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Acb theta v2 #2182

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e1e2fca
Reorganize header file, introduce theta_ctx structure
j-kieffer Aug 20, 2024
8ecb42e
Add basic functions for acb_theta_ctx_t
j-kieffer Aug 20, 2024
5ea9be6
Write tests and check ctx_set_tau and set_z
j-kieffer Aug 20, 2024
081bca3
Add tests for ctx_set_t and ctx_dupl
j-kieffer Aug 21, 2024
bf9fb89
New function sum_work to replace naive_worker
j-kieffer Aug 21, 2024
4f5e75b
Write sum_worker functions
j-kieffer Aug 21, 2024
0de0ccd
Keep theta_sum functions for later (without ctx argument)
j-kieffer Aug 21, 2024
abf05fc
Add exp_2zs in ctx structure and modify functions accordingly
j-kieffer Aug 21, 2024
7d4fff0
t-sum_00 passes for g<=3 but fails for g<=4
j-kieffer Aug 21, 2024
c3be638
Fix bug in ctx_set_z
j-kieffer Aug 21, 2024
f60670c
Write function sum_a0 which compiles; todo: check
j-kieffer Aug 22, 2024
58f57b0
Expose ctx_shift_z for easier testing
j-kieffer Aug 22, 2024
18c7e3d
ctx_shift_z passes test
j-kieffer Aug 22, 2024
dc1fa44
t-sum_a0 passes for g=1
j-kieffer Aug 22, 2024
a1a2ddf
Correct bug in ctx_shift_z
j-kieffer Aug 22, 2024
8bd5fbe
Write and test sum_0b
j-kieffer Aug 22, 2024
0c50493
t-sum_all passes in g=1 case
j-kieffer Aug 22, 2024
050f10f
Fix signs in sum_all, faster tests
j-kieffer Aug 23, 2024
832aa3f
Write and test sum_jet_00; write sum_jet_all
j-kieffer Aug 23, 2024
92072f0
sum_jet_all passes tests
j-kieffer Aug 23, 2024
367ad08
Attempt at new signatures for ql/main functions
j-kieffer Aug 23, 2024
b84a68d
Big rewrite of context functions (does not compile)
j-kieffer Aug 26, 2024
fcea652
Code compiles, silence tests
j-kieffer Aug 26, 2024
216cd4d
Rewrite tests for context functions
j-kieffer Aug 27, 2024
1303af7
Rewrite tests for theta_sum functions
j-kieffer Aug 27, 2024
3ccf696
Attempt at ql_setup; add copy functions for contexts
j-kieffer Aug 27, 2024
992e460
Write and test copy functions
j-kieffer Aug 27, 2024
5912d8a
Attempt at ql_exact and ql_steps
j-kieffer Aug 27, 2024
2d31198
Change sum_a0 to sum_a0_tilde; test ql_setup and ql_steps
j-kieffer Aug 28, 2024
f9aeade
Attempt at ql_split
j-kieffer Aug 28, 2024
7ecf865
Add u in ctx_z for g = 1; test ql_lower_dim
j-kieffer Aug 29, 2024
6f5bc44
Attempt at ql_exact; remove sqr argument
j-kieffer Aug 29, 2024
e7f12c5
Attempt at ql_all_new
j-kieffer Aug 29, 2024
323e4df
Add duplication in ql_all_new
j-kieffer Aug 29, 2024
84533f5
Add errors in ql_all_new; fix bug in test
j-kieffer Aug 29, 2024
06e6964
Write test for ql_exact, todo: check all cases reached
j-kieffer Aug 29, 2024
18df29d
Add pattern as argument to ql_exact
j-kieffer Aug 30, 2024
e08ca3d
Always start with zero vector in ql_exact_lower_dim
j-kieffer Aug 30, 2024
6a892af
Allow all=1 in several functions and tests; fix old bug in ctx_z_shif…
j-kieffer Aug 30, 2024
83675e2
Fix bug in ql_steps for all=1
j-kieffer Aug 30, 2024
bdc2bf1
Correct bug in ql_exact, smarter error bounds, test ql_all_new
j-kieffer Sep 2, 2024
30ca49b
Rename ql_all_new -> all_notransform; fix bug in ql_setup; write and …
j-kieffer Sep 2, 2024
5b8a6d2
Attempt at theta_00
j-kieffer Sep 2, 2024
39bdbbb
Attempt at new functions
j-kieffer Sep 2, 2024
8659001
Code compiles again
j-kieffer Sep 3, 2024
b80572e
Fix bug in ql_all_sum (sqr=1); test all_new
j-kieffer Sep 3, 2024
030f19e
Add tests for main functions; fix some bugs
j-kieffer Sep 3, 2024
9584888
Test jet-00; use jet_all_notransform in g2_sextic_g5
j-kieffer Sep 3, 2024
f124a02
Replace old functions acb_theta_all and _jet_all by new ones
j-kieffer Sep 3, 2024
afeeb13
Separate acb_theta_types.h
j-kieffer Sep 3, 2024
617ae14
Remove old ql_all functions
j-kieffer Sep 4, 2024
62d9d50
Remove old ql_a0 functions
j-kieffer Sep 4, 2024
fb71ff2
Remove g2_jet_naive_1
j-kieffer Sep 4, 2024
041d876
Remove jet_naive_fixed_ab
j-kieffer Sep 4, 2024
3d446df
Cheaper t-g2_sextic; rewrite t-sum_jet_all from t-jet_naive_all
j-kieffer Sep 4, 2024
74ddc7e
Rewrite t-jet_all using sum_jet_all
j-kieffer Sep 4, 2024
34defab
Fix memory leak
j-kieffer Sep 4, 2024
c425475
Use sum_jet_all in t-jet_error_bounds
j-kieffer Sep 4, 2024
98d8d86
Remove t-jet_00_notransform; tested through jet_one_notransform
j-kieffer Sep 4, 2024
77b4f2f
Use sum_jet_all in t-sum_jet_00
j-kieffer Sep 4, 2024
0cc3ada
Remove old jet_naive functions
j-kieffer Sep 4, 2024
3884955
Use sum_all_tilde in t-sum_a0_tilde
j-kieffer Sep 4, 2024
ea007f7
Remove old naive_fixed functions
j-kieffer Sep 4, 2024
933e708
Remove t-00_notransform; test through one_notransform
j-kieffer Sep 4, 2024
e9c7ea5
Use sum_0b in t-sum_00; remove old naive_00
j-kieffer Sep 4, 2024
072fd48
Use all_notransform in t-all
j-kieffer Sep 4, 2024
6c95422
Use modular_theta in t-sum_all_tilde
j-kieffer Sep 4, 2024
0a6458b
Use sum_all_tilde in t-jet_ql_bounds
j-kieffer Sep 4, 2024
eaa6e2e
Remove old naive_all
j-kieffer Sep 4, 2024
2d045bb
Remove t-sum_0b; tested through sum_all_tilde
j-kieffer Sep 4, 2024
717f2d5
Use sum_a0_tilde in t-agm_mul
j-kieffer Sep 4, 2024
d655dcb
Move sum_worker type to acb_theta_types.h; remove old naive_worker, n…
j-kieffer Sep 4, 2024
540d215
Use new function reduce_tau in theta_00
j-kieffer Sep 4, 2024
8c7917a
Use reduce_tau in theta_all
j-kieffer Sep 4, 2024
3bb95c5
Expose jet_exp_qf; use reduce_tau in jet_00
j-kieffer Sep 4, 2024
5cc3e77
Use reduce_tau in jet_all
j-kieffer Sep 4, 2024
57694b1
Use new function reduce_z in theta_00
j-kieffer Sep 4, 2024
e6b6aa4
Use reduce_z in theta_all (no dots!)
j-kieffer Sep 4, 2024
f29edef
Use reduce_z in jet_00
j-kieffer Sep 4, 2024
9fc92e6
Use reduce_z in jet_all; simpler t-jet_00 and t-jet_all; no signs in …
j-kieffer Sep 4, 2024
ef3a782
Remove old naive_reduce; use reduced vectors in t-..._radius directly
j-kieffer Sep 4, 2024
5e68f7a
Make jet_finite_diff static in jet_all_notransform
j-kieffer Sep 4, 2024
8d320a3
Make summation workers static
j-kieffer Sep 4, 2024
52dfd37
Remove most accessors for eld_t's
j-kieffer Sep 4, 2024
d3d63ad
Remove siegel_transform_z
j-kieffer Sep 5, 2024
00d2de7
Replace siegel_yinv by siegel_cho_yinv
j-kieffer Sep 5, 2024
d5b04a2
Use siegel_cho_yinv everywhere
j-kieffer Sep 5, 2024
5456ebe
Remove siegel_cho, siegel_yinv
j-kieffer Sep 5, 2024
7836ab3
Make char_get_a static in sum_jet_all
j-kieffer Sep 5, 2024
cc25534
Remove char_get_slong
j-kieffer Sep 5, 2024
fe78861
Make dist functions static in dist_a0
j-kieffer Sep 5, 2024
7be1368
Replace dist_a0 by agm_distances
j-kieffer Sep 5, 2024
6e16f00
Rename dist_addprec -> agm_addprec
j-kieffer Sep 5, 2024
43b3c04
Make transform_sqrtdet static in transform_kappa
j-kieffer Sep 5, 2024
f83c4e8
Delete temp
j-kieffer Sep 5, 2024
0c1cc0a
Add nb in randtest_vec_reduced
j-kieffer Sep 5, 2024
bf3893a
Use siegel_randtest_compact in t-ql_exact
j-kieffer Sep 5, 2024
84cb022
Sample compact/reduced tau, z where appropriate
j-kieffer Sep 5, 2024
efa0bf5
No reduction in ctx_z_set
j-kieffer Sep 5, 2024
dd86b07
Remove ctx_r
j-kieffer Sep 5, 2024
965874f
Add reduction in ql_lower_dim
j-kieffer Sep 5, 2024
4ae24a0
Correct bug in ctx_z_add_real
j-kieffer Sep 5, 2024
9ac84ee
Do not modify c in ctx_z_shift_a0
j-kieffer Sep 5, 2024
6e04783
Remove multiplications by c (always 1)
j-kieffer Sep 5, 2024
542eb9f
Remove c in ctx_z
j-kieffer Sep 5, 2024
9a3e9bc
Remove z in ctx_z
j-kieffer Sep 5, 2024
da8b820
Remove macro ctx_v
j-kieffer Sep 5, 2024
3f91241
Remove ctx_z_copy
j-kieffer Sep 5, 2024
ac9f40f
Remove ctx_choinv
j-kieffer Sep 5, 2024
7f72b71
Remove ctx_y
j-kieffer Sep 5, 2024
d536952
Make agm_hadamard static in agm_mul
j-kieffer Sep 5, 2024
1d68356
Remove macro eld_coord
j-kieffer Sep 5, 2024
f2e31f6
Make jet_ql_radius static in jet_all_notransform
j-kieffer Sep 5, 2024
d1e9ba1
Remove tau from ctx_tau
j-kieffer Sep 5, 2024
51dd8b5
Rename naive_term -> sum_term
j-kieffer Sep 5, 2024
e7692de
Make ctx_tau_copy static in ql_setup
j-kieffer Sep 5, 2024
5a20b5b
Make ctx_tau_overlaps static in test
j-kieffer Sep 5, 2024
86e675c
Do not include fmpz_mat.h in header
j-kieffer Sep 6, 2024
31e6daf
Rename transform_kappa -> siegel_kappa
j-kieffer Sep 6, 2024
b9fe68c
Use less macros for ctx_tau
j-kieffer Sep 6, 2024
a51960b
Remove macros for exp_tau
j-kieffer Sep 6, 2024
af2cc8c
Add g in ctx_tau, remove macro
j-kieffer Sep 6, 2024
7837da0
Remove macro ctx_is_real
j-kieffer Sep 6, 2024
3476d5a
Remove macros ctx_exp_z
j-kieffer Sep 6, 2024
d7cd3b8
Remove macro ctx_uinv
j-kieffer Sep 6, 2024
9b07606
Remove macro ctx_u
j-kieffer Sep 6, 2024
07e3d31
Rename naive_radius->sum_radius
j-kieffer Sep 6, 2024
e1ced5b
Rename jet_ql_bounds -> sum_bound
j-kieffer Sep 6, 2024
ce12ae0
Start using new function char_table
j-kieffer Sep 6, 2024
d2777e2
Add argument ab in char_table
j-kieffer Sep 6, 2024
cfc881d
Rename transform_char -> char_table
j-kieffer Sep 6, 2024
4d49701
Rename transform_proj -> char_shuffle
j-kieffer Sep 6, 2024
a881e5f
Add flag allow_shift in ctx_tau
j-kieffer Sep 6, 2024
f5f59fe
Restore all tests
j-kieffer Sep 6, 2024
9763c23
Avoid some nans
j-kieffer Sep 6, 2024
94f2574
Document new main functions
j-kieffer Jan 21, 2025
45d0010
Document new acb_siegel functions
j-kieffer Jan 21, 2025
a7272cc
Document new acb_theta_eld functions
j-kieffer Jan 21, 2025
780d8af
Start documentation for ctx_tau
j-kieffer Jan 21, 2025
d062fd3
Document new ctx functions
j-kieffer Jan 21, 2025
12ca222
Move theoretical stuff together
j-kieffer Jan 21, 2025
433f904
Add a word on precision; will remove big theoretical section
j-kieffer Jan 22, 2025
d3b0692
Reorganize header
j-kieffer Jan 22, 2025
a8e57d0
Reorganize header a bit, document new ql functions
j-kieffer Jan 23, 2025
c5f1081
End first pass on theta.rst
j-kieffer Jan 23, 2025
2a2e5f9
Rewrite intro
j-kieffer Jan 24, 2025
b713856
Review doc up to ellipsoids
j-kieffer Jan 24, 2025
231306a
Reorganize doc and header up to summation
j-kieffer Jan 24, 2025
77b0ed5
Review doc up to ql
j-kieffer Jan 24, 2025
1d02a1e
Main documentation done
j-kieffer Jan 24, 2025
823ce6e
Rm spurious file, reorder tests
j-kieffer Jan 24, 2025
0a59c04
Reorganize and document tests; remove prints
j-kieffer Jan 24, 2025
74a982a
Merge branch 'main' of github.com:flintlib/flint into acb_theta-v2
j-kieffer Jan 24, 2025
0efa99c
agm_distances -> eld_distances
j-kieffer Jan 27, 2025
066099f
agm_addprec -> sum_addprec
j-kieffer Jan 27, 2025
9e4749a
sum_bound -> local_bound
j-kieffer Jan 27, 2025
3391594
Odd theta constants are zero in ql_setup; write profiling code for ql…
j-kieffer Jan 27, 2025
635fd5d
Continue profiling; add cst argument to nb_steps
j-kieffer Jan 27, 2025
89f915b
New parameters for g=1
j-kieffer Jan 27, 2025
9440560
More useful profiling, better siegel_randtest_compact, more info in q…
j-kieffer Jan 27, 2025
cbc50fc
Adjust nb_steps for g=2, todo: check splitting
j-kieffer Jan 27, 2025
8c907d3
More logical version of ql_nb_steps; test more precisions when profiling
j-kieffer Jan 28, 2025
73621cc
Yet better ql_nb_steps (tests up to g=2)
j-kieffer Jan 28, 2025
ed99a9b
Further modifs to ql_nb_steps, add experimental data
j-kieffer Jan 29, 2025
9f5983e
Start rewriting ql_nb_steps given experimental data
j-kieffer Jan 29, 2025
175e738
Restore old ql_nb_steps
j-kieffer Jan 30, 2025
15314f4
Write profiling program for ql_setup which showed we need a different…
j-kieffer Jan 31, 2025
00e94ad
Replace sum_all_tilde by sum everywhere; kill t-sum_a0_tilde
j-kieffer Jan 31, 2025
dd280ac
Replace sum_a0_tilde by sum
j-kieffer Jan 31, 2025
7feeb9a
Replace sum_0b and sum_00 by sum
j-kieffer Jan 31, 2025
b705bcd
Manipulate all context fields for g=1; do not compute exp_z in shift_…
j-kieffer Jan 31, 2025
0144221
Fix complex_plot
j-kieffer Feb 3, 2025
66e5c4b
Reduced vectors in t-shift_a0; use lbound instead of midref in sum_ad…
j-kieffer Feb 3, 2025
01938fb
No warning in sum_0x
j-kieffer Feb 3, 2025
5945ba7
Avoid infinite inverses in shift_a0
j-kieffer Feb 3, 2025
ec5f481
Rewrite ql_setup for clarity, use accurate number of guard bits
j-kieffer Feb 3, 2025
7dbad18
Profile acb_theta_sum; add some guard bits when manipulating contexts…
j-kieffer Feb 4, 2025
7091530
Add guard bits in acb_theta_sum; allow more points in ellipsoids
j-kieffer Feb 4, 2025
ecee23c
Tighter sum_radius
j-kieffer Feb 4, 2025
9ccc9a3
Fix precision in sum_radius
j-kieffer Feb 4, 2025
faaa998
Less stringent randtest_compact (cf p-sum in genus 10)
j-kieffer Feb 4, 2025
0f97a98
Remove prints in ql_setup and sum
j-kieffer Feb 4, 2025
39f1968
Correct expensive precision bug in agm_mul_tight, remove agm_mul_tigh…
j-kieffer Feb 6, 2025
ef650c2
Refactor code in ql_exact, use void output
j-kieffer Feb 6, 2025
b00a5ea
Expose rough pattern in ql_nb_steps; expose ql_steps_input_sum for us…
j-kieffer Feb 6, 2025
f163348
Better ql_nb_steps to take previous improvements into account
j-kieffer Feb 6, 2025
bf38ef3
Correct precision bug in acb_theta_sum; write sum_jet for more code f…
j-kieffer Feb 7, 2025
c71d109
Fix error bounds in sum_jet, remove sum_jet_00
j-kieffer Feb 7, 2025
d98f9f4
Avoid do-while loops in all_notransform; better precision management …
j-kieffer Feb 7, 2025
cba1b50
Make ql_steps static in ql_exact; expose agm_mul_all_tight
j-kieffer Feb 7, 2025
e9e24e6
Make ql_steps_input_sum static in ql_exact
j-kieffer Feb 7, 2025
1b58b34
Start writing more efficient jet_notransform functions, todo: allow a…
j-kieffer Feb 7, 2025
be86c64
Silence ql_nb_steps
j-kieffer Feb 8, 2025
3d02a31
Test jet_notransform_ql, fix bugs
j-kieffer Feb 8, 2025
d9ec880
Write profile code for jet_notransform_ql, showing precision bugs
j-kieffer Feb 8, 2025
31173f4
Fix precision bug in jet_ql_notransform, remove argument pattern
j-kieffer Feb 8, 2025
d5e833f
Separate all_a and all_b in sum_jet, todo: test
j-kieffer Feb 9, 2025
f1da1b9
Test sum_jet with all parameters
j-kieffer Feb 9, 2025
185f579
Test jet_notransform_ql with all = 0
j-kieffer Feb 9, 2025
188da43
Write and test acb_theta_jet_notransform
j-kieffer Feb 9, 2025
4462842
Remove 00_notransform and one_notransform
j-kieffer Feb 9, 2025
d82ef69
Remove jet_00_notransform and jet_one_notransform
j-kieffer Feb 9, 2025
cbabde3
Remove jet_all_notransform
j-kieffer Feb 9, 2025
38371ad
Rename jet_notransform_ql to ql_jet_fd; expose ql_jet; use jet_notran…
j-kieffer Feb 9, 2025
492e661
Rename jet_error -> ql_jet_error
j-kieffer Feb 9, 2025
4ebb6ac
Merge jet_00 and jet_all as acb_theta_jet
j-kieffer Feb 9, 2025
085dc2a
More efficient jet_exp_qf for ord = 0
j-kieffer Feb 10, 2025
0171547
Allow sqr parameter in jet_notransform
j-kieffer Feb 10, 2025
5d6c6ba
Merge all_notransform into jet_notransform
j-kieffer Feb 10, 2025
297c04c
Allow sqr parameter in acb_theta_jet; call acb_theta_jet in acb_theta…
j-kieffer Feb 10, 2025
23451e1
Remove acb_theta_00, fix missing include
j-kieffer Feb 10, 2025
a01b1f7
Restore previous signature for acb_theta_all
j-kieffer Feb 10, 2025
a682f44
Rename local_bound -> ql_local_bound; do not use in g2_sextic_chi5
j-kieffer Feb 10, 2025
3a56a33
Allow sqr parameter in siegel_kappa, stronger test
j-kieffer Feb 10, 2025
e5e1196
Use siegel_kappa in siegel_kappa2
j-kieffer Feb 10, 2025
ca52156
Allow all as parameter in agm_mul
j-kieffer Feb 10, 2025
e9b628b
Allow all as parameter in agm_mul_tight; fix normalization conventions
j-kieffer Feb 10, 2025
880b287
Expose ctx_tau_overlaps
j-kieffer Feb 10, 2025
0d985ba
Allow lead parameter in g2_covariants and g2_transvectant
j-kieffer Feb 10, 2025
9d98feb
Fix missing includes in tests; remove t-g2_sextic_chi5
j-kieffer Feb 10, 2025
b1a62a9
Merge g2_psi4, psi6, chi10, chi12 as g2_even_weight
j-kieffer Feb 10, 2025
73cf9bd
Remove macro COV_NB
j-kieffer Feb 10, 2025
709f711
Remove g2_sextic
j-kieffer Feb 10, 2025
8dabcb4
Remove tests and make static/inline functions for char_is_even/goepel…
j-kieffer Feb 10, 2025
dbb569f
Make char_dot_acb static in jet_notransform
j-kieffer Feb 10, 2025
6006385
Delete temp file
j-kieffer Feb 10, 2025
64030a9
Remove debug prints from source files
j-kieffer Feb 10, 2025
bf7a092
Fix memory leak in test
j-kieffer Feb 10, 2025
f2f0803
Fix buts in acb_theta_jet, t-agm_mul_tight
j-kieffer Feb 10, 2025
c92bb13
Strengten all tests by disallowing NaNs and infinities
j-kieffer Feb 11, 2025
5dbcc32
Silence failing tests, accelerate t-agm_mul
j-kieffer Feb 11, 2025
40469ee
Fix bug in ql_setup for hard step, all = 1, k = 0; use less roots for…
j-kieffer Feb 11, 2025
ced0a59
Fix output of ql_local_bound that caused ql_jet_fd to fail
j-kieffer Feb 11, 2025
c54326c
Take possible divisions by chi5=0 into account in g2 tests
j-kieffer Feb 11, 2025
4d40ccc
Try to improve code coverage
j-kieffer Feb 11, 2025
2859776
Stronger test for agm_mul_tight
j-kieffer Feb 11, 2025
fb04c56
Even stronger test for agm_mul_tight showing that error cannot be sma…
j-kieffer Feb 11, 2025
b525d65
Test all_a and all_b in t-sum
j-kieffer Feb 11, 2025
cf6a767
Write t-reduce_z; further comments on code coverage
j-kieffer Feb 11, 2025
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2,389 changes: 1,216 additions & 1,173 deletions doc/source/acb_theta.rst

Large diffs are not rendered by default.

4 changes: 2 additions & 2 deletions doc/source/references.rst
Original file line number Diff line number Diff line change
Expand Up @@ -107,7 +107,7 @@ References

.. [EM2004] \O. Espinosa and V. Moll, "A generalized polygamma function", Integral Transforms and Special Functions (2004), 101-115.

.. [EK2023] \N. D. Elkies and J. Kieffer, "A uniform quasi-linear time algorithm for evaluating theta functions in any dimension", in preparation.
.. [EK2025] \N. D. Elkies and J. Kieffer, "A uniform quasi-linear time algorithm for evaluating theta functions in any dimension", in preparation.

.. [Fie2007] \C. Fieker, "Sparse representation for cyclotomic fields". Experiment. Math. Volume 16, Issue 4 (2007), 493-500. https://doi.org/10.1080/10586458.2007.10129012

Expand Down Expand Up @@ -339,4 +339,4 @@ References

.. [vdH2006] \J. van der Hoeven, "Computations with effective real numbers". Theoretical Computer Science, Volume 351, Issue 1, 14 February 2006, Pages 52-60. https://doi.org/10.1016/j.tcs.2005.09.060

All referenced works: [AbbottBronsteinMulders1999]_, [Apostol1997]_, [Ari2011]_, [Ari2012]_, [Arn2010]_, [Arn2012]_, [ArnoldMonagan2011]_, [BBC1997]_, [BBC2000]_, [BBK2014]_, [BD1992]_, [BF2020]_, [BFSS2006]_, [BJ2013]_, [BM1980]_, [BZ1992]_, [BZ2011]_, [BaiWag1980]_, [BerTas2010]_, [Bin1996]_, [Blo2009]_, [Bodrato2010]_, [Boe2020]_, [Bog2012]_, [Bol1887]_, [Bor1987]_, [Bor2000]_, [Bre1978]_, [Bre1979]_, [Bre2010]_, [BrentKung1978]_, [BuhlerCrandallSompolski1992]_, [CFG2017]_, [CFG2019]_, [CGHJK1996]_, [CP2005]_, [Car1995]_, [Car2004]_, [Chen2003]_, [Cho1999]_, [Coh1996]_, [Coh2000]_, [Col1971]_, [CraPom2005]_, [DHBHS2004]_, [DYF1999]_, [DelegliseNicolasZimmermann2009]_, [DomKanTro1987]_, [Dup2006]_, [Dus1999]_, [EHJ2016]_, [EM2004]_, [EK2023]_, [Fie2007]_, [FieHof2014]_, [Fil1992]_, [GCL1992]_, [GG2003]_, [GS2003]_, [GVL1996]_, [Gas2018]_, [Gos1974]_, [GowWag2008]_, [GraMol2010]_, [HM2017]_, [HS1967]_, [HZ2004]_, [HanZim2004]_, [Har2010]_, [HZ2011]_, [Har2012]_, [Har2015]_, [Har2018]_, [Hart2010]_, [Hen1956]_, [Hoe2001]_, [Hoe2009]_, [Hor1972]_, [Iliopoulos1989]_, [Igu1972]_, [Igu1979]_, [JB2018]_, [JM2018]_, [JR1999]_, [Joh2012]_, [Joh2013]_, [Joh2014a]_, [Joh2014b]_, [Joh2014c]_, [Joh2015]_, [Joh2015b]_, [Joh2016]_, [Joh2017]_, [Joh2017a]_, [Joh2017b]_, [Joh2018a]_, [Joh2018b]_, [JvdP2002]_, [Kahan1991]_, [KanBac1979]_, [Kar1998]_, [Knu1997]_, [Kob2010]_, [Kri2013]_, [LT2016]_, [Leh1970]_, [LukPatWil1996]_, [MN2019]_, [MP2006]_, [MPFR2012]_, [MasRob1996]_, [Mic2007]_, [Miy2010]_, [Mos1971]_, [Mul2000]_, [Mum1983]_, [Mum1984]_, [NIST2012]_, [NakTurWil1997]_, [Olv1997]_, [PP2010]_, [PS1973]_, [PS1991]_, [Paterson1973]_, [PernetStein2010]_, [Pet1999]_, [Pla2011]_, [Pla2017]_, [RF1994]_, [Rad1973]_, [Rademacher1937]_, [Ric1992]_, [Ric1995]_, [Ric1997]_, [Ric2007]_, [Ric2009]_, [RosSch1962]_, [Rum2010]_, [Smi2001]_, [SorWeb2016]_, [Ste2002]_, [Ste2010]_, [Stehle2010]_, [Stein2007]_, [Sut2007]_, [StoMul1998]_, [Str2014]_, [Str1997]_, [Str2012]_, [Tak2000]_, [ThullYap1990]_, [Tre2008]_, [Tru2011]_, [Tru2014]_, [Tur1953]_, [Villard2007]_, [WaktinsZeitlin1993]_, [Wei2000]_, [Whiteman1956]_, [Zip1985]_, [Zun2023]_, [Zun2023b]_, [vHP2012]_, [vdH1995]_, [vdH2006]_
All referenced works: [AbbottBronsteinMulders1999]_, [Apostol1997]_, [Ari2011]_, [Ari2012]_, [Arn2010]_, [Arn2012]_, [ArnoldMonagan2011]_, [BBC1997]_, [BBC2000]_, [BBK2014]_, [BD1992]_, [BF2020]_, [BFSS2006]_, [BJ2013]_, [BM1980]_, [BZ1992]_, [BZ2011]_, [BaiWag1980]_, [BerTas2010]_, [Bin1996]_, [Blo2009]_, [Bodrato2010]_, [Boe2020]_, [Bog2012]_, [Bol1887]_, [Bor1987]_, [Bor2000]_, [Bre1978]_, [Bre1979]_, [Bre2010]_, [BrentKung1978]_, [BuhlerCrandallSompolski1992]_, [CFG2017]_, [CFG2019]_, [CGHJK1996]_, [CP2005]_, [Car1995]_, [Car2004]_, [Chen2003]_, [Cho1999]_, [Coh1996]_, [Coh2000]_, [Col1971]_, [CraPom2005]_, [DHBHS2004]_, [DYF1999]_, [DelegliseNicolasZimmermann2009]_, [DomKanTro1987]_, [Dup2006]_, [Dus1999]_, [EHJ2016]_, [EM2004]_, [EK2025]_, [Fie2007]_, [FieHof2014]_, [Fil1992]_, [GCL1992]_, [GG2003]_, [GS2003]_, [GVL1996]_, [Gas2018]_, [Gos1974]_, [GowWag2008]_, [GraMol2010]_, [HM2017]_, [HS1967]_, [HZ2004]_, [HanZim2004]_, [Har2010]_, [HZ2011]_, [Har2012]_, [Har2015]_, [Har2018]_, [Hart2010]_, [Hen1956]_, [Hoe2001]_, [Hoe2009]_, [Hor1972]_, [Iliopoulos1989]_, [Igu1972]_, [Igu1979]_, [JB2018]_, [JM2018]_, [JR1999]_, [Joh2012]_, [Joh2013]_, [Joh2014a]_, [Joh2014b]_, [Joh2014c]_, [Joh2015]_, [Joh2015b]_, [Joh2016]_, [Joh2017]_, [Joh2017a]_, [Joh2017b]_, [Joh2018a]_, [Joh2018b]_, [JvdP2002]_, [Kahan1991]_, [KanBac1979]_, [Kar1998]_, [Knu1997]_, [Kob2010]_, [Kri2013]_, [LT2016]_, [Leh1970]_, [LukPatWil1996]_, [MN2019]_, [MP2006]_, [MPFR2012]_, [MasRob1996]_, [Mic2007]_, [Miy2010]_, [Mos1971]_, [Mul2000]_, [Mum1983]_, [Mum1984]_, [NIST2012]_, [NakTurWil1997]_, [Olv1997]_, [PP2010]_, [PS1973]_, [PS1991]_, [Paterson1973]_, [PernetStein2010]_, [Pet1999]_, [Pla2011]_, [Pla2017]_, [RF1994]_, [Rad1973]_, [Rademacher1937]_, [Ric1992]_, [Ric1995]_, [Ric1997]_, [Ric2007]_, [Ric2009]_, [RosSch1962]_, [Rum2010]_, [Smi2001]_, [SorWeb2016]_, [Ste2002]_, [Ste2010]_, [Stehle2010]_, [Stein2007]_, [Sut2007]_, [StoMul1998]_, [Str2014]_, [Str1997]_, [Str2012]_, [Tak2000]_, [ThullYap1990]_, [Tre2008]_, [Tru2011]_, [Tru2014]_, [Tur1953]_, [Villard2007]_, [WaktinsZeitlin1993]_, [Wei2000]_, [Whiteman1956]_, [Zip1985]_, [Zun2023]_, [Zun2023b]_, [vHP2012]_, [vdH1995]_, [vdH2006]_
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