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]

Description changed:

--- 
+++ 
@@ -9,4 +9,4 @@
 (%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 Unknown.
+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.

[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