Have GroupAlgebra(Q, R) and G.algebra(R) return the same standard class for group algebras #18700

tscrim · 2015-06-14T15:35:27Z

Consider the following situation:

sage: P = RootSystem(['A',2,1]).weight_lattice()
sage: W = RootSystem(['A',2,1]).weight_space()
sage: W.has_coerce_map_from(P)
True
sage: PA = P.algebra(QQ)
sage: WA = W.algebra(QQ)
sage: WA.has_coerce_map_from(PA)
False

The last line should be True. This comes from the fact that GroupAlgebra implements some extra coercion logic and G.algebra(R) does not return an instance of this class.

To remedy this, we lift a good portion of the GroupAlgebra code to the appropriate categories, where we impose the restriction that a (Semi)Group.Algebra must have a basis indexed by elements of the (semi)group, and have all group algebras redirect to the now (lightweight) class GroupAlgebra_class in order to implement coercions.

Depends on #23000
Depends on #23211

CC: @sagetrac-sage-combinat @anneschilling @nthiery @bsalisbury1 @fchapoton

Component: coercion

Keywords: group algebras

Author: Travis Scrimshaw, Nicolas M. Thiéry

Branch/Commit: 3160e26

Reviewer: Ben Salisbury

Issue created by migration from https://trac.sagemath.org/ticket/18700

The text was updated successfully, but these errors were encountered:

tscrim · 2015-06-14T15:49:55Z

comment:1

Actually, GroupAlgebra already has this behavior. However algebra() does not return the group algebra by default. I think we need 2 changes:

1 - algebra() checks if self is a group (it already checks for inclusion in finite groups).
2 - We need a subclass of CombinatorialFreeModule which inherits the coercions in general, say a SemigroupAlgebra.

I think both changes are relatively easy since for the second we can canabalize a good part of the GroupAlgebra code. However if 2 is contraversal/harder-than-I-thought, then we should just do 1 here as we need this for #18453 and do a followup for 2.

tscrim · 2015-06-14T15:54:20Z

comment:2

Also as a little side bug:

sage: P.algebra(QQ)
Group algebra of the Weight lattice of the Root system of type ['A', 2, 1] over Rational Field
sage: _.category()
Category of root lattice realizations over Integer Rin algebras over Rational Field

Notice the missing g, same thing for W (except there it's ...Fiel algebras over...).

tscrim · 2017-05-01T23:12:05Z

comment:3

This goes through and redirects group algebra construction through GroupAlgebra, as well as cleans up how the categories are constructed.

New commits:

`5e94208`	`Standardizing group algebras through GroupAlgebra.`

tscrim · 2017-05-01T23:12:05Z

Commit: 5e94208

tscrim · 2017-05-01T23:12:05Z

Branch: public/groups/standardize_group_algebras-18700

bsalisbury1 · 2017-05-04T00:07:25Z

comment:4

Hi Travis,

There are doctest failures in a lot of difference places. For example:

----------------------------------------------------------------------
sage -t --long src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py  # 94 doctests failed
sage -t --long src/sage/plot/plot.py  # 1 doctest failed
sage -t --long src/sage/plot/graphics.py  # 2 doctests failed
sage -t --long src/sage/misc/sagedoc.py  # 3 doctests failed
sage -t --long src/sage/combinat/crystals/littelmann_path.py  # 6 doctests failed
sage -t --long src/sage/combinat/rigged_configurations/rigged_configurations.py  # 13 doctests failed
sage -t --long src/sage/combinat/root_system/root_lattice_realization_algebras.py  # 89 doctests failed
sage -t --long src/sage/combinat/posets/posets.py  # 1 doctest failed
sage -t --long src/sage/combinat/root_system/hecke_algebra_representation.py  # 33 doctests failed
sage -t --long src/sage/categories/finite_dimensional_algebras_with_basis.py  # 2 doctests failed
sage -t --long src/sage/combinat/crystals/tensor_product.py  # 5 doctests failed
sage -t --long src/sage/repl/rich_output/pretty_print.py  # 1 doctest failed
sage -t --long src/doc/en/thematic_tutorials/lie/affine_finite_crystals.rst  # 1 doctest failed
sage -t --long src/sage/modules/with_basis/representation.py  # 13 doctests failed
sage -t --long src/sage/categories/sets_cat.py  # 4 doctests failed
sage -t --long src/sage/algebras/lie_algebras/lie_algebra.py  # 2 doctests failed
sage -t --long src/sage/categories/semisimple_algebras.py  # 1 doctest failed
----------------------------------------------------------------------

So many, in fact, that I'm wondering if I did something wrong! Did you get this same failures before you pushed the latest merge to the branch?

tscrim · 2017-05-04T01:07:16Z

comment:5

Those are probably trivial doctest failures because of the change in the how the group algebra elements are printed and I didn't test as well as I thought. I will fix them shortly.

sagetrac-git · 2017-05-04T03:36:01Z

Changed commit from 5e94208 to 39800cc

sagetrac-git · 2017-05-04T03:36:01Z

Branch pushed to git repo; I updated commit sha1. New commits:

`39800cc`	`Fixing doctests and some conversion behavior changes.`

tscrim · 2017-05-04T03:48:30Z

comment:7

This should fix all of the doctest failures that were introduced on this ticket. I did a little bit of a hack for algebras of a module with a basis to wrap them as B[x + y]. Some of the other doctest failures I get on develop (in particular, the failure in posets.py) or cannot reproduce (e.g., the ones in plot).

bsalisbury1 · 2017-05-04T22:53:32Z

comment:8

Still getting a doctest failure...

sage -t src/sage/algebras/group_algebra.py
**********************************************************************
File "src/sage/algebras/group_algebra.py", line 696, in sage.algebras.group_algebra.GroupAlgebra._element_constructor_
Failed example:
    OG(2)
Exception raised:
    Traceback (most recent call last):
      File "/Users/Ben/sage-git/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 509, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/Users/Ben/sage-git/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 872, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.algebras.group_algebra.GroupAlgebra._element_constructor_[11]>", line 1, in <module>
        OG(Integer(2))
      File "sage/structure/parent.pyx", line 941, in sage.structure.parent.Parent.__call__ (/Users/Ben/sage-git/src/build/cythonized/sage/structure/parent.c:9839)
        return mor._call_(x)
      File "sage/structure/coerce_maps.pyx", line 110, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (/Users/Ben/sage-git/src/build/cythonized/sage/structure/coerce_maps.c:4895)
        raise
      File "sage/structure/coerce_maps.pyx", line 105, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (/Users/Ben/sage-git/src/build/cythonized/sage/structure/coerce_maps.c:4762)
        return C._element_constructor(x)
      File "/Users/Ben/sage-git/local/lib/python2.7/site-packages/sage/algebras/group_algebra.py", line 720, in _element_constructor_
        raise TypeError("do not know how to make x (= %s) an element of %s"%(x, self))
    TypeError: do not know how to make x (= 2) an element of Group algebra of General Linear Group of degree 2 over Finite Field of size 7 over Order in Number Field in sqrt5 with defining polynomial x^2 - 5
**********************************************************************
1 item had failures:
   1 of  16 in sage.algebras.group_algebra.GroupAlgebra._element_constructor_
    [132 tests, 1 failure, 6.13 s]

sagetrac-git · 2017-05-04T22:59:12Z

Branch pushed to git repo; I updated commit sha1. New commits:

`2ef2208`	`We have a unit, so we can use that in coercion.`

sagetrac-git · 2017-05-04T22:59:12Z

Changed commit from 39800cc to 2ef2208

tscrim · 2017-05-04T22:59:31Z

comment:10

This was me being stupid. Fixed.

bsalisbury1 · 2017-05-04T23:50:27Z

comment:11

All tests passed on my machine, the html doc builds, and so does the pdf doc. Moreover:

sage: P = RootSystem(['A',2,1]).weight_lattice()
sage: W = RootSystem(['A',2,1]).weight_space()
sage: W.has_coerce_map_from(P)
True
sage: PA = P.algebra(QQ)
sage: WA = W.algebra(QQ)
sage: WA.has_coerce_map_from(PA)
True

bsalisbury1 · 2017-05-04T23:50:27Z

Reviewer: Ben Salisbury

nthiery · 2017-05-05T12:54:01Z

comment:12

Hi,

Sorry for the interuption; I'd like to have a look at this one. If you don't hear from me in the next day, please set it back to positive review.

tscrim · 2017-06-17T05:14:28Z

comment:70

This fixes the docbuild issues for me (plus a few other misc doc issues I noticed while trying to fix it).

bsalisbury1 · 2017-06-18T16:28:22Z

comment:71

Looks good now. Thanks!

tscrim · 2017-06-21T01:46:23Z

Changed author from TravisScrimshaw, Nicolas M. Thiéry to Travis Scrimshaw, Nicolas M. Thiéry

vbraun · 2017-06-21T21:20:05Z

comment:73

Search for algerbas in the patch, obvious typo. There should be a test that catches that

sage -t --long --warn-long 67.9 src/sage/algebras/group_algebra.py
**********************************************************************
File "src/sage/algebras/group_algebra.py", line 138, in sage.algebras.group_algebra.GroupAlgebra_class._coerce_map_from_
Failed example:
    ZG.coerce_map_from(H)
Expected:
    Conversion map:
      From: Cyclic group of order 3 as a permutation group
      To:   Algebra of Dihedral group of order 6 as a permutation group over Integer Ring
Got:
    Coercion map:
      From: Cyclic group of order 3 as a permutation group
      To:   Algebra of Dihedral group of order 6 as a permutation group over Integer Ring

sagetrac-git · 2017-06-21T23:29:00Z

Changed commit from c2e1c05 to a93b1e9

sagetrac-git · 2017-06-21T23:29:00Z

Branch pushed to git repo; I updated commit sha1. New commits:

`6be53f3`	`Move _is_coercion from DefaultConvertMap to Map and make it accurate`
`7dac7e2`	`Fix doctest`
`9a9e437`	`Print default "coerce" maps as "Coercion"`
`d8eec2d`	`Fixed doctests`
`2fa81a7`	`Fix doctests to print exactly as they show up on screen`
`b483c8e`	`Merge branch 'develop' into t/23211/mark_morphisms_as_coercions`
`78807fa`	`fix doctest errors`
`8c67163`	`Merge branch 'u/saraedum/mark_morphisms_as_coercions' of git://trac.sagemath.org/sage into public/groups/standardize_group_algebras-18700`
`a93b1e9`	`Fixing typo and rebasing over #23211.`

tscrim · 2017-06-21T23:36:16Z

Changed dependencies from #23000 to #23000 #23211

tscrim · 2017-06-21T23:36:16Z

comment:76

I've fixed the typo, but we don't explicitly test register_unpickle_override anywhere else. The failure is from #23211, but it is good to know that we have a non-trivial rebase before the next beta round.

tscrim · 2017-06-23T12:02:02Z

comment:77

Perhaps we could sneak this into 8.0? This simplifies a lot of things when working with group algebras.

sagetrac-git · 2017-06-24T02:32:39Z

Branch pushed to git repo; I updated commit sha1. New commits:

`70c7280`	`Merge branch 'develop' into public/groups/standardize_group_algebras-18700`
`e613a51`	`Merge branch 'public/groups/standardize_group_algebras-18700' of git://trac.sagemath.org/sage into public/groups/standardize_group_algebras-18700`
`a18c48c`	`Adding test for old pickle.`

sagetrac-git · 2017-06-24T02:32:39Z

Changed commit from a93b1e9 to a18c48c

sagetrac-git · 2017-06-24T02:33:03Z

Changed commit from a18c48c to 3160e26

sagetrac-git · 2017-06-24T02:33:03Z

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`3160e26`	`Adding test for old pickle.`

tscrim · 2017-06-24T02:33:56Z

comment:80

I've added a test with an old pickle to make sure it works.

nthiery · 2017-06-25T01:30:09Z

comment:82

Hi!

Could you update the title and summary to briefly describe what was actually implemented in this ticket?

Thanks,
Nicolas

vbraun · 2017-06-25T15:45:24Z

Changed branch from public/groups/standardize_group_algebras-18700 to 3160e26

tscrim added this to the sage-6.8 milestone Jun 14, 2015

tscrim added c: coercion labels Jun 14, 2015

tscrim assigned sagetrac-sage-combinat Jun 14, 2015

tscrim added the s: needs review label May 1, 2017

tscrim modified the milestones: sage-6.8, sage-8.0 May 1, 2017

tscrim changed the title ~~Group algebras should have a coercion inherited from coercions of the underlying groups~~ Use GroupAlgebra as the standard class for group algebras May 4, 2017

bsalisbury1 added s: positive review and removed s: needs review labels May 4, 2017

nthiery added s: needs review and removed s: positive review labels May 5, 2017

bsalisbury1 added s: positive review and removed s: needs review labels Jun 18, 2017

vbraun added s: needs work and removed s: positive review labels Jun 21, 2017

tscrim added s: needs review and removed s: needs work labels Jun 21, 2017

bsalisbury1 added s: positive review and removed s: needs review labels Jun 24, 2017

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tscrim changed the title ~~Use GroupAlgebra as the standard class for group algebras~~ Have GroupAlgebra(Q, R) and G.algebra(R) return the same standard class for group algebras Jun 25, 2017

vbraun removed the s: positive review label Jun 25, 2017

vbraun closed this as completed in 8236443 Jun 25, 2017

nthiery mentioned this issue May 20, 2017

Fix inconsistency in Modules.FiniteDimensional.extra_super_categories #23000

Closed

tscrim mentioned this issue Dec 29, 2022

Implement coercions in the category framework #23252

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Have GroupAlgebra(Q, R) and G.algebra(R) return the same standard class for group algebras #18700

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Have GroupAlgebra(Q, R) and G.algebra(R) return the same standard class for group algebras #18700

Have GroupAlgebra(Q, R) and G.algebra(R) return the same standard class for group algebras #18700

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