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############################################################################
# Just an example, recognise a cyclic group of order 2:
############################################################################
FindHomMethodsPerm.Cyclic2 :=
function(ri, H)
local gens,i;
# Test applicability (this would no longer be necessary, because we
# are called only for permutation groups anyway. However, this is an
# example.
if not IsPermGroup(H) then
return NeverApplicable;
fi;
# Now we work:
if Size(H) = 2 then
# First find the first nontrivial generator:
gens := GeneratorsOfGroup(H);
i := 1;
while IsOne(gens[i]) do
i := i + 1;
od;
ri!.firstnontrivialgen := i;
SetNiceGens(ri,[GeneratorsOfGroup(H)[i]]);
Setslptonice(StraightLineProgramNC([[[i,1]]],Length(gens)));
Setslpforelement(ri,SLPforElementFuncsPerm.Cyclic2);
SetFilterObj(ri,IsLeaf);
SetIsRecogInfoForSimpleGroup(ri,true);
return Success; # this indicates success
else
return NeverApplicable; # do not call us again
fi;
end;
SLPforElementFuncsPerm.Cyclic2 :=
function(ri, g)
if IsOne(g) then
return StraightLineProgram([[1, 0]], 1);
else
return StraightLineProgram([[1, 1]], 1);
fi;
end;
# The following would install this method with a very low rank if we would
# like to:
#
# AddMethod(FindHomDbPerm,
# rec(method := FindHomMethodsPerm.Cyclic2,
# rank := 1,
# stamp := "Cyclic2",
# comment := "find a Cyclic2"));
[ Dauer der Verarbeitung: 0.27 Sekunden
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