Add consistency tests for __nonzero__ in TestSuite.

[hivert]

With many datastructure for elements, comparison to zero could be faster than
comparison of two elements. The pythonic way to do that is to use indirectly
e.__nonzero__() for example in if not e: .... However, to be able
to use consistently this idiom, we have to make sure that the return value of
e == e.parent().zero() agrees with bool(e). The purpose of this
patch is to add this tests to the standard test suite and to fixe the Sage
library according to this policy.

On the way, I discovered that for a some morphism of modules, pickling can be
broken if the zero morphism is asked. I also fixes this issue.

See also discussion on #12508. Finally, I left to #12526 the question of removing __nonzero__ from element and writing tuned implantation for all data structures.

CC: @stumpc5 @sagetrac-sage-combinat

Component: categories

Author: Florent Hivert

Reviewer: Nathann Cohen

Merged: sage-5.7.beta1

Issue created by migration from https://trac.sagemath.org/ticket/12510

[hivert]

Author: Florent Hivert

[nathanncohen]

comment:5

Helloooooooo !!

Well, as far as I understand this code I think that it is good to go, except for this thing I just told you about : the new content of QuotientRingElement.__nonzero__ creates this problem

sage: a = e.lift()
sage: any([e])
True
sage: b = e.lift()
# Now b and a are not necessarily equal anymore

If you think that this is not a problem after all, then you can set this ticket to positive_review.

Have fuuuuuuuuuuuuuuuuuuuuuuuunnn !!

Nathann

[hivert]

comment:6

The returned result was wrong so I switched back to raising not implemented. I created #13999 to have the problem fixed. Please review,

Florent

[nathanncohen]

comment:8

Attachment: trac_12510-nonzero_equal_consistency-fh.patch.gz

Gooooooooooooooooooooooood to go !!!

Le jury apprécie : la qualité des workarounds :-D

Nathnan

[hivert]

comment:9

Thanks Nathan !!!

[jdemeyer]

Reviewer: Nathann Cohen

[jdemeyer]

Merged: sage-5.7.beta1