On Mon, Jun 4, 2012 at 1:32 PM, Nils Bruin <nbr...@sfu.ca> wrote:
> On Jun 3, 12:58 pm, John H Palmieri <jhpalmier...@gmail.com> wrote:
>> By the way, you can also define infinite-dimensional vector spaces this way.
>
> Ah, that probably explains why non-trivial linear algebra
> functionality is missing on this class. I don't think you can
> reasonably expect to do that on infinite dimensional vector spaces
> without some extra structure. Simply enumerating bases will not yield
> algorithms ...

There is some work being done to add more "linear algebra" to the
finite dimensional CombinatorialFreeModules and to algebras with
basis; see trac #11111:

- Echelon form of list of vectors
- Submodules and quotients
- Category of SemisimpleAlgebras
- Center, radical, and semisimple quotient of a finite dimensional algebra
- Annihilator
- Matrix and inverse of module morphisms

And some work is being done for the case when the module is graded
(even infinite dimensional ones); see #9280, for an example.

Come join in the fun. ;-)

Franco

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