Make various operations for rational matrix groups faster (fixes a performance regression from GAP 4.15.0) #6138
Conversation
fingolfin
added
topic: performance
fingolfin
force-pushed
the
mh/optimize-nice-mono-rat-mat-groups
branch
from
f78c756 to
516ae73
Compare
|
|
||
| # evaluate relators | ||
| phi := IsomorphismFpGroupByGenerators(H, GeneratorsOfGroup( H )); | ||
| phi := IsomorphismFpGroupByGeneratorsNC(H, GeneratorsOfGroup( H ) : method := "fast"); |
There was a problem hiding this comment.
This is the major bottleneck of this function. Specifically, I was using the example from issue #6135, but taking the direct product with itself to make it more a bit more spicy:
v:=[ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 0, -1, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 0, 0, 0, 0, 1 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 1, 0, 0, 0, 0, 0 ] ], [ [ 0, 0, 0, 0, 0, -1 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ -1, 0, 0, 0, 0, 0 ] ] ];
W:=Group(v);
G:=DirectProduct(W,W);Then IsomorphismFpGroupByGenerators in the code I am commenting on here it takes 3.5 seconds. With the fast option it's down to ~900 milliseconds.
Alas neither is particularly great, the "old" code pre-4.15 is still faster. (Of course there are other examples where the new code is way, WAY faster, otherwise I wouldn't have put it in).
I wonder if constructive recognition would help to do this better (the group in question has very small factors: just A6 and otherwise 2-groups
fingolfin
changed the title
fingolfin
force-pushed
the
mh/optimize-nice-mono-rat-mat-groups
branch
from
516ae73 to
f018b28
Compare
This fixes a performance regression from GAP 4.15.0 and in some cases makes things actually faster than they were then.
fingolfin
force-pushed
the
mh/optimize-nice-mono-rat-mat-groups
branch
from
f018b28 to
9eec33b
Compare
| ## Group([ (1,2)(3,4), (1,3)(2,4) ]), Group(()), | ||
| ## Group([ (), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4) ]) ] | ||
| ## gap> List( Irr( S4 ), chi -> StructureDescription(CentreOfCharacter(chi)) ); | ||
| ## [ "S4", "1", "C2 x C2", "1", "S4" ] |
There was a problem hiding this comment.
@ThomasBreuer thoughts on this change and the one below? I mean, I can also adjust the generator sets once again but I feel this is whack-a-mole...
(Of course this one here is still susceptible to a change in the order of the irreducibles. I considered using Set but "1" occurs twice. Guess I could use Collected or `Sort but that makes it even more artificial...
There was a problem hiding this comment.
The group is SymmetricGroup( 4 ), which uses the Irr method for symmetric groups, thus the order of the irreducibles should be stable. Showing the StructureDescription values is fine.
| ## Group([ (1,2)(3,4), (1,3)(2,4) ]), Group(()), | ||
| ## Group([ (), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4) ]) ] | ||
| ## gap> List( Irr( S4 ), chi -> StructureDescription(CentreOfCharacter(chi)) ); | ||
| ## [ "S4", "1", "C2 x C2", "1", "S4" ] |
There was a problem hiding this comment.
The group is SymmetricGroup( 4 ), which uses the Irr method for symmetric groups, thus the order of the irreducibles should be stable. Showing the StructureDescription values is fine.
…rformance regression from GAP 4.15.0) (#6138) This fixes a performance regression from GAP 4.15.0 and in some cases makes things actually faster than they were then.
|
Backported to |
2 participants
This fixes a performance regression from GAP 4.15.0 and in some cases makes things actually faster than they were then.
The problem was that the preimages of the new nice monomorphism for rational matrix groups in GAP 4.15.0 was way too slow. It worked via a homomorphism to a free group, decomposed elements into words, etc. etc. -- but the inverse really is a homomorphism whose domain is a permutation group, and so we can use that to compute preimages much more quickly.
Fixes #6135