Don't call Maxima with no-variable symbolic relation tests

[rwst]

In the case a relation without variables is to be decided, the procedure is to use Pynac, then RIF and, if it cannot be decided, Maxima. This is fine with expressions containing variables as Maxima can do some proofs. Expressions without variables are handled poorly as the example shows:

sage: val = pi - 2286635172367940241408/1029347477390786609545*sqrt(2)
sage: bool(val>0)
True

(%i2) is (%pi-(1116521080257783321*2^(23/2))/1029347477390786609545>0);
(%o2)                                true

This ticket changes the procedure to no longer try the unreliable Maxima after RIF has failed in a relation without variables. It will just return False.

CC: @simon-king-jena

Component: symbolics

Author: Ralf Stephan

Branch/Commit: e78e84b

Reviewer: Simon King, Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/24658

[rwst]

Branch: u/rws/don_t_call_maxima_with_no_variable_symbolic_relation_tests

[rwst]

New commits:

0a29d40

24658: Don't call Maxima with no-variable symbolic relation tests

[rwst]

Commit: 0a29d40

[rwst]

Author: Ralf Stephan

[simon-king-jena]

comment:5

It should be easy to review (after all, it is just working around a short-coming of maxima), and to me it looks good. However, I do not feel particularly confident about symbolic expressions (which I normally try to avoid by all means).

Also, I wonder about that change:

diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index 7130898..0f943d9 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -2612,7 +2612,7 @@ cdef class Expression(CommutativeRingElement):
         The :meth:`~sage.structure.element.Element.is_zero` method
         is more capable::
 
-            sage: t = pi + (pi - 1)*pi - pi^2
+            sage: t = pi + x*pi + (pi - 1 - x)*pi - pi^2
             sage: t.is_trivial_zero()
             False
             sage: t.is_zero()

Why did you change it? Apparently in order to have a variable in it. So, without the variable, t.is_trivial_zero() would return True, right? Which somehow makes sense, actually. I believe one should retain both tests, to show-case that Sage can now detect some more expressions which are trivially zero.

[simon-king-jena]

comment:6

PS: Also I think that in the new test val = pi - 2286635172367940241408/1029347477390786609545*sqrt(2) (which actually comes out of Ramanujan's formula for pi) the ticket number should be mentioned.

[rwst]

comment:7

Replying to @simon-king-jena:

Also, I wonder about that change:

diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index 7130898..0f943d9 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -2612,7 +2612,7 @@ cdef class Expression(CommutativeRingElement):
         The :meth:`~sage.structure.element.Element.is_zero` method
         is more capable::
 
-            sage: t = pi + (pi - 1)*pi - pi^2
+            sage: t = pi + x*pi + (pi - 1 - x)*pi - pi^2
             sage: t.is_trivial_zero()
             False
             sage: t.is_zero()

Why did you change it?

Because getting what we want (avoid Maxima numeric) and keeping the doctest would need more involved code, basically checking if there are constants, if so substituting them for variables, and then calling Maxima with that. Note that the changed result is not wrong so I'll add it again.

[sagetrac-git]

Changed commit from 0a29d40 to 17827ea

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

17827ea

24658: address reviewer's comments

[rwst]

comment:9

Replying to @simon-king-jena:

So, without the variable, t.is_trivial_zero() would return True, right? Which somehow makes sense, actually. I believe one should retain both tests, to show-case that Sage can now detect some more expressions which are trivially zero.

No is_trivial_zero test for trivial zero, i.e., 0.

[simon-king-jena]

comment:10

Hm. (pi + (pi - 1)*pi - pi^2).is_zero() returning False goes to far, IMHO.

If I understand correctly, the underlying bug is in Maxima's test for positivity/negativity. Is there a corresponding bug in Maxima's test for being zero as well? If it isn't, then I guess one should return to using Maxima for is_zero.

[simon-king-jena]

comment:11

Or, alternatively, is_zero() (but not is_trivial_zero()) should be cleverer in using RIF:

sage: RIF(pi + (pi - 1)*pi - pi^2)>0
False
sage: RIF(pi + (pi - 1)*pi - pi^2)<0
False
sage: RIF(pi + (pi - 1)*pi - pi^2)==0
False
sage: RIF(pi + (pi - 1)*pi - pi^2).is_NaN()
False

Thus, we have a real number (it is not !NaN) that is neither positive nor negative, and thus it would make sense to treat it as zero, although RIF is careful enough to not assert that it actually is zero.

Or prepend it by a simplification?

sage: RIF((pi + (pi - 1)*pi - pi^2).simplify_full()).is_zero()
True

After all, presumably is_zero() is supposed to invest more work into testing than is_trivial_zero().

[rwst]

comment:12

Replying to @simon-king-jena:

Thus, we have a real number (it is not !NaN) that is neither positive nor negative, and thus it would make sense to treat it as zero, although RIF is careful enough to not assert that it actually is zero.

Your own example (val) above would then be treated as zero too.

Or prepend it by a simplification?

That is probably best. One can always construct cases that need long time like ((pi+1)^10000 - pi*(pi+1)^9999 - (pi+1)^9999).simplify_full().

[sagetrac-git]

Changed commit from 17827ea to 590600b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

590600b

24658: if test_relation fails try again simplified

[rwst]

comment:14

OK, this looks fine in symbolics, there may be failing doctests elsewhere.

[rwst]

comment:15

There is a doctest in manifolds that relies on -arctanh(1/2) + 1/2*log(3) == 0. That should be resolved by implementing more special values for atanh. Surprise, I thought we had them all.

[rwst]

comment:16

Maxima cannot simplify arctanh(1/2) - 1/2*log(3). The question is do we formulate the doctest differently, or do we implement rewrite of inverse hyperbolic expressions, e.g. for integer and rational number arguments, either immediately or inside simplify_full.

[rwst]

Dependencies: #24668

[rwst]

comment:17

The new Pynac has the atanh simpifications and so we depend on that upgrade to fix the manifolds doctest fail.

[rwst]

comment:18

This one is serious because it does happen only when doctesting, and bool(SR(...)) does not seem to be involved directly.

File "src/sage/structure/parent.pyx", line 1514, in sage.structure.parent.Parent.hom._is_coercion_cached
Failed example:
    R._is_coercion_cached(QQ)
Expected:
    False
Got:
    True

It goes away if I replace QQ with QQbar. I think that the coercion cache is not really erased with creation of a new parent, and the additional call to test_relation in this ticket fills it with something. There are doctest calls to bool(SR(...)) that happen before that doctest in parent.pyx, let's see...

[rwst]

comment:19

Got it, it comes from the doctest sqrt(2) in CC in line 1051 of pynac.pyx. How can I turn off that it influences the doctest in line 1514?

[rwst]

comment:20

Replying to @rwst:

Got it, it comes from the doctest sqrt(2) in CC in line 1051 of parent.pyx. How can I turn off that it influences the doctest in line 1514?

[rwst]

comment:21

I meant to write parent.pyx.

[rwst]

Changed commit from 590600b to e78e84b

[rwst]

comment:27

The manifolds test passes now so we trigger the sleeping patchbots.

[fchapoton]

Changed dependencies from #24668 #24673 to none

[embray]

comment:30

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

[embray]

comment:31

Moving tickets from the Sage 8.8 milestone that have been actively worked on in the last six months to the next release milestone (optimistically).

[embray]

comment:32

Ticket retargeted after milestone closed

[mkoeppe]

comment:33

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

[mkoeppe]

Reviewer: Simon King, Matthias Koeppe

[mkoeppe]

comment:34

This is a clear improvement.

[vbraun]

Changed branch from u/rws/24658 to e78e84b