More support for finite dimensional modules and algebras with basis #11111

nthiery · 2011-04-01T12:40:31Z

More support for finite dimensional modules and algebras with basis:

Echelon form of list of vectors
Submodules and quotients
Example of a finite dimensional algebra with basis:
the path algebra of the Kronecker quiver
Category SemisimpleAlgebras(...)
Finite group algebras are semisimple in characteristic 0
Center, radical, and semisimple quotient of a finite dimensional algebra
Annihilator
Matrix and inverse of module morphisms
Some more support for term orders in CombinatorialFreeModule
map_support_skip_none in ModulesWithBasis

Depends on #8678

CC: @sagetrac-sage-combinat

Component: categories

Keywords: days20_5, days64, sd67

Author: Florent Hivert, Franco Saliola, Nicolas M. Thiéry

Branch: 7fb5d0c

Reviewer: Franco Saliola, Nicolas M. Thiéry, Aladin Virmaux

Issue created by migration from https://trac.sagemath.org/ticket/11111

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

nthiery · 2011-04-01T12:49:59Z

Changed author from Nicolas M. Thiéry to Florent Hivert, Franco Saliola, Nicolas M. Thiéry

jdemeyer · 2011-09-19T10:21:07Z

comment:2

Where is the patch?

nthiery · 2012-05-06T16:40:39Z

Dependencies: #10963

nthiery · 2014-07-01T20:34:15Z

Branch: u/nthiery/more_support_for_finite_dimensional_modules_and_algebras_with_basis

nthiery · 2014-07-01T20:36:57Z

Changed branch from u/nthiery/more_support_for_finite_dimensional_modules_and_algebras_with_basis to public/11111-more_support_for_finite_dimensional_modules_and_algebras_with_basis

nthiery · 2014-07-01T20:46:29Z

Last 10 new commits:

`4d4b599`	`10668: Fixed refinement of category to handle Parent._abstract_element_class`
`125aa8e`	`10668: Simplify the logic of endsets of modular abelian varieties using the new Endsets construction`
`fc5b0f1`	`10668: trivial doctest output updates w.r.t. the new printing of homsets`
`4b67d7c`	`10668: Explicitly document that Element.__getattr__ can also be useful when refining categories`
`ad87027`	`10668: Fixed doctest`
`9051050`	`10668: fixed ReST typo`
`62948b0`	`8678: Imported and rebased patch from Sage-Combinat queue`
`47e0eb9`	`8678: Imported stuff relevant to morphisms from trac_11111-finite_dimensional_modules-nt.patch`
`553c5de`	`8678: Imported module_morphism_function_extend-fh.patch`
`7abb197`	`11111: Imported trac_11111-finite_dimensional_modules-nt.patch from the Sage-Combinat queue (+ minor proofreading)`

nthiery · 2014-07-01T20:46:29Z

Commit: 7abb197

nthiery · 2014-07-01T20:46:29Z

Changed dependencies from #10963 to #10963, #8678

avirmaux · 2014-07-02T19:39:10Z

comment:12

After compiling it, I cannot launch sage. The error is the following:

[...]
---> 16 from sage.categories.non_unital_algebras import NonUnitalAlgebras
        global sage.categories.non_unital_algebras = undefined
        global NonUnitalAlgebras = undefined

ImportError: No module named non_unital_algebras

sagetrac-git · 2014-07-02T23:30:51Z

Changed commit from 7abb197 to 2a9ccb0

sagetrac-git · 2014-07-02T23:30:51Z

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

`2a9ccb0`	`11111: fixed Sage startup (NonUnitalAlgebras had to be rebased to NonAssociativeAlgebras)`

sagetrac-git · 2014-07-03T00:52:19Z

Changed commit from 2a9ccb0 to bac267e

sagetrac-git · 2014-07-03T00:52:19Z

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

`bac267e`	`11111: fixed some remaining rebasing issues (most tests pass now) + proofreading`

avirmaux · 2014-07-08T02:48:31Z

comment:15

I don't know if it is the proper place to report this bug but let's try as it is relatde to morphisms of finite dimensional modules (and coercion system). The following has been obtained on the t/11111 branch.

sage: A5 = SymmetricGroupAlgebra(QQ, 5)
sage: Z5 = A5.center()
sage: phi = Z5.module_morphism(on_basis=lambda i: Z5.an_element()*Z5.basis()[i], codomain=Z5)
sage: a = list(Z5.basis())[3]
sage: a in phi.domain()
True
sage: phi(a)

and I get
[...]

    445             TODO: make a better unit test once Modules().example() is implemented
    446             """
--> 447             from sage.structure.element import get_coercion_model
    448             import operator
    449             return get_coercion_model().bin_op(left, right, operator.mul)

RuntimeError: maximum recursion depth exceeded while calling a Python object
sage:

avirmaux · 2014-07-08T02:52:45Z

comment:16

In fact this bug is related to the fact that the center of on algebra is a CombinatorialFreeModule and nothing more... Sorry for the noise.

sagetrac-git · 2015-04-16T04:00:31Z

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

`6a3a07d`	`11111: doc for CombinatorialFreeModule._order_cmp`

sagetrac-git · 2015-04-16T04:00:31Z

Changed commit from 2036314 to 6a3a07d

sagetrac-git · 2015-04-16T04:23:57Z

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

`b6d8bff`	`11111: CombinatorialFreeModule.echelon_from -> Modules.WithBasis.ParentMethods.echelon_form; removed duplicate echelonize; delete meaningless and dangerous argument base_ring`

sagetrac-git · 2015-04-16T04:23:57Z

Changed commit from 6a3a07d to b6d8bff

nthiery · 2015-04-16T04:27:14Z

comment:70

Replying to @saliola:

I'm almost done reviewing this. The patch looks great! I've made some "improvements" to the documentation, please take a look.

I double checked your changes, thanks!

Here are a few remaining questions:

First of all, I'm not sure what the commit cfe399d is all about. Was it some sort of auto-merge by git?

Sounds like we both merged in 6.7.beta0 and that was a merge of our
merges ...

categories/finite_dimensional_modules_with_basis.py: the docstring of quotient_module talks about quotient "free" module. What do you mean by free?

I agree, the phrasing is not great. The point that needs to be
highlighted is that this only handles quotients by free submodules
admitting a unitriangular row echelon form, so that the quotient is
again a free module. Any proposition of rewording is welcome!

categories/semisimple_algebras.py: what do you mean by "TODO: trivial implementations for semisimple_quotient"

Err, good point, I don't really know. I guess all the methods that
become trivial in this category, like is_semisimple, ... Maybe we can
just remove this comment.

combinat/free_module.py: _order_cmp requires a docstring

Done.

combinat/free_module.py has a method called echelon_form, which is very similar to echelonize from categories/modules_with_basis.py. They essential do the same thing except that echelon_form allows one to specify a base_ring. Should these be merged? or eliminate one of them?

Oops, good catch. I merged the two of them as echelon_form in the
category. I deleted the base_ring feature which seems useless and
dangerous (the resulting vectors had coefficient in the specified
base_ring but injected back into the original module). We probably
don't need to go through a deprecation period for a broken "feature"
like this.

Running long tests now.

New commits:


af995f4	`Merge branch 'develop' into t/11111/more_support_for_finite_dimensional_modules_and_algebras_with_basis`
a476501	`Merge branch 'public/11111-more_support_for_finite_dimensional_modules_and_algebras_with_basis' of trac.sagemath.org:sage into t/11111/more_support_for_finite_dimensional_modules_and_algebras_with_basis`

New commits:

`6a3a07d`	`11111: doc for CombinatorialFreeModule._order_cmp`
`b6d8bff`	`11111: CombinatorialFreeModule.echelon_from -> Modules.WithBasis.ParentMethods.echelon_form; removed duplicate echelonize; delete meaningless and dangerous argument base_ring`

sagetrac-git · 2015-04-16T05:04:25Z

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

`25881cc`	`11111: docstring improvement for quotient_module`

sagetrac-git · 2015-04-16T05:04:25Z

Changed commit from b6d8bff to 25881cc

saliola · 2015-04-16T05:06:19Z

comment:72

Replying to @nthiery:

Replying to @saliola:

categories/finite_dimensional_modules_with_basis.py: the docstring of quotient_module talks about quotient "free" module. What do you mean by free?

I agree, the phrasing is not great. The point that needs to be
highlighted is that this only handles quotients by free submodules
admitting a unitriangular row echelon form, so that the quotient is
again a free module. Any proposition of rewording is welcome!

I tweaked it a bit, using what you wrote here.

categories/semisimple_algebras.py: what do you mean by "TODO: trivial implementations for semisimple_quotient"

Err, good point, I don't really know. I guess all the methods that
become trivial in this category, like is_semisimple, ... Maybe we can
just remove this comment.

Removed.

Running long tests now.

Positive review, provided that all doctests pass.

sagetrac-git · 2015-04-16T12:12:00Z

Changed commit from 25881cc to 7fb5d0c

sagetrac-git · 2015-04-16T12:12:00Z

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

`7fb5d0c`	`11111: final doc improvements`

nthiery · 2015-04-16T14:20:15Z

Changed keywords from none to days20_5, days64, sd67

nthiery · 2015-04-16T14:23:55Z

comment:76

Running the long tests on sage.math.u-psud.fr triggered the following failures:

sage -t --long src/sage/interfaces/expect.py  # 1 doctest failed
sage -t --long src/sage/tests/cmdline.py  # 3 doctests failed
sage -t --long src/sage/parallel/decorate.py  # 1 doctest failed
sage -t --long src/sage/functions/hypergeometric.py  # 1 doctest failed
sage -t --long src/sage/dev/sagedev.py  # Timed out
sage -t --long src/sage/schemes/elliptic_curves/lseries_ell.py  # Timed out
sage -t --long src/sage/doctest/test.py  # 1 doctest failed
sage -t --long src/sage/combinat/dyck_word.py  # 1 doctest failed
sage -t --long src/sage/misc/temporary_file.py  # 5 doctests failed

All of them passed smoothly when I reran them with:

sage -t --long --failed src/sage

So I assume it was just a transient issue due to the machine being under heavy load.

Hence, positive review!

Thanks a lot everyone, and in particular Franco!

That was a long story from Sage Days 20.5 to Sage Days 67 :-)

nthiery · 2015-04-16T14:24:35Z

Reviewer: Franco Saliola, Nicolas M. Thiéry

vbraun · 2015-04-19T12:24:16Z

Changed dependencies from #8678, #16925 to #8678

vbraun · 2015-04-19T12:24:16Z

comment:78

PSA: I'm not merging tickets if the dependency can't be merged (i.e. don't depend on a duplicate/invalid/wontfix ticket).

vbraun · 2015-04-19T16:44:57Z

Changed branch from public/11111-more_support_for_finite_dimensional_modules_and_algebras_with_basis to 7fb5d0c

nthiery · 2015-04-21T10:35:19Z

Changed commit from 7fb5d0c to none

nthiery · 2015-04-21T10:35:19Z

comment:80

Replying to @vbraun:

PSA: I'm not merging tickets if the dependency can't be merged (i.e. don't depend on a duplicate/invalid/wontfix ticket).

Oh, I see. We should have updated. the dependency from #16925 to #16926. Thanks for the tip!

nthiery · 2015-05-02T06:54:11Z

Changed reviewer from Franco Saliola, Nicolas M. Thiéry to Franco Saliola, Nicolas M. Thiéry, Aladin Virmaux

nthiery added this to the sage-5.11 milestone Apr 1, 2011

nthiery added c: categories labels Apr 1, 2011

nthiery self-assigned this Apr 1, 2011

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nthiery changed the title ~~Add features to FiniteDimensionalModulesWithBasis~~ More support for finite dimensional modules and algebras with basis May 6, 2012

jdemeyer modified the milestones: sage-5.11, sage-5.12 Aug 13, 2013

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014

darijgr modified the milestones: sage-6.4, sage-6.7 Apr 16, 2015

nthiery added s: positive review and removed s: needs review labels Apr 16, 2015

vbraun removed the s: positive review label Apr 19, 2015

vbraun closed this as completed in dcc711f Apr 19, 2015

This was referenced Jul 28, 2011

Support for the descriptor protocol for lazy_import'ed objects #11224

Closed

Representation theory of finite semigroups #12914

Open

avirmaux mannequin mentioned this issue May 3, 2015

Representation theory of finite dimensional associative algebras #16659

Closed

tscrim mentioned this issue Feb 7, 2015

Merge the features of SymmetricGroupAlgebra and SymmetricGroup.algebra #16926

Closed

nthiery mentioned this issue Jan 29, 2023

Finite dimensional modules with basis: improved conversions to vectors and matrices #18310

Open

More support for finite dimensional modules and algebras with basis #11111

More support for finite dimensional modules and algebras with basis #11111

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