#20445: Iteration through finite Coxeter groups
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Reporter: | Owner:
stumpc5 | Status: new
Type: | Milestone: sage-7.2
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
combinatorics | Work issues:
Keywords: | Commit:
Authors: | bc3c926b27ccca4371b28a4dbac0169d639ff191
Report Upstream: N/A | Stopgaps:
Branch: |
u/stumpc5/20445 |
Dependencies: |
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Comment (by stumpc5):
Replying to [comment:15 tscrim]:
> {{{
> CPU times: user 4min 23s, sys: 604 ms, total: 4min 23s
> Wall time: 4min 23s
> }}}
Great, I believe **you can claim to be the first person ever who iterated
through E8 in less than 5 minutes**! (I was expecting that since 1. your
computer was about twice as fast as mine last week, and 2. you took ~8
minutes to iter through E8 in chevie, and my code is about twice as fast
as the chevie code.)
1. I would really like to see how to implement our own permutation group
elements with only what we need. I would hope that to again result in some
speedup. One question there: we have w(-\beta) = -w(\beta), so we would
not need to record the complete permutation on all roots, but on the
positive roots would be enough. That would speed several computations such
as creating new elements and testing for equality), but it would have the
drawback that we constantly need to work mod N (N=nr of positive roots),
e.g., we would have such checks and mod's when multiplying two
permutations.
2. We should get your parallelization to work with this so that people can
then use many cores to actually do stuff with the elements in type E8.
--
Ticket URL: <http://trac.sagemath.org/ticket/20445#comment:17>
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