expand difference of relations before evaluation to a boolean

[behackl]

As described in this discussion, we currently have

sage: bool(x^2 - 1 - (x+1)*(x-1) != 0)
True

Duplicate of #19040.

CC: @cheuberg @rwst

Component: symbolics

Keywords: pynac

Issue created by migration from https://trac.sagemath.org/ticket/20105

[rwst]

comment:1

Note that the change in Pynac simply leads to Maxima being called in Expression.__nonzero__ (waiting time on first invocation). The issue will be resolved in general with #19040 because we expand in __nonzero__ then. But at the moment it's a bug and it's resolved by your Pynac patch.

[cheuberg]

comment:2

As posted on sage-devel:

$ cat test.sage
a = -1/(x+1) + 1/x
b = 1/(x*(x+1))
print bool(a == b), bool(a != b)
$ sage-6.9 test.sage
True False
$ sage-6.10 test.sage
True True
$ sage-7.0 test.sage
True True

[rwst]

comment:3

Actually, the change in Pynac does not resolve this (a!=b) so it's unclear what causes it.

[behackl]

comment:4

I see. Expansion of the difference does not detect the partial fraction stuff going on there. In that case its probably better to wait for #19040 instead of submitting a fix in pynac.

I think that the more interesting question is whether the partial fraction stuff is also resolved with the ticket.

The pynac pull request and this ticket are then duplicates/wontfixes.

[rwst]

comment:5

(deleted)

[behackl]

comment:6

My mistake. The wording in the ticket is actually wrong, somewhen today I must have switched to testing the wrong thing... >.<

[rwst]

comment:7

Ok confirmed.

sage: bool(x^2 - 1 - (x+1)*(x-1) != 0)
True

[behackl]

Changed dependencies from pynac-0.6.3 to none

[rwst]

comment:9

With the new #19040 you will get:

sage: bool(x^2 - 1 - (x+1)*(x-1) != 0)
False
sage: (x^2 - 1 - (x+1)*(x-1) != 0).holds()
False

The first because we expand in __nonzero__, the second because Maxima is called. So, I think this ticket will turn out as duplicate of #19040.

[behackl]

comment:10

Replying to @rwst:

With the new #19040 you will get:

sage: bool(x^2 - 1 - (x+1)*(x-1) != 0)
False
sage: (x^2 - 1 - (x+1)*(x-1) != 0).holds()
False

The first because we expand in __nonzero__, the second because Maxima is called. So, I think this ticket will turn out as duplicate of #19040.

Excellent! Thanks for checking. :-)