Add LatticeSubgroups method for the case IsHandledByNiceMonomorphism
#4639
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for the case `IsHandledByNiceMonomorphism`
ThomasBreuer
added
release notes: use title
| > [ 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0, 0*Z(5) ], | ||
| > [ Z(5), 0*Z(5), Z(5)^2, Z(5)^2, Z(5)^2, Z(5)^0 ], | ||
| > [ Z(5)^3, Z(5), Z(5)^3, 0*Z(5), 0*Z(5), Z(5)^0 ] ] ] );; | ||
| gap> Length( ConjugacyClassesSubgroups( g ) ); |
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How long does this actually take, though?x
When I tried something in this vein earlier today, the "nice" permutation group had relatively large degree and working with was rather slow.
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This example needs about 30 seconds on my notebook.
The permutation group is clearly not optimal --I get degree 7560, the smallest possible degree would be 200.
In larger examples, no reasonable faithful permutation representation exists at all, but this argument affects all methods that are based on the "nice monomorphism" idea.
I would say that the new method yields an improvement for "middle-sized examples" and does not cause problems for situations where better methods may become available. (This is how I understand @hulpke 's suggestion.)
But if we think that it would be better not to provide an admittedly slow way to computations like in this example (compared to what Magma offers) then perhaps we should discuss about restricting the "nice monomorphism" approach to small enough situations.
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Nah, I am fine with this PR, just wondering how effective it is in this example
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What irritates me is that the "nice monomorphism" approach in this example is faster than what one gets when the matgrp package is loaded and FittingFreeLiftSetup for the group is set; I get about 50 seconds in this situation.
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I am actually pleased that the lattice computation goes through with matgrp without a hitch, as I have not really tried it before.
As for the performance, I can think of two possibilities:
- Some calculation still goes through nice monomorphisms -- not every subroutine used has a
solvable radicalanalog - Certain calculations that happen frequently (say element membership) actually take significantly longer in the matrix representation and we need to figure out how to improve this.
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Yes, I had noticed that the NiceMonomorphism value is set in the group after the computations with matgrp.
fingolfin
changed the title
LatticeSubgroups method for the case IsHandledByNiceMonomorphismLatticeSubgroups method for the case IsHandledByNiceMonomorphism
resolves #4637