#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:
-------------------------------------+-------------------------------------
Changes (by nthiery):
* commit: => 50867d895544ee5a449423bde74440ea8470f9ee
* dependencies: => 18310, 6484
Old 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).
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).
The dependency on #6484 is only for speed.
--
Comment:
Last 10 new commits:
||[http://git.sagemath.org/sage.git/commit/?id=cba7c8d1adcad21ace893b5827777348c2e486ef
cba7c8d]||{{{17696: factored out of the examples a basic implementation of
the 0-Hecke monoid}}}||
||[http://git.sagemath.org/sage.git/commit/?id=6e81e4b500f7698446fd19de792744a33667eafa
6e81e4b]||{{{16659: proofreading and little additions to the doc; small
refactoring of the code}}}||
||[http://git.sagemath.org/sage.git/commit/?id=19756de9e9367efc85add11872bbf03d873b948f
19756de]||{{{16659: minor line-split in the doc}}}||
||[http://git.sagemath.org/sage.git/commit/?id=fd8e1ad375037e078905ae220bc9e543d65a67be
fd8e1ad]||{{{16659: refactored _orthogonal_decomposition and updated
doctests accordingly}}}||
||[http://git.sagemath.org/sage.git/commit/?id=cc327efe6f3a221ae089d68558e5296cc9fc295c
cc327ef]||{{{16659: improved documentation for
_orthogonal_decomposition}}}||
||[http://git.sagemath.org/sage.git/commit/?id=e00dfdb8c49ba0105922aeeabab5bcb234bceaf0
e00dfdb]||{{{16659: improved documentation for
_orthogonal_decomposition}}}||
||[http://git.sagemath.org/sage.git/commit/?id=cce7d3db05f6f10fec8c19a055987c61eee4b771
cce7d3d]||{{{17696: added crosslinks}}}||
||[http://git.sagemath.org/sage.git/commit/?id=faf83a1380dde69c2dfd7849c1b8b8d24dcbecd6
faf83a1]||{{{16659: added missing hecke_monoid.py file}}}||
||[http://git.sagemath.org/sage.git/commit/?id=223e55834daf91167b517b7c80f0af92ef627fba
223e558]||{{{18310: Finite dimensional modules with basis: improved
conversions to vectors and matrices}}}||
||[http://git.sagemath.org/sage.git/commit/?id=50867d895544ee5a449423bde74440ea8470f9ee
50867d8]||{{{18311: O(n^3) algorithm for radical_basis in char 0 and
faster Cartan invariants matrix by characters}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/18311#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
