bugs in comparisons between constants, wrapped pyobjects, infinity

[dkrenn]

We have

sage: bool(pi<Infinity)
False
sage: bool(pi>Infinity)
True

which is obviously wrong. It seems that the problem only occurs with pi, because the following give correct results

sage: bool(pi<2*pi)
True
sage: bool(2*pi<Infinity)
True
sage: bool(e<Infinity)  
True
sage: bool(e<pi)
True

This was reported on sage-support by Robert Samal.

See the discussion at https://groups.google.com/forum/?hl=en#!topic/sage-devel/Oip2hzvjFZQ

pynac/pynac#69

---

Previously proposed patch: attachment: trac_12967-symbolic_ring-review.patch.

CC: @kcrisman

Component: symbolics

Keywords: compare pi infinity bool

Author: Travis Scrimshaw, Ralf Stephan

Reviewer: Karl-Dieter Crisman, Daniel Krenn

Issue created by migration from https://trac.sagemath.org/ticket/12967

[burcin]

comment:1

ATM, this is caused by #11506:

sage: pi.pyobject()
pi
sage: type(pi.pyobject())
<class 'sage.symbolic.constants.Pi'>
sage: pi.pyobject() < oo        
False
sage: pi.pyobject() > oo
True

With #12950, comparison of infinities in Pynac changed. Now I get:

sage: bool(pi>Infinity)
False
sage: bool(pi<Infinity) 
False

which is better. I hope with the ordering patches in the Pynac queue this will improve.

The results of comparison with e is not relevant in this case. e is not a constant in Pynac, it is the exp() function. Once you form the relational expression e < Infinity, the comparison is handled differently.

I suggest adding a patch with doctests reflecting the new behavior with #12950 and closing this ticket when #12950 is merged.

[tscrim]

comment:3

Here's the quick patch with some doctests reflecting the new behavior.

[tscrim]

Author: Travis Scrimshaw

[kcrisman]

comment:4

----------------------------------------------------------------------
| Sage Version 5.4.1, Release Date: 2012-11-15                       |
| Type "notebook()" for the browser-based notebook interface.        |
| Type "help()" for help.                                            |
----------------------------------------------------------------------
sage: bool(pi < infinity)
False
sage: bool(oo < pi)
False

That is what should actually be tested, as Burcin points out. Also, I feel like this is unintuitive enough of behavior (that pi is more or less incomparable with infinity and not like this)

sage: bool(2< oo)
True

that we should say something to that effect here, maybe even elsewhere in comparison doc where we have other examples saying that > gives False if we can't prove it's True.

I'm also wondering whether this is really "fixed" and deserves that doctest status.

[tscrim]

comment:5

How about this? Can you think of any other places to put the warning about symbolic ring comparisons? Thanks.