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Fix some bugs in the Rees (0)-matrix semigroups code #768

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May 3, 2016
Merged

Fix some bugs in the Rees (0)-matrix semigroups code #768

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85687e0
Fix bugs in Rees (0-)matrix semigroups over free groups
james-d-mitchell Apr 27, 2016
3387f6f
Fix Rees 0-matrix semigroups over free semigroup
james-d-mitchell Apr 27, 2016
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27 changes: 23 additions & 4 deletions lib/reesmat.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -38,16 +38,30 @@ function(R)
TryNextMethod();
end);

InstallImmediateMethod(IsFinite, IsReesMatrixSubsemigroup, 0,
function(R)
if IsBound(ElementsFamily(FamilyObj(R))!.IsFinite) then
return ElementsFamily(FamilyObj(R))!.IsFinite;
fi;
TryNextMethod();
end);

InstallMethod(IsFinite, "for a Rees matrix subsemigroup",
[IsReesMatrixSubsemigroup],
function(R)
return IsFinite(ParentAttr(R));
if (not IsIdenticalObj(R, ParentAttr(R))) and HasIsFinite(ParentAttr(R)) then
return IsFinite(ParentAttr(R));
fi;
TryNextMethod();
end);

InstallMethod(IsFinite, "for a Rees 0-matrix subsemigroup",
[IsReesZeroMatrixSubsemigroup],
function(R)
return IsFinite(ParentAttr(R));
if (not IsIdenticalObj(R, ParentAttr(R))) and HasIsFinite(ParentAttr(R)) then
return IsFinite(ParentAttr(R));
fi;
TryNextMethod();
end);

#
Expand Down Expand Up @@ -240,6 +254,10 @@ function(S, mat)
fam := NewFamily( "ReesMatrixSemigroupElementsFamily",
IsReesMatrixSemigroupElement);

if HasIsFinite(S) then
fam!.IsFinite := IsFinite(S);
fi;

# create the Rees matrix semigroup
R := Objectify( NewType( CollectionsFamily( fam ), IsWholeFamily and
IsReesMatrixSubsemigroup and IsAttributeStoringRep ), rec() );
Expand Down Expand Up @@ -316,8 +334,9 @@ function(S, mat)
# cannot set IsZeroSimpleSemigroup to be <true> here since the matrix may
# contain a row or column consisting entirely of 0s!
# WW Also S might not be a simple semigroup (which is necessary)!

GeneratorsOfSemigroup(R);
if IsGroup(S) or (HasIsFinite(S) and IsFinite(S)) then
GeneratorsOfSemigroup(R);
fi;
SetIsSimpleSemigroup(R, false);
return R;
end);
Expand Down
20 changes: 18 additions & 2 deletions tst/teststandard/reesmat.tst
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Original file line number Diff line number Diff line change
Expand Up @@ -609,8 +609,11 @@ gap> Length(GreensDClasses(UUU));
4
gap> Size(V);
33
gap> Vt:=Range(IsomorphismTransformationSemigroup(V));
<transformation semigroup of degree 34 with 5 generators>
gap> Vt:=Range(IsomorphismTransformationSemigroup(V));;
gap> Length(GeneratorsOfSemigroup(Vt));
5
gap> DegreeOfTransformationSemigroup(Vt);
34
gap> Size(Vt);
33
gap> Representative(R);
Expand Down Expand Up @@ -1085,6 +1088,19 @@ true
gap> IsFinite(S);
true

# Test bug in IsFinite for RMS or RZMS created over a free group
gap> S := FreeGroup(1);;
gap> R := ReesMatrixSemigroup(S, [[S.1]]);;
gap> IsFinite(R);
false
gap> R := ReesZeroMatrixSemigroup(S, [[S.1]]);;
gap> IsFinite(R);
false

# Test bug in creation of RZMS over a free semigroup
gap> S := FreeSemigroup(1);;
gap> R := ReesZeroMatrixSemigroup(S, [[S.1]]);;

#
gap> STOP_TEST( "reesmat.tst", 54100000);

Expand Down