#18311: Improve radical_basis and cartan_invariants_matrix for a finite
dimensional
algebra
-------------------------------------+-------------------------------------
Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.7
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/representation_theory/finite_dimensional_algebras-18311|
50867d895544ee5a449423bde74440ea8470f9ee
Dependencies: #18310, #6484 | Stopgaps:
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Comment (by nthiery):
Replying to [comment:5 virmaux]:
> I just took some time to read the patch.
Thanks!
> `FiniteDimensionalAlgebrasWithBasis.multiplication_matrix` the name is
not very explicit, what about `basis_action_matrices` ?
Agreed; maybe `multiplication_matrix_on_basis`. Suggestions anyone?
> As well, wether we want sparse matrices or not may be given as an
argument?
Maybe indeed. I am also thinking about an option that would apply to
the whole algebra to state whether its coefficients structure are
sparse or dense.
> Should we overwrite the previous method for Cartan invariant matrix from
#16659 with this new one ? Indeed the return should be the same and it's
much faster!
This one is only valid in large enough characteristic. Also it can be
good to have several algorithm for comparison. But I agree we probably
want to have an option instead (and possibly several private methods
behind the scene).
> In this case maybe we may want to wait that #16659 is positive_reviewed
to avoid merging issues.
Yeah, I'd rather wait for #16659 to be finished.
> Everything else looks good to me (modulo the remaining documentation)
> I can do the aforementioned modifications.
Let's discuss this tomorrow with Florent. We might want to think about
the graded Cartan matrix.
Cheers,
Nicolas
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Ticket URL: <http://trac.sagemath.org/ticket/18311#comment:6>
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