Categories for Weyl character rings and weight rings (was: pickling fails in WeightRing)

[nthiery]

This ticket refactors the code of WeylCharacterRing and WeightRing to use categories and (combinatorial) free modules. Along the way, it adds a couple features (Dan: please list them here), and solves a pickling issue which was caught by #7921:

sage: A2 = WeylCharacterRing(['A',2])
sage: a2 = WeightRing(A2)
sage: TestSuite(a2).run()
Failure in _test_element_pickling:
Traceback (most recent call last):
...
AssertionError: 2*a2(0,0,0) != 2*a2(0,0,0)

Indeed:

sage: x = a2.an_element()
sage: x == loads(dumps(x))
False

Apply attachment: trac_7922-rebased-4.7.alpha3.patch

Remove the following pickles from the pickle jar:

_class__sage_combinat_root_system_weyl_characters_WeightRing__.*
_class__sage_combinat_root_system_weyl_characters_WeylCharacterRing_class__.*
_class__sage_combinat_root_system_weyl_characters_WeylCharacter__.*

Copy the contents of
attachment: trac_7922-new_pickles.tar.gz into data/ext_code/pickle_jar.

CC: @dwbump @sagetrac-sage-combinat

Component: combinatorics

Author: Daniel Bump, Nicolas M. Thiéry

Reviewer: Nicolas M. Thiéry, Dan Bump

Merged: sage-4.7.1.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/7922

[dwbump]

Description changed:

--- 
+++ 
@@ -18,5 +18,7 @@
 False
 ```
 
-I assume that this is an issue in equality test. This should be fixed for free when WeighRing's will use CombinatorialFreeModules
+I assume that this is an issue in equality test. This should be fixed for free when WeightRing's will use CombinatorialFreeModules
 and categories.
+
+The patch trac_7922.patch fixes this bug by converting both WeylCharacterRings and WeightRings to inherit from CombinatorialFreeModule and to use the category framework, a change Nicolas Thiery has requested.

[dwbump]

comment:1

Regarding speed, testing a large number of branching rules show that the patch is a substantial speedup over the old code with a caveat: the old code has an option cache=true for WeylCharacterRings. If this option (which is not the default) is selected for every WeylCharacterRing, then the old code is faster. Typical times:

Old Code	48 seconds
New Code	25 seconds
Old Code, cache=true	18 seconds

Since I made the method _irr_weights a cached method, the caching done in the new code is approximately equivalent to the caching in the old code, so at the moment I don't see any way to improve the situation.

[dwbump]

Reviewer: nthiery

[dwbump]

comment:2

Revised and reposted the patch in view of Nicolas' comment to use _from_dict(coerce=True).

[dwbump]

Converts WeylCharacterRings and WeightRings to use category framework

[dwbump]

comment:3

Attachment: trac_7922.patch.gz

I uploaded a revised version of the patch. The only change is in classical_crystals.py, where the revision of WeylCharacterRings necessitated a revision.

[dwbump]

comment:4

Requires rebuilding the pickle jar.