Weyl group optimizations

[nthiery]

• faster hash method calling the hash of the underlying matrix
  (which is set as immutable for that purpose)
• new __eq__ method
• action on the weight lattice realization:
  optimization of the matrix multiplication

Depends (trivially) on #7753

This indirectly improve most Weyl group routines:

Without the patch:

sage: W = WeylGroup(["F",4])
sage: W.cardinality()
1152
sage: time l=list(W)
CPU times: user 12.14 s, sys: 0.06 s, total: 12.20 s Wall time: 12.20 s

sage: W = WeylGroup(["E",8])
sage: time w0 = W.long_element()
CPU times: user 1.71 s, sys: 0.01 s, total: 1.72 s Wall time: 1.72 s

With the patch:

sage: W = WeylGroup(["F",4])
sage: W.cardinality()
1152
sage: time l=list(W)
CPU times: user 7.96 s, sys: 0.04 s, total: 8.00 s Wall time: 8.01 s

sage: W = WeylGroup(["E",8])
sage: time w0 = W.long_element()
CPU times: user 1.40 s, sys: 0.00 s, total: 1.41 s Wall time: 1.42 s

Honestly, this is still ridiculously slow; luckily there still is much room left for improvements by improved caching and optimizations of the underlying tools (CombinatorialFreeModules, ...).

CC: @dwbump

Component: combinatorics

Keywords: Weyl groups

Author: Nicolas M. Thiéry

Reviewer: Daniel Bump

Merged: sage-4.3.1.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7754

[nthiery]

comment:1

Attachment: trac_7754_weyl_group_optimizations-nt.patch.gz

[dwbump]

comment:2

I tested this patch without #7753. I tested it with and without the
patch in #7751.

It is a very substantial speedup. It cuts a few
seconds off sage -t weyl_groups.py but more importantly it about doubles the speed of computing the reduced word of a Weyl group element, which is the basis of most combinatorial algorithms.

There are three patch fragments, one replacing the hash method with the hash of the underlying matrix, one replacing the __eq__ method, and
one unraveling some unnecessary complexity in the Weyl group action. I tested each patch fragment separately and found that they are all speedups, the last one being very significant.

[nthiery]

comment:3

Thanks Dan for the review!

[mwhansen]

Merged: sage-4.3.1.alpha0

[sagetrac-mvngu]

comment:6

Replying to @dwbump:

It is a very substantial speed-up. It cuts a few
seconds off sage -t weyl_groups.py but more importantly it about doubles the speed of computing the reduced word of a Weyl group element, which is the basis of most combinatorial algorithms.

Hi Dan and Nicolas,

I'm doing a release tour of the features of this ticket, see the Sage wiki page. Is there some sample code I could use to show the speed-up implemented by this ticket?

[nthiery]

comment:8

Hi Dan and Nicolas,

I'm doing a release tour of the features of this ticket, see the Sage wiki page. Is there some sample code I could use to show the speed-up implemented by this ticket?

Yup, see the updated description!