#10305: Add rings for the center of the symmetric group algebras
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Reporter: mguaypaq | Owner: mguaypaq
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.13
Component: combinatorics | Resolution:
Keywords: combinatorics, | Merged in:
rings, symmetric functions | Reviewers: Travis Scrimshaw,
Authors: Mathieu Guay- | Mathieu Guay-Paquet
Paquet, Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 25ff1fd7f9ad2539fb7e95134d96b882bfd40187
u/mguaypaq/ticket/10305 | Stopgaps:
Dependencies: |
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Changes (by mguaypaq):
* commit: => 25ff1fd7f9ad2539fb7e95134d96b882bfd40187
Old description:
> Here is some preliminary code to implement the center of the symmetric
> group algebras, various bases for this and related rings, and coercions
> between these and to/from the ring of symmetric functions.
>
> Things that I plan to do:
> * Fill in all of the TODO doctests with actual doctests.
> * Figure out why some of the coercions aren't discovered by the coercion
> framework. (See the last few examples at the top of the file.)
> * `SymmetricGroupAlgebraCenter` does not actually have a multiplicative
> identity as currently implemented, so it should probably by in a category
> other than `GradedAlgebrasWithBasis`.
> * Reimplement `ConjugacyClassBasis` and `OrthogonalIdempotentBasis` for
> a fixed symmetric group over the integers. Then, the conversion table can
> be cached, the elements can be represented by lists of coefficients
> (possibly numpy arrays) instead of dictionaries, and faster linear
> algebra over the integers can be used. This results in massive (several
> orders of magnitude) speedups.
> * Possibly add the option of saving some of the conversion tables to
> disk, as they can be large and expensive to compute.
> * Add the relevant classes to `sage/combinat/all.py`.
>
> Note that this depends on #7980 and #10304.
>
> Apply:
>
> [attachment:trac_10305-farahat_higman-ts.patch]
New description:
Here is some preliminary code to implement the center of the symmetric
group algebras, various bases for this and related rings, and coercions
between these and to/from the ring of symmetric functions.
Work issues:
* Re-architecting in progress
* Fix the performance of conversion from !SymmetricGroupAlgebraCenter to
!SymmetricGroupAlgebra
* Add the new files (and possibly some old ones?) to the reference manual
* Possibly add the option of saving some of the conversion tables to
disk, as they can be large and expensive to compute.
Note that this depends on #7980 and #10304.
--
Comment:
Sorry for the very long delay. The code is still a work in progress, but
now using the new git workflow! I've been tinkering with the code a lot,
but hopefully this first commit makes some sense. It's mostly about
splitting off the !SymmetricGroupAlgebraCenter code into its own file, but
there's a pretty long-winded commit message to explain the code changes.
I now have a much clearer picture of what rings should be created, in what
order, under what conditions, which coercions should be registered, and
what should be cached where. I'll start chipping away at this for now, and
if anyone wants to validate the design, I bet a conversation on IRC (or
some other real-time communication medium) would be best.
For reviewing, my hope would be that each commit makes sense individually,
and could be reviewed individually to check that it does what it claims to
do in the commit message. Travis, would this be acceptable?
--
Ticket URL: <http://trac.sagemath.org/ticket/10305#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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