#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:
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Nicolas M. Thi\xe9ry', 'oldvalue': ''}):
* cc: hivert, saliola, virmaux, sage-combinat (added)
* author: => Nicolas M. Thiéry
Old description:
New description:
This ticket improves the algorithmic complexity (`n^4` to `n^3` for
`radical_basis`) and further optimizes the code for computing the
radical and the Cartan invariants matrix.
Without:
{{{
sage: A = HeckeMonoid(SymmetricGroup(5)).algebra(QQ)
sage: %time len(A.radical_basis())
CPU times: user 4.25 s, sys: 45.1 ms, total: 4.3 s
Wall time: 4.26 s
104
sage: %time A.cartan_invariants_matrix()
CPU times: user 45.2 s, sys: 267 ms, total: 45.4 s
Wall time: 45.5 s
}}}
With:
{{{
sage: A = HeckeMonoid(SymmetricGroup(5)).algebra(QQ)
sage: %time len(A.radical_basis())
CPU times: user 418 ms, sys: 29.5 ms, total: 447 ms
Wall time: 422 ms
104
sage: %time A.cartan_invariants_matrix_by_characters()
CPU times: user 9.39 s, sys: 208 ms, total: 9.6 s
Wall time: 9.53 s
}}}
(the above examples do not use that this is a monoid algebra, though
of course the sparsity helps).
--
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Ticket URL: <http://trac.sagemath.org/ticket/18311#comment:1>
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