4338"}, + {"rhs": "Equation4333", "lhs": "Equation4338"}, + {"rhs": "Equation4334", "lhs": "Equation4338"}, + {"rhs": "Equation4335", "lhs": "Equation4338"}, + {"rhs": "Equation4336", "lhs": "Equation4338"}, + {"rhs": "Equation4337", "lhs": "Equation4338"}, + {"rhs": "Equation4268", "lhs": "Equation4339"}, + {"rhs": "Equation414", "lhs": "Equation434"}, + {"rhs": "Equation426", "lhs": "Equation434"}, + {"rhs": "Equation430", "lhs": "Equation434"}, + {"rhs": "Equation4269", "lhs": "Equation4340"}, + {"rhs": "Equation4270", "lhs": "Equation4341"}, + {"rhs": "Equation4271", "lhs": "Equation4342"}, + {"rhs": "Equation4339", "lhs": "Equation4342"}, + {"rhs": "Equation4340", "lhs": "Equation4342"}, + {"rhs": "Equation4341", "lhs": "Equation4342"}, + {"rhs": "Equation4343", "lhs": "Equation4344"}, + {"rhs": "Equation4343", "lhs": "Equation4345"}, + {"rhs": "Equation415", "lhs": "Equation435"}, + {"rhs": "Equation428", "lhs": "Equation435"}, + {"rhs": "Equation431", "lhs": "Equation435"}, + {"rhs": "Equation432", "lhs": "Equation435"}, + {"rhs": "Equation433", "lhs": "Equation435"}, + {"rhs": "Equation434", "lhs": "Equation435"}, + {"rhs": "Equation4272", "lhs": "Equation4351"}, + {"rhs": "Equation4339", "lhs": "Equation4352"}, + {"rhs": "Equation4350", "lhs": "Equation4352"}, + {"rhs": "Equation4351", "lhs": "Equation4352"}, + {"rhs": "Equation4340", "lhs": "Equation4354"}, + {"rhs": "Equation4348", "lhs": "Equation4354"}, + {"rhs": "Equation4351", "lhs": "Equation4354"}, + {"rhs": "Equation4280", "lhs": "Equation4355"}, + {"rhs": "Equation4341", "lhs": "Equation4355"}, + {"rhs": "Equation4343", "lhs": "Equation4355"}, + {"rhs": "Equation4346", "lhs": "Equation4355"}, + {"rhs": "Equation4351", "lhs": "Equation4355"}, + {"rhs": "Equation4281", "lhs": "Equation4356"}, + {"rhs": "Equation4342", "lhs": "Equation4356"}, + {"rhs": "Equation4344", "lhs": "Equation4356"}, + {"rhs": "Equation4345", "lhs": "Equation4356"}, + {"rhs": "Equation4352", "lhs": "Equation4356"}, + {"rhs": "Equation4353", "lhs": "Equation4356"}, + {"rhs": "Equation4354", "lhs": "Equation4356"}, + {"rhs": "Equation4355", "lhs": "Equation4356"}, + {"rhs": "Equation4282", "lhs": "Equation4357"}, + {"rhs": "Equation4315", "lhs": "Equation4357"}, + {"rhs": "Equation4339", "lhs": "Equation4357"}, + {"rhs": "Equation4283", "lhs": "Equation4358"}, + {"rhs": "Equation411", "lhs": "Equation436"}, + {"rhs": "Equation4287", "lhs": "Equation4360"}, + {"rhs": "Equation4316", "lhs": "Equation4360"}, + {"rhs": "Equation4340", "lhs": "Equation4360"}, + {"rhs": "Equation4289", "lhs": "Equation4361"}, + {"rhs": "Equation4319", "lhs": "Equation4361"}, + {"rhs": "Equation4342", "lhs": "Equation4361"}, + {"rhs": "Equation4357", "lhs": "Equation4361"}, + {"rhs": "Equation4358", "lhs": "Equation4361"}, + {"rhs": "Equation4359", "lhs": 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{"rhs": "Equation4603", "lhs": "Equation4627"}, + {"rhs": "Equation4612", "lhs": "Equation4627"}, + {"rhs": "Equation4614", "lhs": "Equation4627"}, + {"rhs": "Equation4619", "lhs": "Equation4627"}, + {"rhs": "Equation4596", "lhs": "Equation4628"}, + {"rhs": "Equation4604", "lhs": "Equation4628"}, + {"rhs": "Equation4610", "lhs": "Equation4628"}, + {"rhs": "Equation4617", "lhs": "Equation4628"}, + {"rhs": "Equation4618", "lhs": "Equation4628"}, + {"rhs": "Equation4623", "lhs": "Equation4628"}, + {"rhs": "Equation4624", "lhs": "Equation4628"}, + {"rhs": "Equation4625", "lhs": "Equation4628"}, + {"rhs": "Equation4626", "lhs": "Equation4628"}, + {"rhs": "Equation4627", "lhs": "Equation4628"}, + {"rhs": "Equation411", "lhs": "Equation463"}, + {"rhs": "Equation4583", "lhs": "Equation4630"}, + {"rhs": "Equation4629", "lhs": "Equation4630"}, + {"rhs": "Equation4584", "lhs": "Equation4631"}, + {"rhs": "Equation4629", "lhs": "Equation4632"}, + {"rhs": "Equation4585", "lhs": "Equation4633"}, + {"rhs": "Equation4629", "lhs": "Equation4633"}, + {"rhs": "Equation4630", "lhs": "Equation4634"}, + {"rhs": "Equation4631", "lhs": "Equation4634"}, + {"rhs": "Equation4632", "lhs": "Equation4634"}, + {"rhs": "Equation4633", "lhs": "Equation4634"}, + {"rhs": "Equation4635", "lhs": "Equation4637"}, + {"rhs": "Equation4636", "lhs": "Equation4637"}, + {"rhs": "Equation4635", "lhs": "Equation4638"}, + {"rhs": "Equation411", "lhs": "Equation464"}, + {"rhs": "Equation4585", "lhs": "Equation4640"}, + {"rhs": "Equation4635", "lhs": "Equation4640"}, + {"rhs": "Equation4587", "lhs": "Equation4642"}, + {"rhs": "Equation4635", "lhs": "Equation4642"}, + {"rhs": "Equation4636", "lhs": "Equation4643"}, + {"rhs": "Equation4587", "lhs": "Equation4645"}, + {"rhs": "Equation4587", "lhs": "Equation4646"}, + {"rhs": "Equation4629", "lhs": "Equation4646"}, + {"rhs": "Equation4588", "lhs": "Equation4647"}, + {"rhs": "Equation4589", "lhs": "Equation4648"}, + {"rhs": "Equation4630", "lhs": "Equation4648"}, + {"rhs": "Equation4645", "lhs": "Equation4648"}, + {"rhs": "Equation4646", "lhs": "Equation4648"}, + {"rhs": "Equation4647", "lhs": "Equation4648"}, + {"rhs": "Equation4631", "lhs": "Equation4649"}, + {"rhs": "Equation4638", "lhs": "Equation4649"}, + {"rhs": "Equation4642", "lhs": "Equation4649"}, + {"rhs": "Equation4645", "lhs": "Equation4649"}, + {"rhs": "Equation412", "lhs": "Equation465"}, + {"rhs": "Equation463", "lhs": "Equation465"}, + {"rhs": "Equation464", "lhs": "Equation465"}, + {"rhs": "Equation4594", "lhs": "Equation4651"}, + {"rhs": "Equation4631", "lhs": "Equation4651"}, + {"rhs": "Equation4636", "lhs": "Equation4651"}, + {"rhs": "Equation4639", "lhs": "Equation4651"}, + {"rhs": "Equation4647", "lhs": "Equation4651"}, + {"rhs": "Equation4595", "lhs": "Equation4652"}, + {"rhs": "Equation4633", "lhs": "Equation4652"}, + {"rhs": "Equation4640", "lhs": "Equation4652"}, + {"rhs": "Equation4642", "lhs": "Equation4652"}, + {"rhs": "Equation4646", "lhs": "Equation4652"}, + {"rhs": "Equation4596", "lhs": "Equation4653"}, + {"rhs": "Equation4634", "lhs": "Equation4653"}, + {"rhs": "Equation4637", "lhs": "Equation4653"}, + {"rhs": "Equation4643", "lhs": "Equation4653"}, + {"rhs": "Equation4648", "lhs": "Equation4653"}, + {"rhs": "Equation4649", "lhs": "Equation4653"}, + {"rhs": "Equation4650", "lhs": "Equation4653"}, + {"rhs": "Equation4651", "lhs": "Equation4653"}, + {"rhs": "Equation4652", "lhs": "Equation4653"}, + {"rhs": "Equation4583", "lhs": "Equation4654"}, + {"rhs": "Equation4584", "lhs": "Equation4655"}, + {"rhs": "Equation4585", "lhs": "Equation4656"}, + {"rhs": "Equation4586", "lhs": "Equation4657"}, + {"rhs": "Equation4654", "lhs": "Equation4657"}, + {"rhs": "Equation4655", "lhs": "Equation4657"}, + {"rhs": "Equation4656", "lhs": "Equation4657"}, + {"rhs": "Equation4658", "lhs": "Equation4659"}, + {"rhs": "Equation411", "lhs": "Equation466"}, + {"rhs": "Equation4658", "lhs": "Equation4660"}, + {"rhs": "Equation4587", "lhs": "Equation4666"}, + {"rhs": "Equation4654", "lhs": "Equation4667"}, + {"rhs": "Equation4665", "lhs": "Equation4667"}, + {"rhs": "Equation4666", "lhs": "Equation4667"}, + {"rhs": "Equation4655", "lhs": "Equation4669"}, + {"rhs": "Equation4663", "lhs": "Equation4669"}, + {"rhs": "Equation4666", "lhs": "Equation4669"}, + {"rhs": "Equation411", "lhs": "Equation467"}, + {"rhs": "Equation4595", "lhs": "Equation4670"}, + {"rhs": "Equation4656", "lhs": "Equation4670"}, + {"rhs": "Equation4658", "lhs": "Equation4670"}, + {"rhs": "Equation4661", "lhs": "Equation4670"}, + {"rhs": "Equation4666", "lhs": "Equation4670"}, + {"rhs": "Equation4596", "lhs": "Equation4671"}, + {"rhs": "Equation4657", "lhs": "Equation4671"}, + {"rhs": "Equation4659", "lhs": "Equation4671"}, + {"rhs": "Equation4660", "lhs": "Equation4671"}, + {"rhs": "Equation4667", "lhs": "Equation4671"}, + {"rhs": "Equation4668", "lhs": "Equation4671"}, + {"rhs": "Equation4669", "lhs": "Equation4671"}, + {"rhs": "Equation4670", "lhs": "Equation4671"}, + {"rhs": "Equation4597", "lhs": "Equation4672"}, + {"rhs": "Equation4630", "lhs": "Equation4672"}, + {"rhs": "Equation4654", "lhs": "Equation4672"}, + {"rhs": "Equation4598", "lhs": "Equation4673"}, + {"rhs": "Equation4602", "lhs": "Equation4675"}, + {"rhs": "Equation4631", "lhs": "Equation4675"}, + {"rhs": "Equation4655", "lhs": "Equation4675"}, + {"rhs": "Equation4604", "lhs": "Equation4676"}, + {"rhs": "Equation4634", "lhs": "Equation4676"}, + {"rhs": "Equation4657", "lhs": "Equation4676"}, + {"rhs": "Equation4672", "lhs": "Equation4676"}, + {"rhs": "Equation4673", "lhs": "Equation4676"}, + {"rhs": "Equation4674", "lhs": "Equation4676"}, + {"rhs": "Equation4675", "lhs": "Equation4676"}, + {"rhs": "Equation4635", "lhs": "Equation4677"}, + {"rhs": "Equation4597", "lhs": "Equation4678"}, + {"rhs": "Equation4637", "lhs": "Equation4678"}, + {"rhs": "Equation4659", "lhs": "Equation4678"}, + {"rhs": "Equation4677", "lhs": "Equation4678"}, + {"rhs": "Equation4598", "lhs": "Equation4679"}, + {"rhs": "Equation4635", "lhs": "Equation4679"}, + {"rhs": "Equation412", "lhs": "Equation468"}, + {"rhs": "Equation466", "lhs": "Equation468"}, + {"rhs": "Equation467", "lhs": "Equation468"}, + {"rhs": "Equation4680", "lhs": "Equation4683"}, + {"rhs": "Equation4605", "lhs": "Equation4684"}, + {"rhs": "Equation4610", "lhs": "Equation4686"}, + {"rhs": "Equation4631", "lhs": "Equation4686"}, + {"rhs": "Equation4660", "lhs": "Equation4686"}, + {"rhs": "Equation4684", "lhs": "Equation4686"}, + {"rhs": "Equation4687", "lhs": "Equation4688"}, + {"rhs": "Equation4615", "lhs": "Equation4689"}, + {"rhs": "Equation4645", "lhs": "Equation4689"}, + {"rhs": "Equation4666", "lhs": "Equation4689"}, + {"rhs": "Equation413", "lhs": "Equation469"}, + {"rhs": "Equation463", "lhs": "Equation469"}, + {"rhs": "Equation466", "lhs": "Equation469"}, + {"rhs": "Equation4617", "lhs": "Equation4690"}, + {"rhs": "Equation4648", "lhs": "Equation4690"}, + {"rhs": "Equation4667", "lhs": "Equation4690"}, + {"rhs": 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{"rhs": "Equation420", "lhs": "Equation493"}, + {"rhs": "Equation463", "lhs": "Equation493"}, + {"rhs": "Equation477", "lhs": "Equation493"}, + {"rhs": "Equation421", "lhs": "Equation494"}, + {"rhs": "Equation465", "lhs": "Equation494"}, + {"rhs": "Equation478", "lhs": "Equation494"}, + {"rhs": "Equation491", "lhs": "Equation494"}, + {"rhs": "Equation492", "lhs": "Equation494"}, + {"rhs": "Equation493", "lhs": "Equation494"}, + {"rhs": "Equation422", "lhs": "Equation495"}, + {"rhs": "Equation469", "lhs": "Equation495"}, + {"rhs": "Equation479", "lhs": "Equation495"}, + {"rhs": "Equation483", "lhs": "Equation495"}, + {"rhs": "Equation487", "lhs": "Equation495"}, + {"rhs": "Equation491", "lhs": "Equation495"}, + {"rhs": "Equation422", "lhs": "Equation496"}, + {"rhs": "Equation470", "lhs": "Equation496"}, + {"rhs": "Equation480", "lhs": "Equation496"}, + {"rhs": "Equation484", "lhs": "Equation496"}, + {"rhs": "Equation488", "lhs": "Equation496"}, + {"rhs": "Equation492", "lhs": 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"lhs": "Equation499"}, + {"rhs": "Equation498", "lhs": "Equation499"}, + {"rhs": "Equation3", "lhs": "Equation5"}, + {"rhs": "Equation34", "lhs": "Equation5"}, + {"rhs": "Equation47", "lhs": "Equation50"}, + {"rhs": "Equation411", "lhs": "Equation500"}, + {"rhs": "Equation411", "lhs": "Equation501"}, + {"rhs": "Equation412", "lhs": "Equation502"}, + {"rhs": "Equation500", "lhs": "Equation502"}, + {"rhs": "Equation501", "lhs": "Equation502"}, + {"rhs": "Equation411", "lhs": "Equation503"}, + {"rhs": "Equation411", "lhs": "Equation504"}, + {"rhs": "Equation412", "lhs": "Equation505"}, + {"rhs": "Equation503", "lhs": "Equation505"}, + {"rhs": "Equation504", "lhs": "Equation505"}, + {"rhs": "Equation413", "lhs": "Equation506"}, + {"rhs": "Equation500", "lhs": "Equation506"}, + {"rhs": "Equation503", "lhs": "Equation506"}, + {"rhs": "Equation413", "lhs": "Equation507"}, + {"rhs": "Equation501", "lhs": "Equation507"}, + {"rhs": "Equation504", "lhs": "Equation507"}, + {"rhs": "Equation414", 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{"rhs": "Equation501", "lhs": "Equation538"}, + {"rhs": "Equation427", "lhs": "Equation539"}, + {"rhs": "Equation463", "lhs": "Equation539"}, + {"rhs": "Equation501", "lhs": "Equation539"}, + {"rhs": "Equation435", "lhs": "Equation54"}, + {"rhs": "Equation48", "lhs": "Equation54"}, + {"rhs": "Equation52", "lhs": "Equation54"}, + {"rhs": "Equation53", "lhs": "Equation54"}, + {"rhs": "Equation855", "lhs": "Equation54"}, + {"rhs": "Equation428", "lhs": "Equation540"}, + {"rhs": "Equation465", "lhs": "Equation540"}, + {"rhs": "Equation502", "lhs": "Equation540"}, + {"rhs": "Equation537", "lhs": "Equation540"}, + {"rhs": "Equation538", "lhs": "Equation540"}, + {"rhs": "Equation539", "lhs": "Equation540"}, + {"rhs": "Equation426", "lhs": "Equation541"}, + {"rhs": "Equation466", "lhs": "Equation541"}, + {"rhs": "Equation503", "lhs": "Equation541"}, + {"rhs": "Equation426", "lhs": "Equation542"}, + {"rhs": "Equation467", "lhs": "Equation542"}, + {"rhs": "Equation504", "lhs": "Equation542"}, + {"rhs": "Equation427", "lhs": "Equation543"}, + {"rhs": "Equation466", "lhs": "Equation543"}, + {"rhs": "Equation504", "lhs": "Equation543"}, + {"rhs": "Equation428", "lhs": "Equation544"}, + {"rhs": "Equation468", "lhs": "Equation544"}, + {"rhs": "Equation505", "lhs": "Equation544"}, + {"rhs": "Equation541", "lhs": "Equation544"}, + {"rhs": "Equation542", "lhs": "Equation544"}, + {"rhs": "Equation543", "lhs": "Equation544"}, + {"rhs": "Equation429", "lhs": "Equation545"}, + {"rhs": "Equation463", "lhs": "Equation545"}, + {"rhs": "Equation503", "lhs": "Equation545"}, + {"rhs": "Equation429", "lhs": "Equation546"}, + {"rhs": "Equation464", "lhs": "Equation546"}, + {"rhs": "Equation504", "lhs": "Equation546"}, + {"rhs": "Equation430", "lhs": "Equation547"}, + {"rhs": "Equation463", "lhs": "Equation547"}, + {"rhs": "Equation504", "lhs": "Equation547"}, + {"rhs": "Equation431", "lhs": "Equation548"}, + {"rhs": "Equation465", "lhs": "Equation548"}, + {"rhs": "Equation505", "lhs": 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"lhs": "Equation551"}, + {"rhs": "Equation547", "lhs": "Equation551"}, + {"rhs": "Equation434", "lhs": "Equation552"}, + {"rhs": "Equation471", "lhs": "Equation552"}, + {"rhs": "Equation508", "lhs": "Equation552"}, + {"rhs": "Equation537", "lhs": "Equation552"}, + {"rhs": "Equation542", "lhs": "Equation552"}, + {"rhs": "Equation547", "lhs": "Equation552"}, + {"rhs": "Equation435", "lhs": "Equation553"}, + {"rhs": "Equation472", "lhs": "Equation553"}, + {"rhs": "Equation509", "lhs": "Equation553"}, + {"rhs": "Equation540", "lhs": "Equation553"}, + {"rhs": "Equation544", "lhs": "Equation553"}, + {"rhs": "Equation548", "lhs": "Equation553"}, + {"rhs": "Equation549", "lhs": "Equation553"}, + {"rhs": "Equation550", "lhs": "Equation553"}, + {"rhs": "Equation551", "lhs": "Equation553"}, + {"rhs": "Equation552", "lhs": "Equation553"}, + {"rhs": "Equation426", "lhs": "Equation554"}, + {"rhs": "Equation473", "lhs": "Equation554"}, + {"rhs": "Equation510", "lhs": "Equation554"}, + {"rhs": "Equation426", "lhs": "Equation555"}, + {"rhs": "Equation474", "lhs": "Equation555"}, + {"rhs": "Equation511", "lhs": "Equation555"}, + {"rhs": "Equation427", "lhs": "Equation556"}, + {"rhs": "Equation473", "lhs": "Equation556"}, + {"rhs": "Equation511", "lhs": "Equation556"}, + {"rhs": "Equation428", "lhs": "Equation557"}, + {"rhs": "Equation475", "lhs": "Equation557"}, + {"rhs": "Equation512", "lhs": "Equation557"}, + {"rhs": "Equation554", "lhs": "Equation557"}, + {"rhs": "Equation555", "lhs": "Equation557"}, + {"rhs": "Equation556", "lhs": "Equation557"}, + {"rhs": "Equation426", "lhs": "Equation558"}, + {"rhs": "Equation476", "lhs": "Equation558"}, + {"rhs": "Equation513", "lhs": "Equation558"}, + {"rhs": "Equation47", "lhs": "Equation56"}, + {"rhs": "Equation560", "lhs": "Equation561"}, + {"rhs": "Equation429", "lhs": "Equation562"}, + {"rhs": "Equation473", "lhs": "Equation562"}, + {"rhs": "Equation513", "lhs": "Equation562"}, + {"rhs": "Equation564", "lhs": "Equation565"}, + {"rhs": "Equation432", "lhs": "Equation566"}, + {"rhs": "Equation479", "lhs": "Equation566"}, + {"rhs": "Equation516", "lhs": "Equation566"}, + {"rhs": "Equation554", "lhs": "Equation566"}, + {"rhs": "Equation558", "lhs": "Equation566"}, + {"rhs": "Equation562", "lhs": "Equation566"}, + {"rhs": "Equation445", "lhs": "Equation57"}, + {"rhs": "Equation48", "lhs": "Equation57"}, + {"rhs": "Equation55", "lhs": "Equation57"}, + {"rhs": "Equation56", "lhs": "Equation57"}, + {"rhs": "Equation569", "lhs": "Equation570"}, + {"rhs": "Equation436", "lhs": "Equation571"}, + {"rhs": "Equation463", "lhs": "Equation571"}, + {"rhs": "Equation510", "lhs": "Equation571"}, + {"rhs": "Equation436", "lhs": "Equation572"}, + {"rhs": "Equation464", "lhs": "Equation572"}, + {"rhs": "Equation511", "lhs": "Equation572"}, + {"rhs": "Equation437", "lhs": "Equation573"}, + {"rhs": "Equation463", "lhs": "Equation573"}, + {"rhs": "Equation511", "lhs": "Equation573"}, + {"rhs": "Equation438", "lhs": "Equation574"}, + {"rhs": "Equation465", "lhs": "Equation574"}, + {"rhs": "Equation512", "lhs": "Equation574"}, + {"rhs": "Equation571", "lhs": "Equation574"}, + {"rhs": "Equation572", "lhs": "Equation574"}, + {"rhs": "Equation573", "lhs": "Equation574"}, + {"rhs": "Equation436", "lhs": "Equation575"}, + {"rhs": "Equation466", "lhs": "Equation575"}, + {"rhs": "Equation513", "lhs": "Equation575"}, + {"rhs": "Equation577", "lhs": "Equation578"}, + {"rhs": "Equation439", "lhs": "Equation579"}, + {"rhs": "Equation463", "lhs": "Equation579"}, + {"rhs": "Equation513", "lhs": "Equation579"}, + {"rhs": "Equation49", "lhs": "Equation58"}, + {"rhs": "Equation52", "lhs": "Equation58"}, + {"rhs": "Equation55", "lhs": "Equation58"}, + {"rhs": "Equation661", "lhs": "Equation58"}, + {"rhs": "Equation864", "lhs": "Equation58"}, + {"rhs": "Equation581", "lhs": "Equation582"}, + {"rhs": "Equation442", "lhs": "Equation583"}, + {"rhs": "Equation469", "lhs": "Equation583"}, + {"rhs": "Equation516", "lhs": "Equation583"}, + {"rhs": "Equation571", "lhs": "Equation583"}, + {"rhs": "Equation575", "lhs": "Equation583"}, + {"rhs": "Equation579", "lhs": "Equation583"}, + {"rhs": "Equation586", "lhs": "Equation587"}, + {"rhs": "Equation446", "lhs": "Equation588"}, + {"rhs": "Equation483", "lhs": "Equation588"}, + {"rhs": "Equation520", "lhs": "Equation588"}, + {"rhs": "Equation537", "lhs": "Equation588"}, + {"rhs": "Equation554", "lhs": "Equation588"}, + {"rhs": "Equation571", "lhs": "Equation588"}, + {"rhs": "Equation446", "lhs": "Equation589"}, + {"rhs": "Equation484", "lhs": "Equation589"}, + {"rhs": "Equation521", "lhs": "Equation589"}, + {"rhs": "Equation538", "lhs": "Equation589"}, + {"rhs": "Equation555", "lhs": "Equation589"}, + {"rhs": "Equation572", "lhs": "Equation589"}, + {"rhs": "Equation49", "lhs": "Equation59"}, + {"rhs": "Equation53", "lhs": "Equation59"}, + {"rhs": "Equation56", "lhs": "Equation59"}, + {"rhs": "Equation662", "lhs": "Equation59"}, + {"rhs": "Equation447", "lhs": "Equation590"}, + {"rhs": "Equation483", "lhs": "Equation590"}, + {"rhs": "Equation521", "lhs": "Equation590"}, + {"rhs": "Equation539", "lhs": "Equation590"}, + {"rhs": "Equation556", "lhs": "Equation590"}, + {"rhs": "Equation573", "lhs": "Equation590"}, + {"rhs": "Equation448", "lhs": "Equation591"}, + {"rhs": "Equation485", "lhs": "Equation591"}, + {"rhs": "Equation522", "lhs": "Equation591"}, + {"rhs": "Equation537", "lhs": "Equation591"}, + {"rhs": "Equation555", "lhs": "Equation591"}, + {"rhs": "Equation573", "lhs": "Equation591"}, + {"rhs": "Equation449", "lhs": "Equation592"}, + {"rhs": "Equation486", "lhs": "Equation592"}, + {"rhs": "Equation523", "lhs": "Equation592"}, + {"rhs": "Equation540", "lhs": "Equation592"}, + {"rhs": "Equation557", "lhs": "Equation592"}, + {"rhs": "Equation574", "lhs": "Equation592"}, + {"rhs": "Equation588", "lhs": "Equation592"}, + {"rhs": "Equation589", "lhs": "Equation592"}, + {"rhs": "Equation590", "lhs": "Equation592"}, + {"rhs": "Equation591", "lhs": 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{"rhs": "Equation691", "lhs": "Equation699"}, + {"rhs": "Equation695", "lhs": "Equation699"}, + {"rhs": "Equation1201", "lhs": "Equation7"}, + {"rhs": "Equation123", "lhs": "Equation7"}, + {"rhs": "Equation1311", "lhs": "Equation7"}, + {"rhs": "Equation1365", "lhs": "Equation7"}, + {"rhs": "Equation137", "lhs": "Equation7"}, + {"rhs": "Equation15", "lhs": "Equation7"}, + {"rhs": "Equation227", "lhs": "Equation7"}, + {"rhs": "Equation2380", "lhs": "Equation7"}, + {"rhs": "Equation241", "lhs": "Equation7"}, + {"rhs": "Equation2419", "lhs": "Equation7"}, + {"rhs": "Equation2529", "lhs": "Equation7"}, + {"rhs": "Equation279", "lhs": "Equation7"}, + {"rhs": "Equation2935", "lhs": "Equation7"}, + {"rhs": "Equation2989", "lhs": "Equation7"}, + {"rhs": "Equation30", "lhs": "Equation7"}, + {"rhs": "Equation3138", "lhs": "Equation7"}, + {"rhs": "Equation4", "lhs": "Equation7"}, + {"rhs": "Equation5", "lhs": "Equation7"}, + {"rhs": "Equation613", "lhs": "Equation7"}, + {"rhs": "Equation1567", 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"lhs": "Equation702"}, + {"rhs": "Equation698", "lhs": "Equation702"}, + {"rhs": "Equation699", "lhs": "Equation702"}, + {"rhs": "Equation700", "lhs": "Equation702"}, + {"rhs": "Equation701", "lhs": "Equation702"}, + {"rhs": "Equation614", "lhs": "Equation703"}, + {"rhs": "Equation614", "lhs": "Equation704"}, + {"rhs": "Equation615", "lhs": "Equation705"}, + {"rhs": "Equation703", "lhs": "Equation705"}, + {"rhs": "Equation704", "lhs": "Equation705"}, + {"rhs": "Equation614", "lhs": "Equation706"}, + {"rhs": "Equation614", "lhs": "Equation707"}, + {"rhs": "Equation615", "lhs": "Equation708"}, + {"rhs": "Equation706", "lhs": "Equation708"}, + {"rhs": "Equation707", "lhs": "Equation708"}, + {"rhs": "Equation616", "lhs": "Equation709"}, + {"rhs": "Equation703", "lhs": "Equation709"}, + {"rhs": "Equation706", "lhs": "Equation709"}, + {"rhs": "Equation1568", "lhs": "Equation71"}, + {"rhs": "Equation499", "lhs": "Equation71"}, + {"rhs": "Equation51", "lhs": "Equation71"}, + {"rhs": "Equation64", "lhs": "Equation71"}, + {"rhs": "Equation67", "lhs": "Equation71"}, + {"rhs": "Equation68", "lhs": "Equation71"}, + {"rhs": "Equation69", "lhs": "Equation71"}, + {"rhs": "Equation70", "lhs": "Equation71"}, + {"rhs": "Equation702", "lhs": "Equation71"}, + {"rhs": "Equation616", "lhs": "Equation710"}, + {"rhs": "Equation704", "lhs": "Equation710"}, + {"rhs": "Equation707", "lhs": "Equation710"}, + {"rhs": "Equation617", "lhs": "Equation711"}, + {"rhs": "Equation703", "lhs": "Equation711"}, + {"rhs": "Equation707", "lhs": "Equation711"}, + {"rhs": "Equation618", "lhs": "Equation712"}, + {"rhs": "Equation705", "lhs": "Equation712"}, + {"rhs": "Equation708", "lhs": "Equation712"}, + {"rhs": "Equation709", "lhs": "Equation712"}, + {"rhs": "Equation710", "lhs": "Equation712"}, + {"rhs": "Equation711", "lhs": "Equation712"}, + {"rhs": "Equation614", "lhs": "Equation713"}, + {"rhs": "Equation614", "lhs": "Equation714"}, + {"rhs": "Equation615", "lhs": "Equation715"}, + {"rhs": "Equation713", "lhs": "Equation715"}, + {"rhs": "Equation714", "lhs": "Equation715"}, + {"rhs": "Equation614", "lhs": "Equation716"}, + {"rhs": "Equation717", "lhs": "Equation718"}, + {"rhs": "Equation616", "lhs": "Equation719"}, + {"rhs": "Equation713", "lhs": "Equation719"}, + {"rhs": "Equation716", "lhs": "Equation719"}, + {"rhs": "Equation47", "lhs": "Equation72"}, + {"rhs": "Equation721", "lhs": "Equation722"}, + {"rhs": "Equation619", "lhs": "Equation723"}, + {"rhs": "Equation703", "lhs": "Equation723"}, + {"rhs": "Equation713", "lhs": "Equation723"}, + {"rhs": "Equation619", "lhs": "Equation724"}, + {"rhs": "Equation704", "lhs": "Equation724"}, + {"rhs": "Equation714", "lhs": "Equation724"}, + {"rhs": "Equation620", "lhs": "Equation725"}, + {"rhs": "Equation703", "lhs": "Equation725"}, + {"rhs": "Equation714", "lhs": "Equation725"}, + {"rhs": "Equation621", "lhs": "Equation726"}, + {"rhs": "Equation705", "lhs": "Equation726"}, + {"rhs": "Equation715", "lhs": "Equation726"}, + {"rhs": "Equation723", "lhs": "Equation726"}, + {"rhs": "Equation724", "lhs": "Equation726"}, + {"rhs": "Equation725", "lhs": "Equation726"}, + {"rhs": "Equation619", "lhs": "Equation727"}, + {"rhs": "Equation706", "lhs": "Equation727"}, + {"rhs": "Equation716", "lhs": "Equation727"}, + {"rhs": "Equation47", "lhs": "Equation73"}, + {"rhs": "Equation729", "lhs": "Equation730"}, + {"rhs": "Equation622", "lhs": "Equation731"}, + {"rhs": "Equation703", "lhs": "Equation731"}, + {"rhs": "Equation716", "lhs": "Equation731"}, + {"rhs": "Equation733", "lhs": "Equation734"}, + {"rhs": "Equation625", "lhs": "Equation735"}, + {"rhs": "Equation709", "lhs": "Equation735"}, + {"rhs": "Equation719", "lhs": "Equation735"}, + {"rhs": "Equation723", "lhs": "Equation735"}, + {"rhs": "Equation727", "lhs": "Equation735"}, + {"rhs": "Equation731", "lhs": "Equation735"}, + {"rhs": "Equation738", "lhs": "Equation739"}, + {"rhs": "Equation48", "lhs": "Equation74"}, + {"rhs": "Equation509", "lhs": "Equation74"}, + {"rhs": "Equation72", "lhs": "Equation74"}, + {"rhs": "Equation73", "lhs": "Equation74"}, + {"rhs": "Equation629", "lhs": "Equation740"}, + {"rhs": "Equation666", "lhs": "Equation740"}, + {"rhs": "Equation703", "lhs": "Equation740"}, + {"rhs": "Equation629", "lhs": "Equation741"}, + {"rhs": "Equation667", "lhs": "Equation741"}, + {"rhs": "Equation704", "lhs": "Equation741"}, + {"rhs": "Equation630", "lhs": "Equation742"}, + {"rhs": "Equation666", "lhs": "Equation742"}, + {"rhs": "Equation704", "lhs": "Equation742"}, + {"rhs": "Equation631", "lhs": "Equation743"}, + {"rhs": "Equation668", "lhs": "Equation743"}, + {"rhs": "Equation705", "lhs": "Equation743"}, + {"rhs": "Equation740", "lhs": "Equation743"}, + {"rhs": "Equation741", "lhs": "Equation743"}, + {"rhs": "Equation742", "lhs": "Equation743"}, + {"rhs": "Equation629", "lhs": "Equation744"}, + {"rhs": "Equation669", "lhs": "Equation744"}, + {"rhs": "Equation706", "lhs": "Equation744"}, + {"rhs": "Equation629", "lhs": "Equation745"}, + {"rhs": "Equation670", "lhs": "Equation745"}, + {"rhs": "Equation707", "lhs": "Equation745"}, + {"rhs": "Equation630", "lhs": "Equation746"}, + {"rhs": "Equation669", "lhs": "Equation746"}, + {"rhs": "Equation707", "lhs": "Equation746"}, + {"rhs": "Equation631", "lhs": "Equation747"}, + {"rhs": "Equation671", "lhs": "Equation747"}, + {"rhs": "Equation708", "lhs": "Equation747"}, + {"rhs": "Equation744", "lhs": "Equation747"}, + {"rhs": "Equation745", "lhs": "Equation747"}, + {"rhs": "Equation746", "lhs": "Equation747"}, + {"rhs": "Equation632", "lhs": "Equation748"}, + {"rhs": "Equation666", "lhs": "Equation748"}, + {"rhs": "Equation706", "lhs": "Equation748"}, + {"rhs": "Equation632", "lhs": "Equation749"}, + {"rhs": "Equation667", "lhs": "Equation749"}, + {"rhs": "Equation707", "lhs": "Equation749"}, + {"rhs": "Equation47", "lhs": "Equation75"}, + {"rhs": "Equation633", "lhs": "Equation750"}, + {"rhs": "Equation666", "lhs": "Equation750"}, + {"rhs": "Equation707", "lhs": "Equation750"}, + {"rhs": "Equation634", "lhs": "Equation751"}, + {"rhs": "Equation668", "lhs": "Equation751"}, + {"rhs": "Equation708", "lhs": "Equation751"}, + {"rhs": "Equation748", "lhs": "Equation751"}, + {"rhs": "Equation749", "lhs": "Equation751"}, + {"rhs": "Equation750", "lhs": "Equation751"}, + {"rhs": "Equation635", "lhs": "Equation752"}, + {"rhs": "Equation672", "lhs": "Equation752"}, + {"rhs": "Equation709", "lhs": "Equation752"}, + {"rhs": "Equation740", "lhs": "Equation752"}, + {"rhs": "Equation744", "lhs": "Equation752"}, + {"rhs": "Equation748", "lhs": "Equation752"}, + {"rhs": "Equation635", "lhs": "Equation753"}, + {"rhs": "Equation673", "lhs": "Equation753"}, + {"rhs": "Equation710", "lhs": "Equation753"}, + {"rhs": "Equation741", "lhs": "Equation753"}, + {"rhs": "Equation745", "lhs": "Equation753"}, + {"rhs": "Equation749", "lhs": "Equation753"}, + {"rhs": "Equation636", "lhs": "Equation754"}, + {"rhs": "Equation672", "lhs": "Equation754"}, + {"rhs": "Equation710", "lhs": "Equation754"}, + {"rhs": "Equation742", "lhs": "Equation754"}, + {"rhs": "Equation746", "lhs": "Equation754"}, + {"rhs": "Equation750", "lhs": "Equation754"}, + {"rhs": "Equation637", "lhs": "Equation755"}, + {"rhs": "Equation674", "lhs": "Equation755"}, + {"rhs": "Equation711", "lhs": "Equation755"}, + {"rhs": "Equation740", "lhs": "Equation755"}, + {"rhs": "Equation745", "lhs": "Equation755"}, + {"rhs": "Equation750", "lhs": "Equation755"}, + {"rhs": "Equation638", "lhs": "Equation756"}, + {"rhs": "Equation675", "lhs": "Equation756"}, + {"rhs": "Equation712", "lhs": "Equation756"}, + {"rhs": "Equation743", "lhs": "Equation756"}, + {"rhs": "Equation747", "lhs": "Equation756"}, + {"rhs": "Equation751", "lhs": "Equation756"}, + {"rhs": "Equation752", "lhs": "Equation756"}, + {"rhs": "Equation753", "lhs": "Equation756"}, + {"rhs": "Equation754", "lhs": "Equation756"}, + {"rhs": "Equation755", "lhs": "Equation756"}, + {"rhs": "Equation629", "lhs": "Equation757"}, + {"rhs": "Equation676", "lhs": "Equation757"}, + {"rhs": "Equation713", "lhs": "Equation757"}, + {"rhs": "Equation629", "lhs": "Equation758"}, + {"rhs": "Equation677", "lhs": "Equation758"}, + {"rhs": "Equation714", "lhs": "Equation758"}, + {"rhs": "Equation630", "lhs": "Equation759"}, + {"rhs": "Equation676", "lhs": "Equation759"}, + {"rhs": "Equation714", "lhs": "Equation759"}, + {"rhs": "Equation631", "lhs": "Equation760"}, + {"rhs": "Equation678", "lhs": "Equation760"}, + {"rhs": "Equation715", "lhs": "Equation760"}, + {"rhs": "Equation757", "lhs": "Equation760"}, + {"rhs": "Equation758", "lhs": "Equation760"}, + {"rhs": "Equation759", "lhs": "Equation760"}, + {"rhs": "Equation629", "lhs": "Equation761"}, + {"rhs": "Equation679", "lhs": "Equation761"}, + {"rhs": "Equation716", "lhs": "Equation761"}, + {"rhs": "Equation763", "lhs": "Equation764"}, + {"rhs": "Equation632", "lhs": "Equation765"}, + {"rhs": "Equation676", "lhs": "Equation765"}, + {"rhs": "Equation716", "lhs": "Equation765"}, + {"rhs": "Equation767", "lhs": "Equation768"}, + {"rhs": "Equation635", "lhs": "Equation769"}, + {"rhs": "Equation682", "lhs": "Equation769"}, + {"rhs": "Equation719", "lhs": "Equation769"}, + {"rhs": "Equation757", "lhs": "Equation769"}, + {"rhs": "Equation761", "lhs": "Equation769"}, + {"rhs": "Equation765", "lhs": "Equation769"}, + {"rhs": "Equation772", "lhs": "Equation773"}, + {"rhs": "Equation639", "lhs": "Equation774"}, + {"rhs": "Equation666", "lhs": "Equation774"}, + {"rhs": "Equation713", "lhs": "Equation774"}, + {"rhs": "Equation639", "lhs": "Equation775"}, + {"rhs": "Equation667", "lhs": "Equation775"}, + {"rhs": "Equation714", "lhs": "Equation775"}, + {"rhs": "Equation640", "lhs": "Equation776"}, + {"rhs": "Equation666", "lhs": "Equation776"}, + {"rhs": "Equation714", "lhs": "Equation776"}, + {"rhs": "Equation641", "lhs": "Equation777"}, + {"rhs": "Equation668", "lhs": "Equation777"}, + {"rhs": "Equation715", "lhs": "Equation777"}, + {"rhs": "Equation774", "lhs": "Equation777"}, + {"rhs": "Equation775", "lhs": "Equation777"}, + {"rhs": "Equation776", "lhs": "Equation777"}, + {"rhs": "Equation639", "lhs": "Equation778"}, + {"rhs": "Equation669", "lhs": "Equation778"}, + {"rhs": "Equation716", "lhs": "Equation778"}, + {"rhs": "Equation49", "lhs": "Equation78"}, + {"rhs": "Equation72", "lhs": "Equation78"}, + {"rhs": "Equation735", "lhs": "Equation78"}, + {"rhs": "Equation75", "lhs": "Equation78"}, + {"rhs": "Equation780", "lhs": "Equation781"}, + {"rhs": "Equation642", "lhs": "Equation782"}, + {"rhs": "Equation666", "lhs": "Equation782"}, + {"rhs": "Equation716", "lhs": "Equation782"}, + {"rhs": "Equation784", "lhs": "Equation785"}, + {"rhs": "Equation645", "lhs": "Equation786"}, + {"rhs": "Equation672", "lhs": "Equation786"}, + {"rhs": "Equation719", "lhs": "Equation786"}, + {"rhs": "Equation774", "lhs": "Equation786"}, + {"rhs": "Equation778", "lhs": "Equation786"}, + {"rhs": "Equation782", "lhs": "Equation786"}, + {"rhs": "Equation649", "lhs": "Equation791"}, + {"rhs": "Equation686", "lhs": "Equation791"}, + {"rhs": "Equation723", "lhs": "Equation791"}, + {"rhs": "Equation740", "lhs": "Equation791"}, + {"rhs": "Equation757", "lhs": "Equation791"}, + {"rhs": "Equation774", "lhs": "Equation791"}, + {"rhs": "Equation649", "lhs": "Equation792"}, + {"rhs": "Equation687", "lhs": "Equation792"}, + {"rhs": "Equation724", "lhs": "Equation792"}, + {"rhs": "Equation741", "lhs": "Equation792"}, + {"rhs": "Equation758", "lhs": "Equation792"}, + {"rhs": "Equation775", "lhs": "Equation792"}, + {"rhs": "Equation650", "lhs": "Equation793"}, + {"rhs": "Equation686", "lhs": "Equation793"}, + {"rhs": "Equation724", "lhs": "Equation793"}, + {"rhs": "Equation742", "lhs": "Equation793"}, + {"rhs": "Equation759", "lhs": "Equation793"}, + {"rhs": "Equation776", "lhs": "Equation793"}, + {"rhs": "Equation651", "lhs": "Equation794"}, + {"rhs": "Equation688", "lhs": "Equation794"}, + {"rhs": "Equation725", "lhs": "Equation794"}, + {"rhs": "Equation740", "lhs": "Equation794"}, + {"rhs": "Equation758", "lhs": "Equation794"}, + {"rhs": "Equation776", "lhs": "Equation794"}, + {"rhs": "Equation652", "lhs": "Equation795"}, + {"rhs": "Equation689", "lhs": "Equation795"}, + {"rhs": "Equation726", "lhs": "Equation795"}, + {"rhs": "Equation743", "lhs": "Equation795"}, + {"rhs": "Equation760", "lhs": "Equation795"}, + {"rhs": "Equation777", "lhs": "Equation795"}, + {"rhs": "Equation791", "lhs": "Equation795"}, + {"rhs": "Equation792", "lhs": "Equation795"}, + {"rhs": "Equation793", "lhs": "Equation795"}, + {"rhs": "Equation794", "lhs": "Equation795"}, + {"rhs": "Equation649", "lhs": "Equation796"}, + {"rhs": "Equation690", "lhs": "Equation796"}, + {"rhs": "Equation727", "lhs": "Equation796"}, + {"rhs": "Equation744", "lhs": "Equation796"}, + {"rhs": "Equation761", "lhs": "Equation796"}, + {"rhs": "Equation778", "lhs": "Equation796"}, + {"rhs": "Equation653", "lhs": "Equation801"}, + {"rhs": "Equation686", "lhs": "Equation801"}, + {"rhs": "Equation727", "lhs": "Equation801"}, + {"rhs": "Equation748", "lhs": "Equation801"}, + {"rhs": "Equation765", "lhs": "Equation801"}, + {"rhs": "Equation782", "lhs": "Equation801"}, + {"rhs": "Equation804", "lhs": "Equation805"}, + {"rhs": "Equation657", "lhs": "Equation806"}, + {"rhs": "Equation694", "lhs": "Equation806"}, + {"rhs": "Equation731", "lhs": "Equation806"}, + {"rhs": "Equation740", "lhs": "Equation806"}, + {"rhs": "Equation761", "lhs": "Equation806"}, + {"rhs": "Equation782", "lhs": "Equation806"}, + {"rhs": "Equation661", "lhs": "Equation811"}, + {"rhs": "Equation698", "lhs": "Equation811"}, + {"rhs": "Equation735", "lhs": "Equation811"}, + {"rhs": "Equation752", "lhs": "Equation811"}, + {"rhs": "Equation769", "lhs": "Equation811"}, + {"rhs": "Equation786", "lhs": "Equation811"}, + {"rhs": "Equation791", "lhs": "Equation811"}, + {"rhs": "Equation796", "lhs": "Equation811"}, + {"rhs": "Equation801", "lhs": "Equation811"}, + {"rhs": "Equation806", "lhs": "Equation811"}, + {"rhs": "Equation815", "lhs": "Equation816"}, + {"rhs": "Equation817", "lhs": "Equation818"}, + {"rhs": "Equation817", "lhs": "Equation819"}, + {"rhs": "Equation1603", "lhs": "Equation82"}, + {"rhs": "Equation52", "lhs": "Equation82"}, + {"rhs": "Equation62", "lhs": "Equation82"}, + {"rhs": "Equation72", "lhs": "Equation82"}, + {"rhs": "Equation994", "lhs": "Equation82"}, + {"rhs": "Equation817", "lhs": "Equation820"}, + {"rhs": "Equation818", "lhs": "Equation821"}, + {"rhs": "Equation819", "lhs": "Equation821"}, + {"rhs": "Equation820", "lhs": "Equation821"}, + {"rhs": "Equation817", "lhs": "Equation822"}, + {"rhs": "Equation817", "lhs": "Equation823"}, + {"rhs": "Equation818", "lhs": "Equation824"}, + {"rhs": "Equation822", "lhs": "Equation824"}, + {"rhs": "Equation823", "lhs": "Equation824"}, + {"rhs": "Equation817", "lhs": "Equation825"}, + {"rhs": "Equation817", "lhs": "Equation826"}, + {"rhs": "Equation818", "lhs": "Equation827"}, + {"rhs": "Equation825", "lhs": "Equation827"}, + {"rhs": "Equation826", "lhs": "Equation827"}, + {"rhs": "Equation819", "lhs": "Equation828"}, + {"rhs": "Equation822", "lhs": "Equation828"}, + {"rhs": "Equation825", "lhs": "Equation828"}, + {"rhs": "Equation819", "lhs": "Equation829"}, + {"rhs": "Equation823", "lhs": "Equation829"}, + {"rhs": "Equation826", "lhs": "Equation829"}, + {"rhs": "Equation52", "lhs": "Equation83"}, + {"rhs": "Equation63", "lhs": "Equation83"}, + {"rhs": "Equation73", "lhs": "Equation83"}, + {"rhs": "Equation995", "lhs": "Equation83"}, + {"rhs": "Equation820", "lhs": "Equation830"}, + {"rhs": "Equation822", "lhs": "Equation830"}, + {"rhs": "Equation826", "lhs": "Equation830"}, + {"rhs": "Equation821", "lhs": "Equation831"}, + {"rhs": "Equation824", "lhs": "Equation831"}, + {"rhs": "Equation827", "lhs": "Equation831"}, + {"rhs": "Equation828", "lhs": "Equation831"}, + {"rhs": "Equation829", "lhs": "Equation831"}, + {"rhs": "Equation830", "lhs": "Equation831"}, + {"rhs": "Equation817", "lhs": "Equation832"}, + {"rhs": "Equation817", "lhs": "Equation833"}, + {"rhs": "Equation818", "lhs": "Equation834"}, + {"rhs": "Equation832", "lhs": "Equation834"}, + {"rhs": "Equation833", "lhs": "Equation834"}, + {"rhs": "Equation817", "lhs": "Equation835"}, + {"rhs": "Equation817", "lhs": "Equation836"}, + {"rhs": "Equation818", "lhs": "Equation837"}, + {"rhs": "Equation835", "lhs": "Equation837"}, + {"rhs": "Equation836", "lhs": "Equation837"}, + {"rhs": "Equation819", "lhs": "Equation838"}, + {"rhs": "Equation832", "lhs": "Equation838"}, + {"rhs": "Equation835", "lhs": "Equation838"}, + {"rhs": "Equation819", "lhs": "Equation839"}, + {"rhs": "Equation833", "lhs": "Equation839"}, + {"rhs": "Equation836", "lhs": "Equation839"}, + {"rhs": "Equation1606", "lhs": "Equation84"}, + {"rhs": "Equation53", "lhs": "Equation84"}, + {"rhs": "Equation62", "lhs": "Equation84"}, + {"rhs": "Equation73", "lhs": "Equation84"}, + {"rhs": "Equation820", "lhs": "Equation840"}, + {"rhs": "Equation832", "lhs": "Equation840"}, + {"rhs": "Equation836", "lhs": "Equation840"}, + {"rhs": "Equation821", "lhs": "Equation841"}, + {"rhs": "Equation834", "lhs": "Equation841"}, + {"rhs": "Equation837", "lhs": "Equation841"}, + {"rhs": "Equation838", "lhs": "Equation841"}, + {"rhs": "Equation839", "lhs": "Equation841"}, + {"rhs": "Equation840", "lhs": "Equation841"}, + {"rhs": "Equation817", "lhs": "Equation842"}, + {"rhs": "Equation817", "lhs": "Equation843"}, + {"rhs": "Equation818", "lhs": "Equation844"}, + {"rhs": "Equation842", "lhs": "Equation844"}, + {"rhs": "Equation843", "lhs": "Equation844"}, + {"rhs": "Equation817", "lhs": "Equation845"}, + {"rhs": "Equation817", "lhs": "Equation846"}, + {"rhs": "Equation818", "lhs": "Equation847"}, + {"rhs": "Equation845", "lhs": "Equation847"}, + {"rhs": "Equation846", "lhs": "Equation847"}, + {"rhs": "Equation819", "lhs": "Equation848"}, + {"rhs": "Equation842", "lhs": "Equation848"}, + {"rhs": "Equation845", "lhs": "Equation848"}, + {"rhs": "Equation819", "lhs": "Equation849"}, + {"rhs": "Equation843", "lhs": "Equation849"}, + {"rhs": "Equation846", "lhs": "Equation849"}, + {"rhs": "Equation1607", "lhs": "Equation85"}, + {"rhs": "Equation54", "lhs": "Equation85"}, + {"rhs": "Equation553", "lhs": "Equation85"}, + {"rhs": "Equation64", "lhs": "Equation85"}, + {"rhs": "Equation74", "lhs": "Equation85"}, + {"rhs": "Equation82", "lhs": "Equation85"}, + {"rhs": "Equation83", "lhs": "Equation85"}, + {"rhs": "Equation84", "lhs": "Equation85"}, + {"rhs": "Equation998", "lhs": "Equation85"}, + {"rhs": "Equation820", "lhs": "Equation850"}, + {"rhs": "Equation842", "lhs": "Equation850"}, + {"rhs": "Equation846", "lhs": "Equation850"}, + {"rhs": "Equation821", "lhs": "Equation851"}, + {"rhs": "Equation844", "lhs": "Equation851"}, + {"rhs": "Equation847", "lhs": "Equation851"}, + {"rhs": "Equation848", "lhs": "Equation851"}, + {"rhs": "Equation849", "lhs": "Equation851"}, + {"rhs": "Equation850", "lhs": "Equation851"}, + {"rhs": "Equation822", "lhs": "Equation852"}, + {"rhs": "Equation832", "lhs": "Equation852"}, + {"rhs": "Equation842", "lhs": "Equation852"}, + {"rhs": "Equation822", "lhs": "Equation853"}, + {"rhs": "Equation833", "lhs": "Equation853"}, + {"rhs": "Equation843", "lhs": "Equation853"}, + {"rhs": "Equation823", "lhs": "Equation854"}, + {"rhs": "Equation832", "lhs": "Equation854"}, + {"rhs": "Equation843", "lhs": "Equation854"}, + {"rhs": "Equation824", "lhs": "Equation855"}, + {"rhs": "Equation834", "lhs": "Equation855"}, + {"rhs": "Equation844", "lhs": "Equation855"}, + {"rhs": "Equation852", "lhs": "Equation855"}, + {"rhs": "Equation853", "lhs": "Equation855"}, + {"rhs": "Equation854", "lhs": "Equation855"}, + {"rhs": "Equation822", "lhs": "Equation856"}, + {"rhs": "Equation835", "lhs": "Equation856"}, + {"rhs": "Equation845", "lhs": "Equation856"}, + {"rhs": "Equation822", "lhs": "Equation857"}, + {"rhs": "Equation836", "lhs": "Equation857"}, + {"rhs": "Equation846", "lhs": "Equation857"}, + {"rhs": "Equation823", "lhs": "Equation858"}, + {"rhs": "Equation835", "lhs": "Equation858"}, + {"rhs": "Equation846", "lhs": "Equation858"}, + {"rhs": "Equation824", "lhs": "Equation859"}, + {"rhs": "Equation837", "lhs": "Equation859"}, + {"rhs": "Equation847", "lhs": "Equation859"}, + {"rhs": "Equation856", "lhs": "Equation859"}, + {"rhs": "Equation857", "lhs": "Equation859"}, + {"rhs": "Equation858", "lhs": "Equation859"}, + {"rhs": "Equation52", "lhs": "Equation86"}, + {"rhs": "Equation65", "lhs": "Equation86"}, + {"rhs": "Equation75", "lhs": "Equation86"}, + {"rhs": "Equation999", "lhs": "Equation86"}, + {"rhs": "Equation825", "lhs": "Equation860"}, + {"rhs": "Equation832", "lhs": "Equation860"}, + {"rhs": "Equation845", "lhs": "Equation860"}, + {"rhs": "Equation825", "lhs": "Equation861"}, + {"rhs": "Equation833", "lhs": "Equation861"}, + {"rhs": "Equation846", "lhs": "Equation861"}, + {"rhs": "Equation826", "lhs": "Equation862"}, + {"rhs": "Equation832", "lhs": "Equation862"}, + {"rhs": "Equation846", "lhs": "Equation862"}, + {"rhs": "Equation827", "lhs": "Equation863"}, + {"rhs": "Equation834", "lhs": "Equation863"}, + {"rhs": "Equation847", "lhs": "Equation863"}, + {"rhs": "Equation860", "lhs": "Equation863"}, + {"rhs": "Equation861", "lhs": "Equation863"}, + {"rhs": "Equation862", "lhs": "Equation863"}, + {"rhs": "Equation828", "lhs": "Equation864"}, + {"rhs": "Equation838", "lhs": "Equation864"}, + {"rhs": "Equation848", "lhs": "Equation864"}, + {"rhs": "Equation852", "lhs": "Equation864"}, + {"rhs": "Equation856", "lhs": "Equation864"}, + {"rhs": "Equation860", "lhs": "Equation864"}, + {"rhs": "Equation828", "lhs": "Equation865"}, + {"rhs": "Equation839", "lhs": "Equation865"}, + {"rhs": "Equation849", "lhs": "Equation865"}, + {"rhs": "Equation853", "lhs": "Equation865"}, + {"rhs": "Equation857", "lhs": "Equation865"}, + {"rhs": "Equation861", "lhs": "Equation865"}, + {"rhs": "Equation829", "lhs": "Equation866"}, + {"rhs": "Equation838", "lhs": 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{"rhs": "Equation879", "lhs": "Equation887"}, + {"rhs": "Equation883", "lhs": "Equation887"}, + {"rhs": "Equation821", "lhs": "Equation888"}, + {"rhs": "Equation881", "lhs": "Equation888"}, + {"rhs": "Equation884", "lhs": "Equation888"}, + {"rhs": "Equation885", "lhs": "Equation888"}, + {"rhs": "Equation886", "lhs": "Equation888"}, + {"rhs": "Equation887", "lhs": "Equation888"}, + {"rhs": "Equation822", "lhs": "Equation889"}, + {"rhs": "Equation869", "lhs": "Equation889"}, + {"rhs": "Equation879", "lhs": "Equation889"}, + {"rhs": "Equation88", "lhs": "Equation89"}, + {"rhs": "Equation822", "lhs": "Equation890"}, + {"rhs": "Equation870", "lhs": "Equation890"}, + {"rhs": "Equation880", "lhs": "Equation890"}, + {"rhs": "Equation823", "lhs": "Equation891"}, + {"rhs": "Equation869", "lhs": "Equation891"}, + {"rhs": "Equation880", "lhs": "Equation891"}, + {"rhs": "Equation824", "lhs": "Equation892"}, + {"rhs": "Equation871", "lhs": "Equation892"}, + {"rhs": "Equation881", "lhs": 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{"rhs": "Equation976", "lhs": "Equation98"}, + {"rhs": "Equation844", "lhs": "Equation980"}, + {"rhs": "Equation871", "lhs": "Equation980"}, + {"rhs": "Equation918", "lhs": "Equation980"}, + {"rhs": "Equation977", "lhs": "Equation980"}, + {"rhs": "Equation978", "lhs": "Equation980"}, + {"rhs": "Equation979", "lhs": "Equation980"}, + {"rhs": "Equation842", "lhs": "Equation981"}, + {"rhs": "Equation872", "lhs": "Equation981"}, + {"rhs": "Equation919", "lhs": "Equation981"}, + {"rhs": "Equation983", "lhs": "Equation984"}, + {"rhs": "Equation845", "lhs": "Equation985"}, + {"rhs": "Equation869", "lhs": "Equation985"}, + {"rhs": "Equation919", "lhs": "Equation985"}, + {"rhs": "Equation987", "lhs": "Equation988"}, + {"rhs": "Equation848", "lhs": "Equation989"}, + {"rhs": "Equation875", "lhs": "Equation989"}, + {"rhs": "Equation922", "lhs": "Equation989"}, + {"rhs": "Equation977", "lhs": "Equation989"}, + {"rhs": "Equation981", "lhs": "Equation989"}, + {"rhs": "Equation985", "lhs": 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{"rhs": "Equation4622", "lhs": "Equation40"}, + {"rhs": "Equation408", "lhs": "Equation400"}, + {"rhs": "Equation4256", "lhs": "Equation400"}, + {"rhs": "Equation4056", "lhs": "Equation4011"}, + {"rhs": "Equation4051", "lhs": "Equation4015"}, + {"rhs": "Equation3834", "lhs": "Equation402"}, + {"rhs": "Equation4237", "lhs": "Equation402"}, + {"rhs": "Equation4036", "lhs": "Equation4028"}, + {"rhs": "Equation4238", "lhs": "Equation403"}, + {"rhs": "Equation4236", "lhs": "Equation404"}, + {"rhs": "Equation4596", "lhs": "Equation404"}, + {"rhs": "Equation4628", "lhs": "Equation405"}, + {"rhs": "Equation3861", "lhs": "Equation406"}, + {"rhs": "Equation4671", "lhs": "Equation409"}, + {"rhs": "Equation3733", "lhs": "Equation41"}, + {"rhs": "Equation3774", "lhs": "Equation41"}, + {"rhs": "Equation3793", "lhs": "Equation41"}, + {"rhs": "Equation3811", "lhs": "Equation41"}, + {"rhs": "Equation3829", "lhs": "Equation41"}, + {"rhs": "Equation3849", "lhs": "Equation41"}, + {"rhs": "Equation4236", "lhs": "Equation4169"}, + {"rhs": "Equation4240", "lhs": "Equation4172"}, + {"rhs": "Equation4255", "lhs": "Equation4180"}, + {"rhs": "Equation4260", "lhs": "Equation4184"}, + {"rhs": "Equation4259", "lhs": "Equation4214"}, + {"rhs": "Equation4254", "lhs": "Equation4218"}, + {"rhs": "Equation4239", "lhs": "Equation4231"}, + {"rhs": "Equation4268", "lhs": "Equation4286"}, + {"rhs": "Equation4268", "lhs": "Equation4288"}, + {"rhs": "Equation4308", "lhs": "Equation4294"}, + {"rhs": "Equation4275", "lhs": "Equation4296"}, + {"rhs": "Equation4275", "lhs": "Equation4297"}, + {"rhs": "Equation4268", "lhs": "Equation4299"}, + {"rhs": "Equation4268", "lhs": "Equation4301"}, + {"rhs": "Equation4275", "lhs": "Equation4304"}, + {"rhs": "Equation4275", "lhs": "Equation4305"}, + {"rhs": "Equation4277", "lhs": "Equation4311"}, + {"rhs": "Equation4277", "lhs": "Equation4312"}, + {"rhs": "Equation4283", "lhs": "Equation4317"}, + {"rhs": "Equation4269", "lhs": "Equation4318"}, + {"rhs": "Equation4286", "lhs": "Equation4319"}, + {"rhs": "Equation4291", "lhs": "Equation4323"}, + {"rhs": "Equation4336", "lhs": "Equation4324"}, + {"rhs": "Equation4273", "lhs": "Equation4325"}, + {"rhs": "Equation4269", "lhs": "Equation4327"}, + {"rhs": "Equation4283", "lhs": "Equation4328"}, + {"rhs": "Equation4291", "lhs": "Equation4330"}, + {"rhs": "Equation4273", "lhs": "Equation4331"}, + {"rhs": "Equation4301", "lhs": "Equation4333"}, + {"rhs": "Equation4296", "lhs": "Equation4334"}, + {"rhs": "Equation4279", "lhs": "Equation4337"}, + {"rhs": "Equation4311", "lhs": "Equation4338"}, + {"rhs": "Equation4314", "lhs": "Equation4339"}, + {"rhs": "Equation4284", "lhs": "Equation4340"}, + {"rhs": "Equation4288", "lhs": "Equation4342"}, + {"rhs": "Equation4318", "lhs": "Equation4342"}, + {"rhs": "Equation4320", "lhs": "Equation4344"}, + {"rhs": "Equation4290", "lhs": "Equation4345"}, + {"rhs": "Equation4355", "lhs": "Equation4346"}, + {"rhs": "Equation4284", "lhs": "Equation4348"}, + {"rhs": "Equation4320", "lhs": "Equation4348"}, + {"rhs": "Equation4290", "lhs": "Equation4350"}, + {"rhs": "Equation4314", "lhs": "Equation4350"}, + {"rhs": "Equation4299", "lhs": "Equation4352"}, + {"rhs": "Equation4331", "lhs": "Equation4352"}, + {"rhs": "Equation4304", "lhs": "Equation4354"}, + {"rhs": "Equation4327", "lhs": "Equation4354"}, + {"rhs": "Equation4312", "lhs": "Equation4356"}, + {"rhs": "Equation4337", "lhs": "Equation4356"}, + {"rhs": "Equation4361", "lhs": "Equation4359"}, + {"rhs": "Equation4290", "lhs": "Equation4364"}, + {"rhs": "Equation4313", "lhs": "Equation4365"}, + {"rhs": "Equation4338", "lhs": "Equation4365"}, + {"rhs": "Equation4356", "lhs": "Equation4365"}, + {"rhs": "Equation4361", "lhs": "Equation4365"}, + {"rhs": "Equation4363", "lhs": "Equation4365"}, + {"rhs": "Equation4371", "lhs": "Equation4365"}, + {"rhs": "Equation4375", "lhs": "Equation4365"}, + {"rhs": "Equation4376", "lhs": "Equation4365"}, + {"rhs": "Equation4377", "lhs": "Equation4365"}, + {"rhs": "Equation4378", "lhs": "Equation4365"}, + {"rhs": "Equation4379", "lhs": "Equation4365"}, + {"rhs": "Equation4365", "lhs": "Equation4366"}, + {"rhs": "Equation4378", "lhs": "Equation4367"}, + {"rhs": "Equation4375", "lhs": "Equation4370"}, + {"rhs": "Equation4368", "lhs": "Equation4372"}, + {"rhs": "Equation4372", "lhs": "Equation4377"}, + {"rhs": "Equation4597", "lhs": "Equation4381"}, + {"rhs": "Equation4631", "lhs": "Equation4382"}, + {"rhs": "Equation4656", "lhs": "Equation4383"}, + {"rhs": "Equation4676", "lhs": "Equation4384"}, + {"rhs": "Equation4666", "lhs": "Equation4385"}, + {"rhs": "Equation4647", "lhs": "Equation4386"}, + {"rhs": "Equation4690", "lhs": "Equation4387"}, + {"rhs": "Equation4622", "lhs": "Equation4388"}, + {"rhs": "Equation4693", "lhs": "Equation4391"}, + {"rhs": "Equation46", "lhs": "Equation44"}, + {"rhs": "Equation4672", "lhs": "Equation4400"}, + {"rhs": "Equation4675", "lhs": "Equation4402"}, + {"rhs": "Equation4672", "lhs": "Equation4407"}, + {"rhs": "Equation4426", "lhs": "Equation4410"}, + {"rhs": "Equation4675", "lhs": "Equation4411"}, + {"rhs": "Equation4689", "lhs": "Equation4416"}, + {"rhs": "Equation4689", "lhs": "Equation4419"}, + {"rhs": "Equation4672", "lhs": "Equation4437"}, + {"rhs": "Equation4675", "lhs": "Equation4439"}, + {"rhs": "Equation4672", "lhs": "Equation4444"}, + {"rhs": "Equation4463", "lhs": "Equation4447"}, + {"rhs": "Equation4675", "lhs": "Equation4448"}, + {"rhs": "Equation4689", "lhs": "Equation4453"}, + {"rhs": "Equation4689", "lhs": "Equation4456"}, + {"rhs": "Equation4672", "lhs": "Equation4474"}, + {"rhs": "Equation4675", "lhs": "Equation4476"}, + {"rhs": "Equation4672", "lhs": "Equation4481"}, + {"rhs": "Equation4500", "lhs": "Equation4484"}, + {"rhs": "Equation4675", "lhs": "Equation4485"}, + {"rhs": "Equation4504", "lhs": "Equation4487"}, + {"rhs": "Equation4689", "lhs": "Equation4490"}, + {"rhs": "Equation4689", "lhs": "Equation4493"}, + {"rhs": "Equation4503", "lhs": "Equation4495"}, + {"rhs": "Equation4431", "lhs": "Equation4534"}, + {"rhs": "Equation4468", "lhs": "Equation4534"}, + {"rhs": "Equation4505", "lhs": "Equation4534"}, + {"rhs": "Equation4522", "lhs": "Equation4534"}, + {"rhs": "Equation4539", "lhs": "Equation4534"}, + {"rhs": "Equation4556", "lhs": "Equation4534"}, + {"rhs": "Equation4561", "lhs": "Equation4534"}, + {"rhs": "Equation4576", "lhs": "Equation4534"}, + {"rhs": "Equation4577", "lhs": "Equation4534"}, + {"rhs": "Equation4578", "lhs": "Equation4534"}, + {"rhs": "Equation4579", "lhs": "Equation4534"}, + {"rhs": "Equation4580", "lhs": "Equation4534"}, + {"rhs": "Equation4581", "lhs": "Equation4534"}, + {"rhs": "Equation4582", "lhs": "Equation4534"}, + {"rhs": "Equation4571", "lhs": "Equation4547"}, + {"rhs": "Equation4583", "lhs": "Equation4601"}, + {"rhs": "Equation4583", "lhs": "Equation4603"}, + {"rhs": "Equation4623", "lhs": "Equation4609"}, + {"rhs": "Equation4590", "lhs": "Equation4611"}, + {"rhs": "Equation4590", "lhs": "Equation4612"}, + {"rhs": "Equation4583", "lhs": "Equation4614"}, + {"rhs": "Equation4583", "lhs": "Equation4616"}, + {"rhs": "Equation4590", "lhs": "Equation4619"}, + {"rhs": "Equation4590", "lhs": "Equation4620"}, + {"rhs": "Equation4592", "lhs": "Equation4626"}, + {"rhs": "Equation4592", "lhs": "Equation4627"}, + {"rhs": "Equation4598", "lhs": "Equation4632"}, + {"rhs": "Equation4584", "lhs": "Equation4633"}, + {"rhs": "Equation4601", "lhs": "Equation4634"}, + {"rhs": "Equation4606", "lhs": "Equation4638"}, + {"rhs": "Equation4651", "lhs": "Equation4639"}, + {"rhs": "Equation4588", "lhs": "Equation4640"}, + {"rhs": "Equation4584", "lhs": "Equation4642"}, + {"rhs": "Equation4598", "lhs": "Equation4643"}, + {"rhs": "Equation4606", "lhs": "Equation4645"}, + {"rhs": "Equation4588", "lhs": "Equation4646"}, + {"rhs": "Equation4616", "lhs": "Equation4648"}, + {"rhs": "Equation4611", "lhs": "Equation4649"}, + {"rhs": "Equation4594", "lhs": "Equation4652"}, + {"rhs": "Equation4626", "lhs": "Equation4653"}, + {"rhs": "Equation4629", "lhs": "Equation4654"}, + {"rhs": "Equation4599", "lhs": "Equation4655"}, + {"rhs": "Equation4603", "lhs": "Equation4657"}, + {"rhs": "Equation4633", "lhs": "Equation4657"}, + {"rhs": "Equation4635", "lhs": "Equation4659"}, + {"rhs": "Equation4605", "lhs": "Equation4660"}, + {"rhs": "Equation4670", "lhs": "Equation4661"}, + {"rhs": "Equation4599", "lhs": "Equation4663"}, + {"rhs": "Equation4635", "lhs": "Equation4663"}, + {"rhs": "Equation4605", "lhs": "Equation4665"}, + {"rhs": "Equation4629", "lhs": "Equation4665"}, + {"rhs": "Equation4614", "lhs": "Equation4667"}, + {"rhs": "Equation4646", "lhs": "Equation4667"}, + {"rhs": "Equation4619", "lhs": "Equation4669"}, + {"rhs": "Equation4642", "lhs": "Equation4669"}, + {"rhs": "Equation4627", "lhs": "Equation4671"}, + {"rhs": "Equation4652", "lhs": "Equation4671"}, + {"rhs": "Equation4676", "lhs": "Equation4674"}, + {"rhs": "Equation4605", "lhs": "Equation4679"}, + {"rhs": "Equation4694", "lhs": "Equation4680"}, + {"rhs": "Equation4628", "lhs": "Equation4681"}, + {"rhs": "Equation4653", "lhs": "Equation4681"}, + {"rhs": "Equation4671", "lhs": "Equation4681"}, + {"rhs": "Equation4676", "lhs": "Equation4681"}, + {"rhs": "Equation4678", "lhs": "Equation4681"}, + {"rhs": "Equation4680", "lhs": "Equation4681"}, + {"rhs": "Equation4686", "lhs": "Equation4681"}, + {"rhs": "Equation4690", "lhs": "Equation4681"}, + {"rhs": "Equation4691", "lhs": "Equation4681"}, + {"rhs": "Equation4692", "lhs": "Equation4681"}, + {"rhs": "Equation4693", "lhs": "Equation4681"}, + {"rhs": "Equation4693", "lhs": "Equation4682"}, + {"rhs": "Equation4690", "lhs": "Equation4685"}, + {"rhs": "Equation4683", "lhs": "Equation4687"}, + {"rhs": "Equation4687", "lhs": "Equation4692"}, + {"rhs": "Equation19", "lhs": "Equation5"}, + {"rhs": "Equation3451", "lhs": "Equation5"}, + {"rhs": "Equation355", "lhs": "Equation5"}, + {"rhs": "Equation94", "lhs": "Equation5"}, + {"rhs": "Equation1020", "lhs": "Equation8"}, + {"rhs": "Equation1832", "lhs": "Equation8"}, + {"rhs": "Equation3319", "lhs": "Equation8"}, + {"rhs": "Equation3915", "lhs": "Equation8"}, + {"rhs": "Equation411", "lhs": "Equation8"}, + {"rhs": "Equation1024", "lhs": "Equation9"}, + {"rhs": "Equation1839", "lhs": "Equation9"}, + {"rhs": "Equation3320", "lhs": "Equation9"}, + {"rhs": "Equation3921", "lhs": "Equation9"}, + {"rhs": "Equation4282", "lhs": "Equation9"}, + {"rhs": "Equation993", "lhs": "Equation1000"}, + {"rhs": "Equation1000", "lhs": "Equation1001"}, + {"rhs": "Equation1001", "lhs": "Equation1002"}, + {"rhs": "Equation1003", "lhs": "Equation1005"}, + {"rhs": "Equation1005", "lhs": "Equation1006"}, + {"rhs": "Equation1006", "lhs": "Equation1007"}, + {"rhs": "Equation1008", "lhs": "Equation1010"}, + {"rhs": "Equation1010", "lhs": "Equation1011"}, + {"rhs": "Equation1011", "lhs": "Equation1012"}, + {"rhs": "Equation1013", "lhs": "Equation1015"}, + {"rhs": "Equation1015", "lhs": "Equation1016"}, + {"rhs": "Equation1016", "lhs": "Equation1017"}, + {"rhs": "Equation1017", "lhs": "Equation1018"}, + {"rhs": "Equation1019", "lhs": "Equation1123"}, + {"rhs": "Equation1124", "lhs": "Equation1126"}, + {"rhs": "Equation1126", "lhs": "Equation1127"}, + {"rhs": "Equation1128", "lhs": "Equation1134"}, + {"rhs": "Equation1134", "lhs": "Equation1135"}, + {"rhs": "Equation1136", "lhs": "Equation1138"}, + {"rhs": "Equation1138", "lhs": "Equation1139"}, + {"rhs": "Equation1140", "lhs": "Equation1142"}, + {"rhs": "Equation1142", "lhs": "Equation1143"}, + {"rhs": "Equation1143", "lhs": "Equation1144"}, + {"rhs": "Equation1145", "lhs": "Equation1168"}, + {"rhs": "Equation1168", "lhs": "Equation1169"}, + {"rhs": "Equation1170", "lhs": "Equation1172"}, + {"rhs": "Equation1172", "lhs": "Equation1173"}, + {"rhs": "Equation1174", "lhs": "Equation1176"}, + {"rhs": "Equation1176", "lhs": "Equation1177"}, + {"rhs": "Equation1177", "lhs": "Equation1178"}, + {"rhs": "Equation1179", "lhs": "Equation1185"}, + {"rhs": "Equation1185", "lhs": "Equation1186"}, + {"rhs": "Equation1187", "lhs": "Equation1189"}, + {"rhs": "Equation1189", "lhs": "Equation1190"}, + {"rhs": "Equation1191", "lhs": "Equation1193"}, + {"rhs": "Equation1193", "lhs": "Equation1194"}, + {"rhs": "Equation1194", "lhs": "Equation1195"}, + {"rhs": "Equation4313", "lhs": "Equation1201"}, + {"rhs": "Equation4431", "lhs": "Equation1201"}, + {"rhs": "Equation1196", "lhs": "Equation1203"}, + {"rhs": "Equation1203", "lhs": "Equation1204"}, + {"rhs": "Equation1204", "lhs": "Equation1205"}, + {"rhs": "Equation1206", "lhs": "Equation1208"}, + {"rhs": "Equation1208", "lhs": "Equation1209"}, + {"rhs": "Equation1209", "lhs": "Equation1210"}, + {"rhs": "Equation1211", "lhs": "Equation1213"}, + {"rhs": "Equation1213", "lhs": "Equation1214"}, + {"rhs": "Equation1214", "lhs": "Equation1215"}, + {"rhs": "Equation1216", "lhs": "Equation1218"}, + {"rhs": "Equation1218", "lhs": "Equation1219"}, + {"rhs": "Equation1219", "lhs": "Equation1220"}, + {"rhs": "Equation1220", "lhs": "Equation1221"}, + {"rhs": "Equation1222", "lhs": "Equation128"}, + {"rhs": "Equation129", "lhs": "Equation131"}, + {"rhs": "Equation131", "lhs": "Equation132"}, + {"rhs": "Equation132", "lhs": "Equation1326"}, + {"rhs": "Equation1327", "lhs": "Equation1329"}, + {"rhs": "Equation1329", "lhs": "Equation133"}, + {"rhs": "Equation133", "lhs": "Equation1330"}, + {"rhs": "Equation1331", "lhs": "Equation1337"}, + {"rhs": "Equation1337", "lhs": "Equation1338"}, + {"rhs": "Equation1339", "lhs": "Equation1341"}, + {"rhs": "Equation1341", "lhs": "Equation1342"}, + {"rhs": "Equation1343", "lhs": "Equation1345"}, + {"rhs": "Equation1345", "lhs": "Equation1346"}, + {"rhs": "Equation1346", "lhs": "Equation1347"}, + {"rhs": "Equation1348", "lhs": "Equation1371"}, + {"rhs": "Equation1371", "lhs": "Equation1372"}, + {"rhs": "Equation1373", "lhs": "Equation1375"}, + {"rhs": "Equation1375", "lhs": "Equation1376"}, + {"rhs": "Equation1377", "lhs": "Equation1379"}, + {"rhs": "Equation1379", "lhs": "Equation1380"}, + {"rhs": "Equation1380", "lhs": "Equation1381"}, + {"rhs": "Equation1382", "lhs": "Equation1388"}, + {"rhs": "Equation1388", "lhs": "Equation1389"}, + {"rhs": "Equation1389", "lhs": "Equation139"}, + {"rhs": "Equation139", "lhs": "Equation1390"}, + {"rhs": "Equation1390", "lhs": "Equation1392"}, + {"rhs": "Equation1392", "lhs": "Equation1393"}, + {"rhs": "Equation1394", "lhs": "Equation1396"}, + {"rhs": "Equation1396", "lhs": "Equation1397"}, + {"rhs": "Equation1397", "lhs": "Equation1398"}, + {"rhs": "Equation1399", "lhs": "Equation140"}, + {"rhs": "Equation140", "lhs": "Equation1406"}, + {"rhs": "Equation1406", "lhs": "Equation1407"}, + {"rhs": "Equation1407", "lhs": "Equation1408"}, + {"rhs": "Equation141", "lhs": "Equation1411"}, + {"rhs": "Equation1411", "lhs": "Equation1412"}, + {"rhs": "Equation1412", "lhs": "Equation1413"}, + {"rhs": "Equation1414", "lhs": "Equation1416"}, + {"rhs": "Equation1416", "lhs": "Equation1417"}, + {"rhs": "Equation1417", "lhs": "Equation1418"}, + {"rhs": "Equation1419", "lhs": "Equation1421"}, + {"rhs": "Equation1421", "lhs": "Equation1422"}, + {"rhs": "Equation1422", "lhs": "Equation1423"}, + {"rhs": "Equation1423", "lhs": "Equation1424"}, + {"rhs": "Equation1425", "lhs": "Equation143"}, + {"rhs": "Equation143", "lhs": "Equation144"}, + {"rhs": "Equation145", "lhs": "Equation147"}, + {"rhs": "Equation147", "lhs": "Equation148"}, + {"rhs": "Equation148", "lhs": "Equation149"}, + {"rhs": "Equation3688", "lhs": "Equation1496"}, + {"rhs": "Equation321", "lhs": "Equation1497"}, + {"rhs": "Equation4338", "lhs": "Equation1505"}, + {"rhs": "Equation150", "lhs": "Equation1529"}, + {"rhs": "Equation1530", "lhs": "Equation1532"}, + {"rhs": "Equation1532", "lhs": "Equation1533"}, + {"rhs": "Equation1534", "lhs": "Equation1540"}, + {"rhs": "Equation1540", "lhs": "Equation1541"}, + {"rhs": "Equation1542", "lhs": "Equation1544"}, + {"rhs": "Equation1544", "lhs": "Equation1545"}, + {"rhs": "Equation1546", "lhs": "Equation1548"}, + {"rhs": "Equation1548", "lhs": "Equation1549"}, + {"rhs": "Equation1549", "lhs": "Equation1550"}, + {"rhs": "Equation40", "lhs": "Equation1565"}, + {"rhs": "Equation1551", "lhs": "Equation1574"}, + {"rhs": "Equation1574", "lhs": "Equation1575"}, + {"rhs": "Equation1576", "lhs": "Equation1578"}, + {"rhs": "Equation1578", "lhs": "Equation1579"}, + {"rhs": "Equation1580", "lhs": "Equation1582"}, + {"rhs": "Equation1582", "lhs": "Equation1583"}, + {"rhs": "Equation1583", "lhs": "Equation1584"}, + {"rhs": "Equation1585", "lhs": "Equation1591"}, + {"rhs": "Equation1591", "lhs": "Equation1592"}, + {"rhs": "Equation1593", "lhs": "Equation1595"}, + {"rhs": "Equation1595", "lhs": "Equation1596"}, + {"rhs": "Equation1597", "lhs": "Equation1599"}, + {"rhs": "Equation1599", "lhs": "Equation1600"}, + {"rhs": "Equation1600", "lhs": "Equation1601"}, + {"rhs": "Equation41", "lhs": "Equation1604"}, + {"rhs": "Equation41", "lhs": "Equation1606"}, + {"rhs": "Equation4653", "lhs": "Equation1606"}, + {"rhs": "Equation1602", "lhs": "Equation1609"}, + {"rhs": "Equation1609", "lhs": "Equation1610"}, + {"rhs": "Equation1610", "lhs": "Equation1611"}, + {"rhs": "Equation1612", "lhs": "Equation1614"}, + {"rhs": "Equation1614", "lhs": "Equation1615"}, + {"rhs": "Equation1615", "lhs": "Equation1616"}, + {"rhs": "Equation1617", "lhs": "Equation1619"}, + {"rhs": "Equation1619", "lhs": "Equation1620"}, + {"rhs": "Equation1620", "lhs": "Equation1621"}, + {"rhs": "Equation1622", "lhs": "Equation1624"}, + {"rhs": "Equation1624", "lhs": "Equation1625"}, + {"rhs": "Equation1625", "lhs": "Equation1626"}, + {"rhs": "Equation1626", "lhs": "Equation1627"}, + {"rhs": "Equation1628", "lhs": "Equation17"}, + {"rhs": "Equation4431", "lhs": "Equation1700"}, + {"rhs": "Equation41", "lhs": "Equation171"}, + {"rhs": "Equation369", "lhs": "Equation1712"}, + {"rhs": "Equation371", "lhs": "Equation1715"}, + {"rhs": "Equation373", "lhs": "Equation1717"}, + {"rhs": "Equation17", "lhs": "Equation1732"}, + {"rhs": "Equation1733", "lhs": "Equation1735"}, + {"rhs": "Equation1735", "lhs": "Equation1736"}, + {"rhs": "Equation1737", "lhs": "Equation1743"}, + {"rhs": "Equation1743", "lhs": "Equation1744"}, + {"rhs": "Equation1745", "lhs": "Equation1747"}, + {"rhs": "Equation1747", "lhs": "Equation1748"}, + {"rhs": "Equation1749", "lhs": "Equation1751"}, + {"rhs": "Equation1751", "lhs": "Equation1752"}, + {"rhs": "Equation1752", "lhs": "Equation1753"}, + {"rhs": "Equation41", "lhs": "Equation1757"}, + {"rhs": "Equation1754", "lhs": "Equation1777"}, + {"rhs": "Equation1777", "lhs": "Equation1778"}, + {"rhs": "Equation1779", "lhs": "Equation1781"}, + {"rhs": "Equation1781", "lhs": "Equation1782"}, + {"rhs": "Equation1783", "lhs": "Equation1785"}, + {"rhs": "Equation1785", "lhs": "Equation1786"}, + {"rhs": "Equation1786", "lhs": "Equation1787"}, + {"rhs": "Equation41", "lhs": "Equation1791"}, + {"rhs": "Equation1788", "lhs": "Equation1794"}, + {"rhs": "Equation1794", "lhs": "Equation1795"}, + {"rhs": "Equation1796", "lhs": "Equation1798"}, + {"rhs": "Equation1798", "lhs": "Equation1799"}, + {"rhs": "Equation1799", "lhs": "Equation18"}, + {"rhs": "Equation18", "lhs": "Equation180"}, + {"rhs": "Equation180", "lhs": "Equation1800"}, + {"rhs": "Equation1800", "lhs": "Equation1802"}, + {"rhs": "Equation1802", "lhs": "Equation1803"}, + {"rhs": "Equation1803", "lhs": "Equation1804"}, + {"rhs": "Equation1805", "lhs": "Equation181"}, + {"rhs": "Equation181", "lhs": "Equation1812"}, + {"rhs": "Equation1812", "lhs": "Equation1813"}, + {"rhs": "Equation1813", "lhs": "Equation1814"}, + {"rhs": "Equation1815", "lhs": "Equation1817"}, + {"rhs": "Equation1817", "lhs": "Equation1818"}, + {"rhs": "Equation1818", "lhs": "Equation1819"}, + {"rhs": "Equation1820", "lhs": "Equation1822"}, + {"rhs": "Equation1822", "lhs": "Equation1823"}, + {"rhs": "Equation1823", "lhs": "Equation1824"}, + {"rhs": "Equation1825", "lhs": "Equation1827"}, + {"rhs": "Equation1827", "lhs": "Equation1828"}, + {"rhs": "Equation1828", "lhs": "Equation1829"}, + {"rhs": "Equation1829", "lhs": "Equation183"}, + {"rhs": "Equation183", "lhs": "Equation1830"}, + {"rhs": "Equation1831", "lhs": "Equation184"}, + {"rhs": "Equation41", "lhs": "Equation188"}, + {"rhs": "Equation41", "lhs": "Equation1889"}, + {"rhs": "Equation4356", "lhs": "Equation1892"}, + {"rhs": "Equation4505", "lhs": "Equation1892"}, + {"rhs": "Equation4379", "lhs": "Equation1893"}, + {"rhs": "Equation4582", "lhs": "Equation1893"}, + {"rhs": "Equation41", "lhs": "Equation1899"}, + {"rhs": "Equation4379", "lhs": "Equation1903"}, + {"rhs": "Equation4582", "lhs": "Equation1903"}, + {"rhs": "Equation185", "lhs": "Equation191"}, + {"rhs": "Equation4379", "lhs": "Equation1915"}, + {"rhs": "Equation4582", "lhs": "Equation1915"}, + {"rhs": "Equation4379", "lhs": "Equation1918"}, + {"rhs": "Equation4582", "lhs": "Equation1918"}, + {"rhs": "Equation191", "lhs": "Equation192"}, + {"rhs": "Equation41", "lhs": "Equation1930"}, + {"rhs": "Equation4379", "lhs": "Equation1930"}, + {"rhs": "Equation4582", "lhs": "Equation1930"}, + {"rhs": "Equation193", "lhs": "Equation1935"}, + {"rhs": "Equation1936", "lhs": "Equation1938"}, + {"rhs": "Equation1938", "lhs": "Equation1939"}, + {"rhs": "Equation1940", "lhs": "Equation1946"}, + {"rhs": "Equation1946", "lhs": "Equation1947"}, + {"rhs": "Equation1948", "lhs": "Equation195"}, + {"rhs": "Equation195", "lhs": "Equation1950"}, + {"rhs": "Equation1950", "lhs": "Equation1951"}, + {"rhs": "Equation1952", "lhs": "Equation1954"}, + {"rhs": "Equation1954", "lhs": "Equation1955"}, + {"rhs": "Equation1955", "lhs": "Equation1956"}, + {"rhs": "Equation1957", "lhs": "Equation196"}, + {"rhs": "Equation4379", "lhs": "Equation1969"}, + {"rhs": "Equation4582", "lhs": "Equation1969"}, + {"rhs": "Equation4596", "lhs": "Equation1969"}, + {"rhs": "Equation4379", "lhs": "Equation1972"}, + {"rhs": "Equation4582", "lhs": "Equation1972"}, + {"rhs": "Equation319", "lhs": "Equation1978"}, + {"rhs": "Equation197", "lhs": "Equation1980"}, + {"rhs": "Equation1980", "lhs": "Equation1981"}, + {"rhs": "Equation1982", "lhs": "Equation1984"}, + {"rhs": "Equation1984", "lhs": "Equation1985"}, + {"rhs": "Equation1986", "lhs": "Equation1988"}, + {"rhs": "Equation1988", "lhs": "Equation1989"}, + {"rhs": "Equation1989", "lhs": "Equation199"}, + {"rhs": "Equation199", "lhs": "Equation1990"}, + {"rhs": "Equation320", "lhs": "Equation1995"}, + {"rhs": "Equation1991", "lhs": "Equation1997"}, + {"rhs": "Equation1997", "lhs": "Equation1998"}, + {"rhs": "Equation2", "lhs": "Equation20"}, + {"rhs": "Equation20", "lhs": "Equation200"}, + {"rhs": "Equation200", "lhs": "Equation2001"}, + {"rhs": "Equation2001", "lhs": "Equation2002"}, + {"rhs": "Equation2003", "lhs": "Equation2005"}, + {"rhs": "Equation2005", "lhs": "Equation2006"}, + {"rhs": "Equation2006", "lhs": "Equation2007"}, + {"rhs": "Equation2008", "lhs": "Equation201"}, + {"rhs": "Equation201", "lhs": "Equation2015"}, + {"rhs": "Equation2015", "lhs": "Equation2016"}, + {"rhs": "Equation2016", "lhs": "Equation2017"}, + {"rhs": "Equation202", "lhs": "Equation2020"}, + {"rhs": "Equation2020", "lhs": "Equation2021"}, + {"rhs": "Equation2021", "lhs": "Equation2022"}, + {"rhs": "Equation2023", "lhs": "Equation2025"}, + {"rhs": "Equation2025", "lhs": "Equation2026"}, + {"rhs": "Equation2026", "lhs": "Equation2027"}, + {"rhs": "Equation2028", "lhs": "Equation2030"}, + {"rhs": "Equation2030", "lhs": "Equation2031"}, + {"rhs": "Equation2031", "lhs": "Equation2032"}, + {"rhs": "Equation2032", "lhs": "Equation2033"}, + {"rhs": "Equation2034", "lhs": "Equation21"}, + {"rhs": "Equation41", "lhs": "Equation2106"}, + {"rhs": "Equation4379", "lhs": "Equation2106"}, + {"rhs": "Equation4582", "lhs": "Equation2106"}, + {"rhs": "Equation41", "lhs": "Equation2120"}, + {"rhs": "Equation4653", "lhs": "Equation2123"}, + {"rhs": "Equation21", "lhs": "Equation2138"}, + {"rhs": "Equation2139", "lhs": "Equation2141"}, + {"rhs": "Equation2141", "lhs": "Equation2142"}, + {"rhs": "Equation3688", "lhs": "Equation2146"}, + {"rhs": "Equation2143", "lhs": "Equation2149"}, + {"rhs": "Equation2149", "lhs": "Equation2150"}, + {"rhs": "Equation2151", "lhs": "Equation2153"}, + {"rhs": "Equation2153", "lhs": "Equation2154"}, + {"rhs": "Equation2155", "lhs": "Equation2157"}, + {"rhs": "Equation2157", "lhs": "Equation2158"}, + {"rhs": "Equation2158", "lhs": "Equation2159"}, + {"rhs": "Equation40", "lhs": "Equation2174"}, + {"rhs": "Equation41", "lhs": "Equation2177"}, + {"rhs": "Equation4379", "lhs": "Equation2177"}, + {"rhs": "Equation4582", "lhs": "Equation2177"}, + {"rhs": "Equation2160", "lhs": "Equation2183"}, + {"rhs": "Equation2183", "lhs": "Equation2184"}, + {"rhs": "Equation2185", "lhs": "Equation2187"}, + {"rhs": "Equation2187", "lhs": "Equation2188"}, + {"rhs": "Equation2189", "lhs": "Equation2191"}, + {"rhs": "Equation2191", "lhs": "Equation2192"}, + {"rhs": "Equation2192", "lhs": "Equation2193"}, + {"rhs": "Equation22", "lhs": "Equation2200"}, + {"rhs": "Equation2200", "lhs": "Equation2201"}, + {"rhs": "Equation2202", "lhs": "Equation2204"}, + {"rhs": "Equation2204", "lhs": "Equation2205"}, + {"rhs": "Equation2206", "lhs": "Equation2208"}, + {"rhs": "Equation2208", "lhs": "Equation2209"}, + {"rhs": "Equation2209", "lhs": "Equation2210"}, + {"rhs": "Equation4653", "lhs": "Equation2214"}, + {"rhs": "Equation373", "lhs": "Equation2215"}, + {"rhs": "Equation2211", "lhs": "Equation2218"}, + {"rhs": "Equation2218", "lhs": "Equation2219"}, + {"rhs": "Equation2219", "lhs": "Equation2220"}, + {"rhs": "Equation2221", "lhs": "Equation2223"}, + {"rhs": "Equation2223", "lhs": "Equation2224"}, + {"rhs": "Equation2224", "lhs": "Equation2225"}, + {"rhs": "Equation2226", "lhs": "Equation2228"}, + {"rhs": "Equation2228", "lhs": "Equation2229"}, + {"rhs": "Equation46", "lhs": "Equation223"}, + {"rhs": "Equation2229", "lhs": "Equation2230"}, + {"rhs": "Equation2231", "lhs": "Equation2233"}, + {"rhs": "Equation2233", "lhs": "Equation2234"}, + {"rhs": "Equation2234", "lhs": "Equation2235"}, + {"rhs": "Equation2235", "lhs": "Equation2236"}, + {"rhs": "Equation46", "lhs": "Equation2292"}, + {"rhs": "Equation46", "lhs": "Equation2295"}, + {"rhs": "Equation46", "lhs": "Equation2298"}, + {"rhs": "Equation46", "lhs": "Equation230"}, + {"rhs": "Equation46", "lhs": "Equation2302"}, + {"rhs": "Equation46", "lhs": "Equation2305"}, + {"rhs": "Equation46", "lhs": "Equation2312"}, + {"rhs": "Equation2237", "lhs": "Equation232"}, + {"rhs": "Equation46", "lhs": "Equation2320"}, + {"rhs": "Equation46", "lhs": "Equation2329"}, + {"rhs": "Equation46", "lhs": "Equation2332"}, + {"rhs": "Equation46", "lhs": "Equation2339"}, + {"rhs": "Equation233", "lhs": "Equation2341"}, + {"rhs": "Equation2342", "lhs": "Equation2344"}, + {"rhs": "Equation2344", "lhs": "Equation2345"}, + {"rhs": "Equation2346", "lhs": "Equation235"}, + {"rhs": "Equation235", "lhs": "Equation2352"}, + {"rhs": "Equation2352", "lhs": "Equation2353"}, + {"rhs": "Equation2354", "lhs": "Equation2356"}, + {"rhs": "Equation2356", "lhs": "Equation2357"}, + {"rhs": "Equation2358", "lhs": "Equation236"}, + {"rhs": "Equation236", "lhs": "Equation2360"}, + {"rhs": "Equation2360", "lhs": "Equation2361"}, + {"rhs": "Equation2361", "lhs": "Equation2362"}, + {"rhs": "Equation46", "lhs": "Equation2366"}, + {"rhs": "Equation46", "lhs": "Equation2374"}, + {"rhs": "Equation237", "lhs": "Equation2386"}, + {"rhs": "Equation2386", "lhs": "Equation2387"}, + {"rhs": "Equation2388", "lhs": "Equation2390"}, + {"rhs": "Equation2390", "lhs": "Equation2391"}, + {"rhs": "Equation2392", "lhs": "Equation2394"}, + {"rhs": "Equation2394", "lhs": "Equation2395"}, + {"rhs": "Equation2395", "lhs": "Equation2396"}, + {"rhs": "Equation46", "lhs": "Equation2400"}, + {"rhs": "Equation2397", "lhs": "Equation2403"}, + {"rhs": "Equation2403", "lhs": "Equation2404"}, + {"rhs": "Equation2405", "lhs": "Equation2407"}, + {"rhs": "Equation2407", "lhs": "Equation2408"}, + {"rhs": "Equation2409", "lhs": "Equation2411"}, + {"rhs": "Equation2411", "lhs": "Equation2412"}, + {"rhs": "Equation2412", "lhs": "Equation2413"}, + {"rhs": "Equation2414", "lhs": "Equation2421"}, + {"rhs": "Equation2421", "lhs": "Equation2422"}, + {"rhs": "Equation2422", "lhs": "Equation2423"}, + {"rhs": "Equation2424", "lhs": "Equation2426"}, + {"rhs": "Equation2426", "lhs": "Equation2427"}, + {"rhs": "Equation2427", "lhs": "Equation2428"}, + {"rhs": "Equation2429", "lhs": "Equation243"}, + {"rhs": "Equation243", "lhs": "Equation2431"}, + {"rhs": "Equation2431", "lhs": "Equation2432"}, + {"rhs": "Equation2432", "lhs": "Equation2433"}, + {"rhs": "Equation2434", "lhs": "Equation2436"}, + {"rhs": "Equation2436", "lhs": "Equation2437"}, + {"rhs": "Equation2437", "lhs": "Equation2438"}, + {"rhs": "Equation2438", "lhs": "Equation2439"}, + {"rhs": "Equation2439", "lhs": "Equation244"}, + {"rhs": "Equation244", "lhs": "Equation2440"}, + {"rhs": "Equation2440", "lhs": "Equation245"}, + {"rhs": "Equation245", "lhs": "Equation247"}, + {"rhs": "Equation247", "lhs": "Equation248"}, + {"rhs": "Equation46", "lhs": "Equation2495"}, + {"rhs": "Equation46", "lhs": "Equation2498"}, + {"rhs": "Equation46", "lhs": "Equation2501"}, + {"rhs": "Equation46", "lhs": "Equation2505"}, + {"rhs": "Equation46", "lhs": "Equation2508"}, + {"rhs": "Equation249", "lhs": "Equation251"}, + {"rhs": "Equation46", "lhs": "Equation2515"}, + {"rhs": "Equation251", "lhs": "Equation252"}, + {"rhs": "Equation46", "lhs": "Equation2523"}, + {"rhs": "Equation252", "lhs": "Equation253"}, + {"rhs": "Equation46", "lhs": "Equation2532"}, + {"rhs": "Equation46", "lhs": "Equation2535"}, + {"rhs": "Equation46", "lhs": "Equation2542"}, + {"rhs": "Equation254", "lhs": "Equation2544"}, + {"rhs": "Equation2545", "lhs": "Equation2547"}, + {"rhs": "Equation2547", "lhs": "Equation2548"}, + {"rhs": "Equation2549", "lhs": "Equation2555"}, + {"rhs": "Equation2555", "lhs": "Equation2556"}, + {"rhs": "Equation2557", "lhs": "Equation2559"}, + {"rhs": "Equation2559", "lhs": "Equation2560"}, + {"rhs": "Equation2561", "lhs": "Equation2563"}, + {"rhs": "Equation2563", "lhs": "Equation2564"}, + {"rhs": "Equation2564", "lhs": "Equation2565"}, + {"rhs": "Equation46", "lhs": "Equation2569"}, + {"rhs": "Equation46", "lhs": "Equation2577"}, + {"rhs": "Equation2566", "lhs": "Equation2589"}, + {"rhs": "Equation2589", "lhs": "Equation2590"}, + {"rhs": "Equation2591", "lhs": "Equation2593"}, + {"rhs": "Equation2593", "lhs": "Equation2594"}, + {"rhs": "Equation2595", "lhs": "Equation2597"}, + {"rhs": "Equation2597", "lhs": "Equation2598"}, + {"rhs": "Equation2598", "lhs": "Equation2599"}, + {"rhs": "Equation46", "lhs": "Equation2603"}, + {"rhs": "Equation2600", "lhs": "Equation2606"}, + {"rhs": "Equation2606", "lhs": "Equation2607"}, + {"rhs": "Equation2608", "lhs": "Equation2610"}, + {"rhs": "Equation2610", "lhs": "Equation2611"}, + {"rhs": "Equation2612", "lhs": "Equation2614"}, + {"rhs": "Equation2614", "lhs": "Equation2615"}, + {"rhs": "Equation2615", "lhs": "Equation2616"}, + {"rhs": "Equation2617", "lhs": "Equation2624"}, + {"rhs": "Equation2624", "lhs": "Equation2625"}, + {"rhs": "Equation2625", "lhs": "Equation2626"}, + {"rhs": "Equation2627", "lhs": "Equation2629"}, + {"rhs": "Equation2629", "lhs": "Equation2630"}, + {"rhs": "Equation2630", "lhs": "Equation2631"}, + {"rhs": "Equation2632", "lhs": "Equation2634"}, + {"rhs": "Equation2634", "lhs": "Equation2635"}, + {"rhs": "Equation2635", "lhs": "Equation2636"}, + {"rhs": "Equation2637", "lhs": "Equation2639"}, + {"rhs": "Equation2639", "lhs": "Equation2640"}, + {"rhs": "Equation2640", "lhs": "Equation2641"}, + {"rhs": "Equation2641", "lhs": "Equation2642"}, + {"rhs": "Equation4628", "lhs": "Equation2708"}, + {"rhs": "Equation3849", "lhs": "Equation2711"}, + {"rhs": "Equation3762", "lhs": "Equation2726"}, + {"rhs": "Equation393", "lhs": "Equation2730"}, + {"rhs": "Equation355", "lhs": "Equation2731"}, + {"rhs": "Equation46", "lhs": "Equation2735"}, + {"rhs": 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"Equation2801", "lhs": "Equation2802"}, + {"rhs": "Equation2803", "lhs": "Equation2809"}, + {"rhs": "Equation2809", "lhs": "Equation2810"}, + {"rhs": "Equation2811", "lhs": "Equation2813"}, + {"rhs": "Equation2813", "lhs": "Equation2814"}, + {"rhs": "Equation2815", "lhs": "Equation2817"}, + {"rhs": "Equation2817", "lhs": "Equation2818"}, + {"rhs": "Equation2818", "lhs": "Equation2819"}, + {"rhs": "Equation46", "lhs": "Equation2824"}, + {"rhs": "Equation2820", "lhs": "Equation2827"}, + {"rhs": "Equation2827", "lhs": "Equation2828"}, + {"rhs": "Equation2828", "lhs": "Equation2829"}, + {"rhs": "Equation2830", "lhs": "Equation2832"}, + {"rhs": "Equation2832", "lhs": "Equation2833"}, + {"rhs": "Equation2833", "lhs": "Equation2834"}, + {"rhs": "Equation2835", "lhs": "Equation2837"}, + {"rhs": "Equation2837", "lhs": "Equation2838"}, + {"rhs": "Equation2838", "lhs": "Equation2839"}, + {"rhs": "Equation2839", "lhs": "Equation284"}, + {"rhs": "Equation284", "lhs": "Equation2840"}, + {"rhs": "Equation2840", "lhs": "Equation2842"}, + {"rhs": "Equation2842", "lhs": "Equation2843"}, + {"rhs": "Equation2843", "lhs": "Equation2844"}, + {"rhs": "Equation2844", "lhs": "Equation2845"}, + {"rhs": "Equation2846", "lhs": "Equation285"}, + {"rhs": "Equation285", "lhs": "Equation287"}, + {"rhs": "Equation287", "lhs": "Equation288"}, + {"rhs": "Equation46", "lhs": "Equation2904"}, + {"rhs": "Equation4671", "lhs": "Equation2907"}, + {"rhs": "Equation4694", "lhs": "Equation2918"}, + {"rhs": "Equation4671", "lhs": "Equation2929"}, + {"rhs": "Equation4694", "lhs": "Equation2930"}, + {"rhs": "Equation46", "lhs": "Equation2933"}, + {"rhs": "Equation4694", "lhs": "Equation2945"}, + {"rhs": "Equation289", "lhs": "Equation295"}, + {"rhs": "Equation295", "lhs": "Equation2950"}, + {"rhs": "Equation2951", "lhs": "Equation2953"}, + {"rhs": "Equation2953", "lhs": "Equation2954"}, + {"rhs": "Equation2955", "lhs": "Equation296"}, + {"rhs": "Equation296", "lhs": "Equation2961"}, + {"rhs": "Equation2961", "lhs": "Equation2962"}, + {"rhs": "Equation2963", "lhs": "Equation2965"}, + {"rhs": "Equation2965", "lhs": "Equation2966"}, + {"rhs": "Equation2967", "lhs": "Equation2969"}, + {"rhs": "Equation2969", "lhs": "Equation297"}, + {"rhs": "Equation297", "lhs": "Equation2970"}, + {"rhs": "Equation2970", "lhs": "Equation2971"}, + {"rhs": "Equation4671", "lhs": "Equation2983"}, + {"rhs": "Equation4694", "lhs": "Equation2984"}, + {"rhs": "Equation46", "lhs": "Equation2987"}, + {"rhs": "Equation2972", "lhs": "Equation299"}, + {"rhs": "Equation299", "lhs": "Equation2995"}, + {"rhs": "Equation2995", "lhs": "Equation2996"}, + {"rhs": "Equation2997", "lhs": "Equation2999"}, + {"rhs": "Equation2999", "lhs": "Equation300"}, + {"rhs": "Equation300", "lhs": "Equation3000"}, + {"rhs": "Equation3001", "lhs": "Equation3003"}, + {"rhs": "Equation3003", "lhs": "Equation3004"}, + {"rhs": "Equation3004", "lhs": "Equation3005"}, + {"rhs": "Equation3006", "lhs": "Equation301"}, + {"rhs": 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"Equation3046", "lhs": "Equation3047"}, + {"rhs": "Equation3047", "lhs": "Equation3048"}, + {"rhs": "Equation3049", "lhs": "Equation305"}, + {"rhs": "Equation4671", "lhs": "Equation3110"}, + {"rhs": "Equation4694", "lhs": "Equation3111"}, + {"rhs": "Equation4694", "lhs": "Equation3121"}, + {"rhs": "Equation46", "lhs": "Equation3125"}, + {"rhs": "Equation46", "lhs": "Equation3129"}, + {"rhs": "Equation46", "lhs": "Equation3133"}, + {"rhs": "Equation46", "lhs": "Equation3136"}, + {"rhs": "Equation46", "lhs": "Equation3137"}, + {"rhs": "Equation4694", "lhs": "Equation3148"}, + {"rhs": "Equation306", "lhs": "Equation3153"}, + {"rhs": "Equation3154", "lhs": "Equation3156"}, + {"rhs": "Equation3156", "lhs": "Equation3157"}, + {"rhs": "Equation46", "lhs": "Equation3162"}, + {"rhs": "Equation3158", "lhs": "Equation3164"}, + {"rhs": "Equation3164", "lhs": "Equation3165"}, + {"rhs": "Equation3166", "lhs": "Equation3168"}, + {"rhs": "Equation3168", "lhs": "Equation3169"}, + {"rhs": "Equation3170", "lhs": "Equation3172"}, + {"rhs": "Equation3172", "lhs": "Equation3173"}, + {"rhs": "Equation3173", "lhs": "Equation3174"}, + {"rhs": "Equation46", "lhs": "Equation3187"}, + {"rhs": "Equation4379", "lhs": "Equation3189"}, + {"rhs": "Equation4582", "lhs": "Equation3189"}, + {"rhs": "Equation4694", "lhs": "Equation3190"}, + {"rhs": "Equation3175", "lhs": "Equation3198"}, + {"rhs": "Equation3198", "lhs": "Equation3199"}, + {"rhs": "Equation3199", "lhs": "Equation32"}, + {"rhs": "Equation32", "lhs": "Equation3200"}, + {"rhs": "Equation3200", "lhs": "Equation3202"}, + {"rhs": "Equation3202", "lhs": "Equation3203"}, + {"rhs": "Equation3204", "lhs": "Equation3206"}, + {"rhs": "Equation3206", "lhs": "Equation3207"}, + {"rhs": "Equation3207", "lhs": "Equation3208"}, + {"rhs": "Equation46", "lhs": "Equation3213"}, + {"rhs": "Equation3209", "lhs": "Equation3215"}, + {"rhs": "Equation3215", "lhs": "Equation3216"}, + {"rhs": "Equation3217", "lhs": "Equation3219"}, + {"rhs": "Equation327", "lhs": "Equation322"}, + {"rhs": "Equation328", "lhs": "Equation322"}, + {"rhs": "Equation329", "lhs": "Equation322"}, + {"rhs": "Equation330", "lhs": "Equation322"}, + {"rhs": "Equation3307", "lhs": "Equation322"}, + {"rhs": "Equation331", "lhs": "Equation322"}, + {"rhs": "Equation3311", "lhs": "Equation322"}, + {"rhs": "Equation3314", "lhs": "Equation322"}, + {"rhs": "Equation3325", "lhs": "Equation322"}, + {"rhs": "Equation3328", "lhs": "Equation322"}, + {"rhs": "Equation3332", "lhs": "Equation322"}, + {"rhs": "Equation3336", "lhs": "Equation322"}, + {"rhs": "Equation3337", "lhs": "Equation322"}, + {"rhs": "Equation3339", "lhs": "Equation322"}, + {"rhs": "Equation3510", "lhs": "Equation322"}, + {"rhs": "Equation3514", "lhs": "Equation322"}, + {"rhs": "Equation3517", "lhs": "Equation322"}, + {"rhs": "Equation3528", "lhs": "Equation322"}, + {"rhs": "Equation3531", "lhs": "Equation322"}, + {"rhs": "Equation3535", "lhs": "Equation322"}, + {"rhs": "Equation3539", "lhs": "Equation322"}, + {"rhs": "Equation38", "lhs": "Equation322"}, + {"rhs": "Equation42", "lhs": "Equation322"}, + {"rhs": "Equation3219", "lhs": "Equation3220"}, + {"rhs": "Equation3221", "lhs": "Equation3223"}, + {"rhs": "Equation3223", "lhs": "Equation3224"}, + {"rhs": "Equation3224", "lhs": "Equation3225"}, + {"rhs": "Equation46", "lhs": "Equation3229"}, + {"rhs": "Equation3226", "lhs": "Equation3233"}, + {"rhs": "Equation3233", "lhs": "Equation3234"}, + {"rhs": "Equation3234", "lhs": "Equation3235"}, + {"rhs": "Equation3236", "lhs": "Equation3238"}, + {"rhs": "Equation3238", "lhs": "Equation3239"}, + {"rhs": "Equation3239", "lhs": "Equation3240"}, + {"rhs": "Equation3241", "lhs": "Equation3243"}, + {"rhs": "Equation3243", "lhs": "Equation3244"}, + {"rhs": "Equation3244", "lhs": "Equation3245"}, + {"rhs": "Equation3246", "lhs": "Equation3248"}, + {"rhs": "Equation3248", "lhs": "Equation3249"}, + {"rhs": "Equation3249", "lhs": "Equation3250"}, + {"rhs": "Equation3250", "lhs": "Equation3251"}, + {"rhs": "Equation40", "lhs": "Equation3282"}, + {"rhs": "Equation3252", "lhs": "Equation33"}, + {"rhs": "Equation324", "lhs": "Equation3305"}, + {"rhs": "Equation4269", "lhs": "Equation3312"}, + {"rhs": "Equation332", "lhs": "Equation3344"}, + {"rhs": "Equation45", "lhs": "Equation3356"}, + {"rhs": "Equation4391", "lhs": "Equation3357"}, + {"rhs": "Equation4385", "lhs": "Equation3358"}, + {"rhs": "Equation4385", "lhs": "Equation338"}, + {"rhs": "Equation342", "lhs": "Equation3382"}, + {"rhs": "Equation4275", "lhs": "Equation3388"}, + {"rhs": "Equation4387", "lhs": "Equation3391"}, + {"rhs": "Equation4278", "lhs": "Equation3392"}, + {"rhs": "Equation4327", "lhs": "Equation3392"}, + {"rhs": "Equation3721", "lhs": "Equation3398"}, + {"rhs": "Equation4386", "lhs": "Equation3404"}, + {"rhs": "Equation4387", "lhs": "Equation3408"}, + {"rhs": "Equation3802", "lhs": "Equation3410"}, + {"rhs": "Equation41", "lhs": "Equation3423"}, + {"rhs": "Equation4281", "lhs": "Equation3424"}, + {"rhs": "Equation4394", "lhs": "Equation3424"}, + {"rhs": "Equation342", "lhs": "Equation3433"}, + {"rhs": "Equation3731", "lhs": "Equation3437"}, + {"rhs": "Equation342", "lhs": "Equation3438"}, + {"rhs": "Equation40", "lhs": "Equation3485"}, + {"rhs": "Equation33", "lhs": "Equation35"}, + {"rhs": "Equation3341", "lhs": "Equation3508"}, + {"rhs": "Equation45", "lhs": "Equation3559"}, + {"rhs": "Equation35", "lhs": "Equation36"}, + {"rhs": "Equation41", "lhs": "Equation3626"}, + {"rhs": "Equation40", "lhs": "Equation3688"}, + {"rhs": "Equation40", "lhs": "Equation3689"}, + {"rhs": "Equation40", "lhs": "Equation3691"}, + {"rhs": "Equation40", "lhs": "Equation3692"}, + {"rhs": "Equation40", "lhs": "Equation3699"}, + {"rhs": "Equation40", "lhs": "Equation3703"}, + {"rhs": "Equation40", "lhs": "Equation3704"}, + {"rhs": "Equation42", "lhs": "Equation3711"}, + {"rhs": "Equation45", "lhs": "Equation3762"}, + {"rhs": "Equation41", "lhs": "Equation3829"}, + {"rhs": "Equation41", "lhs": "Equation3830"}, + {"rhs": "Equation41", "lhs": "Equation3833"}, + {"rhs": "Equation41", "lhs": "Equation3834"}, + {"rhs": "Equation41", "lhs": "Equation3835"}, + {"rhs": "Equation41", "lhs": "Equation3848"}, + {"rhs": "Equation41", "lhs": "Equation3849"}, + {"rhs": "Equation41", "lhs": "Equation3854"}, + {"rhs": "Equation41", "lhs": "Equation3860"}, + {"rhs": "Equation381", "lhs": "Equation388"}, + {"rhs": "Equation39", "lhs": "Equation388"}, + {"rhs": "Equation395", "lhs": "Equation388"}, + {"rhs": "Equation3968", "lhs": "Equation388"}, + {"rhs": "Equation3976", "lhs": "Equation388"}, + {"rhs": "Equation3984", "lhs": "Equation388"}, + {"rhs": "Equation399", "lhs": "Equation388"}, + {"rhs": "Equation4001", "lhs": "Equation388"}, + {"rhs": "Equation4010", "lhs": "Equation388"}, + {"rhs": "Equation4018", "lhs": "Equation388"}, + {"rhs": "Equation403", "lhs": "Equation388"}, + {"rhs": "Equation4035", "lhs": "Equation388"}, + {"rhs": "Equation4045", "lhs": "Equation388"}, + {"rhs": "Equation4050", "lhs": "Equation388"}, + {"rhs": "Equation407", "lhs": "Equation388"}, + {"rhs": "Equation4171", "lhs": "Equation388"}, + {"rhs": "Equation4179", "lhs": "Equation388"}, + {"rhs": "Equation4187", "lhs": "Equation388"}, + {"rhs": "Equation4204", "lhs": "Equation388"}, + {"rhs": "Equation4213", "lhs": "Equation388"}, + {"rhs": "Equation4221", "lhs": "Equation388"}, + {"rhs": "Equation4374", "lhs": "Equation388"}, + {"rhs": "Equation45", "lhs": "Equation388"}, + {"rhs": "Equation40", "lhs": "Equation3891"}, + {"rhs": "Equation4395", "lhs": "Equation390"}, + {"rhs": "Equation42", "lhs": "Equation3914"}, + {"rhs": "Equation3916", "lhs": "Equation3941"}, + {"rhs": "Equation3916", "lhs": "Equation3949"}, + {"rhs": "Equation391", "lhs": "Equation3965"}, + {"rhs": "Equation3953", "lhs": "Equation3978"}, + {"rhs": "Equation3953", "lhs": "Equation3986"}, + {"rhs": "Equation376", "lhs": "Equation3991"}, + {"rhs": "Equation4628", "lhs": "Equation3991"}, + {"rhs": "Equation376", "lhs": "Equation3995"}, + {"rhs": "Equation4628", "lhs": "Equation3995"}, + {"rhs": "Equation376", "lhs": "Equation3999"}, + {"rhs": "Equation4628", "lhs": "Equation3999"}, + {"rhs": "Equation376", "lhs": "Equation4003"}, + {"rhs": "Equation4628", "lhs": "Equation4003"}, + {"rhs": "Equation376", "lhs": "Equation4008"}, + {"rhs": "Equation4628", "lhs": "Equation4008"}, + {"rhs": "Equation376", "lhs": "Equation4020"}, + {"rhs": "Equation4628", "lhs": "Equation4020"}, + {"rhs": "Equation376", "lhs": "Equation4025"}, + {"rhs": "Equation4628", "lhs": "Equation4025"}, + {"rhs": "Equation41", "lhs": "Equation4032"}, + {"rhs": "Equation376", "lhs": "Equation4033"}, + {"rhs": "Equation4628", "lhs": "Equation4033"}, + {"rhs": "Equation376", "lhs": "Equation4042"}, + {"rhs": "Equation4628", "lhs": "Equation4042"}, + {"rhs": "Equation376", "lhs": "Equation4047"}, + {"rhs": "Equation4628", "lhs": "Equation4047"}, + {"rhs": "Equation3991", "lhs": "Equation4048"}, + {"rhs": "Equation3991", "lhs": "Equation4053"}, + {"rhs": "Equation376", "lhs": "Equation4057"}, + {"rhs": "Equation4628", "lhs": "Equation4057"}, + {"rhs": "Equation3991", "lhs": "Equation4063"}, + {"rhs": "Equation40", "lhs": "Equation4094"}, + {"rhs": "Equation42", "lhs": "Equation4117"}, + {"rhs": "Equation4655", "lhs": "Equation4142"}, + {"rhs": "Equation4656", "lhs": "Equation4143"}, + {"rhs": "Equation4676", "lhs": "Equation4144"}, + {"rhs": "Equation4060", "lhs": "Equation4168"}, + {"rhs": "Equation4395", "lhs": "Equation4174"}, + {"rhs": "Equation4397", "lhs": "Equation4177"}, + {"rhs": "Equation4397", "lhs": "Equation4181"}, + {"rhs": "Equation374", "lhs": "Equation4191"}, + {"rhs": "Equation375", "lhs": "Equation4192"}, + {"rhs": "Equation376", "lhs": "Equation4194"}, + {"rhs": "Equation3714", "lhs": "Equation4197"}, + {"rhs": "Equation376", "lhs": "Equation4198"}, + {"rhs": "Equation4676", "lhs": "Equation42"}, + {"rhs": "Equation376", "lhs": "Equation4202"}, + {"rhs": "Equation4694", "lhs": "Equation4202"}, + {"rhs": "Equation4625", "lhs": "Equation4204"}, + {"rhs": "Equation3717", "lhs": "Equation4205"}, + {"rhs": "Equation4119", "lhs": "Equation4211"}, + {"rhs": "Equation4624", "lhs": "Equation4211"}, + {"rhs": "Equation4122", "lhs": "Equation4215"}, + {"rhs": "Equation4624", "lhs": "Equation4215"}, + {"rhs": "Equation376", "lhs": "Equation4219"}, + {"rhs": "Equation4694", "lhs": "Equation4219"}, + {"rhs": "Equation374", "lhs": "Equation4220"}, + {"rhs": "Equation41", "lhs": "Equation4235"}, + {"rhs": "Equation374", "lhs": "Equation4237"}, + {"rhs": "Equation3713", "lhs": "Equation4244"}, + {"rhs": "Equation4119", "lhs": "Equation4245"}, + {"rhs": "Equation4596", "lhs": "Equation4245"}, + {"rhs": "Equation374", "lhs": "Equation4250"}, + {"rhs": "Equation4122", "lhs": "Equation4250"}, + {"rhs": "Equation4596", "lhs": "Equation4250"}, + {"rhs": "Equation376", "lhs": "Equation4260"}, + {"rhs": "Equation4628", "lhs": "Equation4260"}, + {"rhs": "Equation4677", "lhs": "Equation43"}, + {"rhs": "Equation4276", "lhs": "Equation4389"}, + {"rhs": "Equation4277", "lhs": "Equation4425"}, + {"rhs": "Equation4279", "lhs": "Equation4462"}, + {"rhs": "Equation4280", "lhs": "Equation4499"}, + {"rhs": "Equation4278", "lhs": "Equation45"}, + {"rhs": "Equation4327", "lhs": "Equation45"}, + {"rhs": "Equation4281", "lhs": "Equation4575"}, + {"rhs": "Equation37", "lhs": "Equation514"}, + {"rhs": "Equation515", "lhs": "Equation517"}, + {"rhs": "Equation517", "lhs": "Equation518"}, + {"rhs": "Equation519", "lhs": "Equation525"}, + {"rhs": "Equation525", "lhs": "Equation526"}, + {"rhs": "Equation527", "lhs": "Equation529"}, + {"rhs": "Equation529", "lhs": "Equation530"}, + {"rhs": "Equation531", "lhs": "Equation533"}, + {"rhs": "Equation533", "lhs": "Equation534"}, + {"rhs": "Equation534", "lhs": "Equation535"}, + {"rhs": "Equation536", "lhs": "Equation559"}, + {"rhs": "Equation559", "lhs": "Equation560"}, + {"rhs": "Equation561", "lhs": "Equation563"}, + {"rhs": "Equation563", "lhs": "Equation564"}, + {"rhs": "Equation565", "lhs": "Equation567"}, + {"rhs": "Equation567", "lhs": "Equation568"}, + {"rhs": "Equation568", "lhs": "Equation569"}, + {"rhs": "Equation570", "lhs": "Equation576"}, + {"rhs": "Equation576", "lhs": "Equation577"}, + {"rhs": "Equation578", "lhs": "Equation580"}, + {"rhs": "Equation580", "lhs": "Equation581"}, + {"rhs": "Equation582", "lhs": "Equation584"}, + {"rhs": "Equation584", "lhs": "Equation585"}, + {"rhs": "Equation585", "lhs": "Equation586"}, + {"rhs": "Equation41", "lhs": "Equation591"}, + {"rhs": "Equation4653", "lhs": "Equation591"}, + {"rhs": "Equation587", "lhs": "Equation594"}, + {"rhs": "Equation594", "lhs": "Equation595"}, + {"rhs": "Equation595", "lhs": "Equation596"}, + {"rhs": "Equation597", "lhs": "Equation599"}, + {"rhs": "Equation599", "lhs": "Equation6"}, + {"rhs": "Equation6", "lhs": "Equation600"}, + {"rhs": "Equation600", "lhs": "Equation601"}, + {"rhs": "Equation602", "lhs": "Equation604"}, + {"rhs": "Equation604", "lhs": "Equation605"}, + {"rhs": "Equation605", "lhs": "Equation606"}, + {"rhs": "Equation607", "lhs": "Equation609"}, + {"rhs": "Equation609", "lhs": "Equation610"}, + {"rhs": "Equation610", "lhs": "Equation611"}, + {"rhs": "Equation611", "lhs": "Equation612"}, + {"rhs": "Equation7", "lhs": "Equation717"}, + {"rhs": "Equation718", "lhs": "Equation720"}, + {"rhs": "Equation720", "lhs": "Equation721"}, + {"rhs": "Equation722", "lhs": "Equation728"}, + {"rhs": "Equation728", "lhs": "Equation729"}, + {"rhs": "Equation730", "lhs": "Equation732"}, + {"rhs": "Equation732", "lhs": "Equation733"}, + {"rhs": "Equation734", "lhs": "Equation736"}, + {"rhs": "Equation736", "lhs": "Equation737"}, + {"rhs": "Equation737", "lhs": "Equation738"}, + {"rhs": "Equation41", "lhs": "Equation742"}, + {"rhs": "Equation4653", "lhs": "Equation742"}, + {"rhs": "Equation739", "lhs": "Equation76"}, + {"rhs": "Equation76", "lhs": "Equation762"}, + {"rhs": "Equation762", "lhs": "Equation763"}, + {"rhs": "Equation764", "lhs": "Equation766"}, + {"rhs": "Equation766", "lhs": "Equation767"}, + {"rhs": "Equation768", "lhs": "Equation77"}, + {"rhs": "Equation77", "lhs": "Equation770"}, + {"rhs": "Equation770", "lhs": "Equation771"}, + {"rhs": "Equation771", "lhs": "Equation772"}, + {"rhs": "Equation773", "lhs": "Equation779"}, + {"rhs": "Equation779", "lhs": "Equation780"}, + {"rhs": "Equation781", "lhs": "Equation783"}, + {"rhs": "Equation783", "lhs": "Equation784"}, + {"rhs": "Equation785", "lhs": "Equation787"}, + {"rhs": "Equation787", "lhs": "Equation788"}, + {"rhs": "Equation788", "lhs": "Equation789"}, + {"rhs": "Equation789", "lhs": "Equation79"}, + {"rhs": "Equation79", "lhs": "Equation790"}, + {"rhs": "Equation790", "lhs": "Equation797"}, + {"rhs": "Equation797", "lhs": "Equation798"}, + {"rhs": "Equation798", "lhs": "Equation799"}, + {"rhs": "Equation799", "lhs": "Equation80"}, + {"rhs": "Equation80", "lhs": "Equation800"}, + {"rhs": "Equation800", "lhs": "Equation802"}, + {"rhs": "Equation802", "lhs": "Equation803"}, + {"rhs": "Equation803", "lhs": "Equation804"}, + {"rhs": "Equation805", "lhs": "Equation807"}, + {"rhs": "Equation807", "lhs": "Equation808"}, + {"rhs": "Equation808", "lhs": "Equation809"}, + {"rhs": "Equation809", "lhs": "Equation81"}, + {"rhs": "Equation81", "lhs": "Equation810"}, + {"rhs": "Equation810", "lhs": "Equation812"}, + {"rhs": "Equation812", "lhs": "Equation813"}, + {"rhs": "Equation813", "lhs": "Equation814"}, + {"rhs": "Equation814", "lhs": "Equation815"}, + {"rhs": "Equation816", "lhs": "Equation87"}, + {"rhs": "Equation41", "lhs": "Equation877"}, + {"rhs": "Equation4653", "lhs": "Equation877"}, + {"rhs": "Equation87", "lhs": "Equation88"}, + {"rhs": "Equation41", "lhs": "Equation899"}, + {"rhs": "Equation4653", "lhs": "Equation899"}, + {"rhs": "Equation89", "lhs": "Equation91"}, + {"rhs": "Equation91", "lhs": "Equation92"}, + {"rhs": "Equation92", "lhs": "Equation920"}, + {"rhs": "Equation921", "lhs": "Equation923"}, + {"rhs": "Equation923", "lhs": "Equation924"}, + {"rhs": "Equation925", "lhs": "Equation93"}, + {"rhs": "Equation93", "lhs": "Equation931"}, + {"rhs": "Equation931", "lhs": "Equation932"}, + {"rhs": "Equation933", "lhs": "Equation935"}, + {"rhs": "Equation935", "lhs": "Equation936"}, + {"rhs": "Equation937", "lhs": "Equation939"}, + {"rhs": "Equation939", "lhs": "Equation940"}, + {"rhs": "Equation940", "lhs": "Equation941"}, + {"rhs": "Equation942", "lhs": "Equation95"}, + {"rhs": "Equation41", "lhs": "Equation953"}, + {"rhs": "Equation4653", "lhs": "Equation953"}, + {"rhs": "Equation95", "lhs": "Equation96"}, + {"rhs": "Equation96", "lhs": "Equation965"}, + {"rhs": "Equation965", "lhs": "Equation966"}, + {"rhs": "Equation967", "lhs": "Equation969"}, + {"rhs": "Equation969", "lhs": "Equation97"}, + {"rhs": "Equation97", "lhs": "Equation970"}, + {"rhs": "Equation971", "lhs": "Equation973"}, + {"rhs": "Equation973", "lhs": "Equation974"}, + {"rhs": "Equation974", "lhs": "Equation975"}, + {"rhs": "Equation40", "lhs": "Equation979"}, + {"rhs": "Equation98", "lhs": "Equation982"}, + {"rhs": "Equation982", "lhs": "Equation983"}, + {"rhs": "Equation984", "lhs": "Equation986"}, + {"rhs": "Equation986", "lhs": "Equation987"}, + {"rhs": "Equation988", "lhs": "Equation990"}, + {"rhs": "Equation990", "lhs": "Equation991"}, + {"rhs": "Equation991", "lhs": "Equation992"}]}