Opened 10 years ago

Last modified 3 years ago

#11285 new enhancement

Request to add feature: Decomposing a finite dimensional vector space with respect to a collection of matrices acting on the vector space.

Reported by: chrisjamesberg Owned by: AlexGhitza
Priority: major Milestone: sage-wishlist
Component: algebra Keywords: days30, days88
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description (last modified by vdelecroix)

I would like to request a new feature for Sage. I would like to be able to input a collection of n by n matrices which I think of as acting on an n dimensional vector space and have sage output a decomposition of the vector space into irreducible components with respect to the action of these matrices.

addendum: it would even be better to have a method that provides the finest decomposition up to subgroups of finite index!

Attachments (1)

trac_11285-decompose_vecspace-ts.patch (3.9 KB) - added by tscrim 8 years ago.

Download all attachments as: .zip

Change History (7)

comment:1 Changed 10 years ago by chrisjamesberg

  • Summary changed from Request to add feature: Decomposing a finite dimensional vector space with respect to a collection of actions. to Request to add feature: Decomposing a finite dimensional vector space with respect to a collection of matrices acting on the vector space.

comment:2 Changed 10 years ago by saliola

  • Keywords days30 added

comment:3 Changed 8 years ago by tscrim

I've uploaded the start of a patch which works well if the basis is suitably chosen. I just apply all the matrices and see where it takes the natural basis vectors, and merges into appropriate subspaces. In the documentation there is the start of a good test example if anyone can get this to work...

Changed 8 years ago by tscrim

comment:4 Changed 8 years ago by nthiery

Hi Travis,

You want to get in touch with Aladin, for this is decomposing a module for a general finite dimensional algebra, and he is working on the representation theory of those algebras.

comment:5 Changed 3 years ago by saliola

  • Keywords days88 added

comment:6 Changed 3 years ago by vdelecroix

  • Description modified (diff)
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