SymmetricGroupAlgebra: updates w.r.t. categories and free modules

[nthiery]

The goal of the patch is to adapt SymmetricGroupAlgebra to categories and to add some improvements. The patch improve SymmetricGroupAlgebra in two ways:

• SymmetricGroupAlgebra is now in the category FiniteDimensionalAlgebraWithBasis. Note: A forthcomming patch from Valentin Féray will put it in the correct GroupAlgebras category;

• When creating SGA(n) a coercion from SGA(n-1) is declared.

I'm submitting the patch on behalf on Nicolas after reviewing it.

Depends on the categories framework #5891, #6136.

Cheers,

Florent

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: symmetric group, free module

Author: Nicolas M. Thiéry

Reviewer: Florent Hivert

Merged: sage-4.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/6138

[hivert]

comment:1

Attachment: categories-symmetric_group_algebra-6138-nt.patch.gz

[hivert]

Author: Nicolas M. Thiéry

[hivert]

Reviewer: Florent Hivert

[mwhansen]

comment:3

For this, isn't it possible to lazily add the coercion using coerce_map_from?

[nthiery]

comment:4

Replying to @mwhansen:

For this, isn't it possible to lazily add the coercion using coerce_map_from?

Probably so. It would be best handled by some "templated coercion declarations", as I had started to implement in MuPAD. Let's just leave it as is for the moment, until we have enough use cases to come up with the right design.

[nthiery]

Updated patch fixes two missing doctests (apply only this one)

[mwhansen]

Merged: sage-4.3.alpha0

[mwhansen]

comment:5

Attachment: trac_6138-categories-symmetric_group_algebra-6138-nt.patch.gz