incorrect test for equality of vectors over SR

[DaveWitteMorris]

As reported in this sage-devel thread, sage can report that two unequal vectors over the symbolic ring SR are equal:

sage: assume(x > 0)
sage: v = vector(SR, [x])
sage: w = vector(SR, [1])
sage: v == w
True

The problem comes from the fact that if lx != rx: is not the same as if not(lx == rx): when lx and rx are in SR. More precisely, for a symbolic relation such as f(x) == g(x), the docstring of sage.symbolic.expression.__bool__ says bool will return True if the relation is true for all possible values of x, and will return False otherwise. Therefore, it is often the case that bool(f(x) == g(x)) and bool(f(x) != g(x)) are both False.

sage: assume(x > 0)
sage: bool(x == 1)
False
sage: bool(x != 1)
False

The test for equality of vectors uses the comparison if lx != rx: on each component, but it should use if not(lx == rx):. What happens in the example is that there is a value of x for which x is equal to 1. This means that bool(x != 1) is False, so sagemath erroneously concludes that v == w should be true.

Related ticket: #33698. This bug does not arise without assume(x > 0), because inequality of symbolic relations does not follow the docstring's description when there are no assumptions.

Component: symbolics

Author: Dave Morris

Branch/Commit: d7d7bda

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/33697

[DaveWitteMorris]

Branch: public/33697

[DaveWitteMorris]

comment:2

Changed milestone to 9.6, but perhaps should be 9.7 because 9.6 is in release-candidate stage (and perhaps the priority should not be "critical").

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New commits:

d7d7bda

trac 33697: equality of SR vectors

[DaveWitteMorris]

Commit: d7d7bda

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:3

LGTM. I also agree on both points.

[DaveWitteMorris]

comment:4

Thanks!

[vbraun]

Changed branch from public/33697 to d7d7bda