Fix coercions for descent and symmetric group algebras

[tscrim]

This splits off the first issue of #15475 (which has already been reviewed by Darij). This will also address the issues noted on https://groups.google.com/forum/#!topic/sage-devel/rXobHQXrCck.

CC: @darijgr

Component: coercion

Keywords: symmetric group algebra, descent algebra

Author: Travis Scrimshaw

Branch: d8ea764

Reviewer: Darij Grinberg

Issue created by migration from https://trac.sagemath.org/ticket/16678

[tscrim]

Branch: public/coercion/fix_sga_coercions-16678

[tscrim]

Commit: e1ff769

[tscrim]

Last 10 new commits:

7637ab2	Implemented `_coerce_map_from_` for SGA.
0763ba5	More fixes and doctests.
db24a90	Fixed the issue...finally... Also some other minor cleanup.
fb8c9c9	Added comment about register_embedding.
702e7a1	Changed to use `_coerce_map_from_` and made it more robust/general.
f662ae3	documentation fixes to canonical_embedding of symmetric group algebra (yes, these maps aren't always embeddings, and the inequality was backwards)
ff4e546	oops, another doc fix
b3d98ba	Merge commit 'ff4e546a838e9e9a4be86b3a89d8596658beb3f4' into public/coercions/fix_sga_coercions-16678
31c8ac9	Additional fixes noted on sage-devel thread.
e1ff769	Fixed stupid mistake.

[sagetrac-git]

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

30e769e

Removed erroneous character in permgroup.py.

[sagetrac-git]

Changed commit from e1ff769 to 30e769e

[sagetrac-git]

Changed commit from 30e769e to 3fa802d

[sagetrac-git]

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

3fa802d

a couple doctests and a blunder of my own

[darijgr]

comment:4

Thanks for the split, which was rather appropriate. Positive_review on my side.

[tscrim]

comment:5

Thanks Darij.

[vbraun]

comment:6

sage -t --long src/sage/categories/groups.py
**********************************************************************
File "src/sage/categories/groups.py", line 531, in sage.categories.groups.Groups.Algebras.example
Failed example:
    GroupAlgebras(QQ).example(SymmetricGroup(4))
Expected:
    Group algebra of Symmetric group of order 4! as a permutation group over Rational Field
Got:
    Symmetric group algebra of order 4 over Rational Field
**********************************************************************
File "src/sage/categories/groups.py", line 578, in sage.categories.groups.Groups.Algebras.ParentMethods.algebra_generators
Failed example:
    GroupAlgebras(QQ).example(SymmetricGroup(10)).algebra_generators()
Expected:
    Finite family {(1,2): B[(1,2)], (1,2,3,4,5,6,7,8,9,10): B[(1,2,3,4,5,6,7,8,9,10)]}
Got:
    [[2, 1, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9, 10, 1]]
**********************************************************************
sage -t --long src/sage/combinat/root_system/hecke_algebra_representation.py
**********************************************************************
File "src/sage/combinat/root_system/hecke_algebra_representation.py", line 81, in sage.combinat.root_system.hecke_algebra_representation.HeckeAlgebraRepresentation.__init__
Failed example:
    HeckeAlgebraRepresentation(domain, action, CartanType(["A",2]), 1, -1)
Expected:
    A representation of the (1, -1)-Hecke algebra of type ['A', 2]
    on Group algebra of Symmetric group of order 3! as a permutation group over Rational Field
Got:
    A representation of the (1, -1)-Hecke algebra of type ['A', 2] on Symmetric group algebra of order 3 over Rational Field
**********************************************************************
File "src/sage/combinat/root_system/hecke_algebra_representation.py", line 229, in sage.combinat.root_system.hecke_algebra_representation.HeckeAlgebraRepresentation.on_basis
Failed example:
    rho.on_basis(W.one(), (1,2,1))
Expected:
    B[(1,3)]
Got:
    (1,3)
**********************************************************************

[sagetrac-git]

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

500735d	Merge branch 'public/coercion/fix_sga_coercions-16678' of trac.sagemath.org:sage into public/coercion/fix_sga_coercions-16678
d8ea764	Fixed trivial doctest failures.

[sagetrac-git]

Changed commit from 3fa802d to d8ea764

[tscrim]

comment:8

Trivial failures due to SGA's being returned from SymmetricGroup(n).algebra().

[vbraun]

Changed branch from public/coercion/fix_sga_coercions-16678 to d8ea764

[nthiery]

comment:10

See followup #16625. Sorry I did not spot this earlier; it's too bad the change was released in 6.3, since now we are reverting a backward incompatible change, making it compabible back to <=6.2 but not 6.3 ...

[nthiery]

Changed commit from d8ea764 to none

[darijgr]

comment:11

#16925, not #16625.

I'm seeing it right that only the SymmetricGroup.Algebra part of this ticket will be reverted?

[nthiery]

comment:12

Replying to @darijgr:

#16925, not #16625.

Oops, I am up-down dislexic apparently :-)

I'm seeing it right that only the SymmetricGroup.Algebra part of this ticket will be reverted?

Definitely.