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 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 trac_7922-new_pickles.tar.gz into data/ext_code/pickle_jar.

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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.

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

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Converts WeylCharacterRings? and WeightRings? to use category framework

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

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Requires rebuilding the pickle jar.

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#7922: WeylCharacters? inherit from CombinatorialFreemodule? (substantial speedup)

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Since #9838 was merged in sage-4.6.1.alpha1, this patch needed rebasing.

I therefore posted trac_7922-rebased-4.6.1.

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7922: thematic tutorial revision

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This patch slightly conflicts with #8442 which was merged. So I'm posting a second patch trac_7922-doc.patch which revises the thematic tutorial.

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#7922: Revision of Weyl Character Rings

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I have posted trac_7922-rebased-4.7.alpha1.patch, which addresses many of the comments in the reviewer patch:

 http://combinat.sagemath.org/patches/file/tip/trac_7922-review-nt.patch

Those changes that are not addressed are discussed here:

 http://groups.google.com/group/sage-combinat-devel/browse_thread/thread/277e146862632d72

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#7922: revised pickle jar

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#7922: explanation of how the pickle jar is remade

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See pickle-notes for an explanation of how the pickle jar was remade.

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The revised patch trac_7922-rebased-4.7.alpha2 includes the revised coercion mechanism and other changes proposed by Nicolas.

In view of this message:

 http://trac.sagemath.org/sage_trac/ticket/10354#comment:11

I posted a tarball containing only the new pickles, and a list of obsolete pickles to be discarded.

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#7922: revision of Weyl Character Rings

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#7922: replacement pickles

[nthiery]

Hi Dan,

I just did a final proofreading, fixed a couple typos, updated coerce_to_sl in the doctests of the thematic tutorials, and removed some trailing white space and tabs.

For me it is now all good to go. Please check my reviewer's patch on the sage-combinat patch server. If it's ok with you, you can fold/upload and set a positive review here on my behalf.

 http://combinat.sagemath.org/patches/file/tip/trac_7922-final-review-nt.patch

Cheers,

Nicolas

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#7922: Categories for Weyl character rings and weight rings

[nthiery]

Hi Dan,

I just checked out your final changes on the Sage-Combinat queue (trac_7922_alpha3-changes.patch), and it looks all good. So the final rebased patch you just posted (and which includes the above) is good to go.

Positive review!

[jdemeyer]

This needs a few small fixes:

1. at various places doc/en/thematic_tutorials/lie/weyl_character_ring.rst, the indentation is inconsistent. It should be 4 spaces but in the newly added examples it is more or less random.
2. in doc/en/thematic_tutorials/lie/weyl_character_ring.rst, the test on line 250 takes a very long time but is not marked as such.

Please add an additional patch fixing these issues.