#16659: Decomposition of finite dimensional associative algebras
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Reporter: virmaux | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: algebra | Resolution:
Keywords: representation | Merged in:
theory | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: u/virmaux/t/16659 | 434765db324c0e6da9ddab9dd4b02632d12703f9
Dependencies: #11111 | Stopgaps:
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Comment (by saliola):
== finite_dimensional_algebras_with_basis.py (part 2) ==
I think that `cartan_invariant_matrix` should be
`cartan_invariants_matrix`; update the documentation of this method to
read:
{{{
Return the matrix of Cartan invariants of ``self``.
}}}
In the method `cartan_invariant_matrix`, you compute the dimension of the
simple modules, but this is just the cartan invariants for the semisimple
quotient. Perhaps you can use this to clean up the code.
At the very least, I think that the code to compute the dimension of the
simple
modules should be refactored into a separate method.
{{{``side``-sided}}} should be just {{{``side``}}}.
`projective_decomposition` --> `projective_indecomposables` or
`projective_indecomposable_modules`
`_cartan_matrix_coef` --> `_cartan_matrix_coeff` (two fs)
missing documentation string for `_cartan_matrix_coeff`
Perhaps it is a good idea to define a method called `pierce_decomposition`
that returns the Pierce decomposition of the algebra; and maybe
`pierce_component`? This would simplify `_cartan_matrix_coef`.
--
Ticket URL: <http://trac.sagemath.org/ticket/16659#comment:28>
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