Changes between Initial Version and Version 1 of Ticket #18311


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Timestamp:
Apr 27, 2015, 10:51:37 AM (8 years ago)
Author:
Nicolas M. Thiéry
Comment:

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  • Ticket #18311

    • Property Cc Florent Hivert Franco Saliola Aladin Virmaux Sage Combinat CC user added
    • Property Authors changed from to Nicolas M. Thiéry
  • Ticket #18311 – Description

    initial v1  
     1This ticket improves the algorithmic complexity (`n^4` to `n^3` for
     2`radical_basis`) and further optimizes the code for computing the
     3radical and the Cartan invariants matrix.
     4
     5Without:
     6{{{
     7sage: A = HeckeMonoid(SymmetricGroup(5)).algebra(QQ)
     8sage: %time len(A.radical_basis())
     9CPU times: user 4.25 s, sys: 45.1 ms, total: 4.3 s
     10Wall time: 4.26 s
     11104
     12sage: %time A.cartan_invariants_matrix()
     13CPU times: user 45.2 s, sys: 267 ms, total: 45.4 s
     14Wall time: 45.5 s
     15}}}
     16
     17With:
     18{{{
     19sage: A = HeckeMonoid(SymmetricGroup(5)).algebra(QQ)
     20sage: %time len(A.radical_basis())
     21CPU times: user 418 ms, sys: 29.5 ms, total: 447 ms
     22Wall time: 422 ms
     23104
     24sage: %time A.cartan_invariants_matrix_by_characters()
     25CPU times: user 9.39 s, sys: 208 ms, total: 9.6 s
     26Wall time: 9.53 s
     27}}}
     28
     29(the above examples do not use that this is a monoid algebra, though
     30of course the sparsity helps).