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## Testing if Green's D classes can be compared for finite semigroups
gap> s := Transformation([1,1,3,4,5]);;
gap> c := Transformation([2,3,4,5,1]);;
gap> op5 := Semigroup(s,c);;
gap> dcl := GreensDClasses(op5);;
gap> ForAny(Cartesian(dcl,dcl), x->IsGreensLessThanOrEqual(x[1],x[2]));
true
## Testing that GroupHClassOfGreensDClass is implemented
gap> h := GroupHClassOfGreensDClass(dcl[4]);;
## Testing AssociatedReesMatrixSemigroupOfDClass.
## IsZeroSimpleSemigroup, IsomorphismReesMatrixSemigroup,
## and MatrixOfReesZeroMatrixSemigroup
## create Greens D classes correctly.
gap> rms := AssociatedReesMatrixSemigroupOfDClass(dcl[5]);;
gap> s := Transformation([1,1,2]);;
gap> c := Transformation([2,3,1]);;
gap> op3 := Semigroup(s,c);;
gap> IsRegularSemigroup(op3);;
gap> dcl := GreensDClasses(op3);;
gap> dcl := SortedList(ShallowCopy(dcl));;
gap> d2 := dcl[2];; d1:= dcl[1];;
gap> i2 := SemigroupIdealByGenerators(op3,[Representative(d2)]);;
gap> GeneratorsOfSemigroup(i2);;
gap> i1 := SemigroupIdealByGenerators(i2,[Representative(d1)]);;
gap> GeneratorsOfSemigroup(i1);;
gap> c1 := ReesCongruenceOfSemigroupIdeal(i1);;
gap> q := i2/c1;;
gap> IsZeroSimpleSemigroup(q);;
gap> irms := IsomorphismReesZeroMatrixSemigroup(q);;
gap> MatrixOfReesZeroMatrixSemigroup(Range(irms));;
gap> g := Group( (1,2),(1,2,3) );;
gap> i := TrivialSubgroup( g );;
gap> CentralizerModulo( g, i, (1,2) );
Group([ (1,2) ])
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