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Make use of LieTypeNonConstr output #489

@fingolfin

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@fingolfin

The recognition method LieTypeNonConstr (should perhaps better be called LieTypeNaming or so?) produces interesting information that we however do not currently seem to use well.

$ gap -b examples/challenges-by-frank-luebeck/example7.g.gz
# Read matrix group "example7" over GF(3) in dimension 100.
gap> SetInfoLevel(InfoRecog,2); SetInfoLevel(InfoMethSel,3);
gap> ri:=RecognizeGroup(example7); time;
...
#I  Finished rank 500 method "ThreeLargeElOrders": NeverApplicable.
#I  Calling rank 400 method "LieTypeNonConstr"...
#I  LieTypeNonConstr: found L10(59049), lookup up hints...
#I  Looking up hints for L10(59049)...
#I  No hint worked, giving up.
#I  LieTypeNonConstr: giving up.
#I  Finished rank 400 method "LieTypeNonConstr": TemporaryFailure.
#I  Calling rank 100 method "StabilizerChainProj"...
#I  Looking for short orbit (0)...
#I  Have 720001 points.
#I  Have 1440001 points.
#I  Have 2160001 points.
#I  Have 2880001 points.
#I  Have 3600001 points.
...

So it figures out we are looking at L10(59049) = PSL(10,3^10) but then it does nothing with that!

Specifically, we have SLCR.FindHom (see also issue #59) which could be called here?

Or perhaps the real issue is that ThreeLargeElOrders does not work (it would otherwise call SLCR.FindHom) ?

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