bool of symbolic inequality does not agree with documentation

[DaveWitteMorris]

The docstring of sage.symbolic.expression.__bool__ says that a relation f(x) op g(x) will evaluate to True if it is satisfied for all values of x, and will evaluate to False otherwise. ("We cannot return undecidable or throw an exception at the moment so False is returned for unknown outcomes.") But that is not how inequality behaves:

sage: bool(x != 1)  # false for `x = 1`, so should be `False`
True

The doctest for this behavior passes because inequality does behave as described if an assumption is added (and a previous doctest added an assumption):

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

We need to either change the docstring or change the behaviour of inequality. Also, adding an assumption should not change the behaviour.

Related tickets:

• This problem was discovered while tracking down the bug in incorrect test for equality of vectors over SR #33697.
• Some trac tickets (such as wrong symbolic results in case the answer is not known #17700 and Assumption bug of positive symbolic variable #21923) have discussed using 3-valued logic (or raising an exception) instead of returning False for unknown outcomes.

Component: symbolics

Branch/Commit: public/33698r1 @ 245a3fc

Issue created by migration from https://trac.sagemath.org/ticket/33698

[DaveWitteMorris]

Branch: public/33698

[DaveWitteMorris]

Changed branch from public/33698 to public/33698r1

[DaveWitteMorris]

comment:3

I fixed the doctest in src/sage/symbolic/expression.pyx (by adding forget()), so a doctest fails now, because of the problem in the ticket description. (Sorry, I forgot to do "git commit" before my first push, but I think the branch is ok now.)

---

New commits:

245a3fc

trac 33698: bool of symbolic inequality

[DaveWitteMorris]

Commit: 245a3fc