#16659: Decomposition of finite dimensional associative algebras
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Reporter: virmaux | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: algebra | Resolution:
Keywords: representation | Merged in:
theory | Reviewers: Franco Saliola
Authors: Aladin Virmaux | Work issues: merge in develop.
Report Upstream: N/A | Commit:
Branch: u/saliola/t/16659 | 7362f035239f8fdbc992888478a9f4b7d102193c
Dependencies: #11111 | Stopgaps:
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Changes (by saliola):
* commit: 8f6a8670d2708b960a9f89490a59c76b9099d451 =>
7362f035239f8fdbc992888478a9f4b7d102193c
Comment:
I pushed some changes:
1. `radical_basis`: I removed the optional `cache_products` option since
the speed up by Aladin seems not to use this [should be verified by the
reviewer]. I also re-wrote the code to make it more readable (I hope it is
more readable, at least).
2. `principal_ideal`:
(a) I swapped 'left' and 'right', because they were backwards. The
principal left ideal generated by `a` is `Aa`, not `aA`. I added doctests
to test this.
(b) the implementation only worked for 'triangularizable' algebras
(for a suitable definition of triangularizable). I fixed the method to
handle the generic case.
3. `central_orthogonal_idempotents`: I added a TESTS section to test that
the idempotents constructed in the examples are "idempotents",
"orthogonal" and "central". (I didn't run the tests yet though.)
Some of the above changes might break some tests in other parts of the
code that rely on it (for example, `principal_ideal`).
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=7362f035239f8fdbc992888478a9f4b7d102193c
7362f03]||{{{16659: some documentation and tests}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/16659#comment:54>
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