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IsSelfDualSemigroup returns false negatives #1014

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james-d-mitchell opened this issue May 20, 2024 · 0 comments
Open

IsSelfDualSemigroup returns false negatives #1014

james-d-mitchell opened this issue May 20, 2024 · 0 comments
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@james-d-mitchell
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For example, with only Smallsemi loaded:

gap> S := SmallSemigroup(6, 2);;
gap> IsSelfDualSemigroup(S);
true

with Semigroups loaded:

gap> S := SmallSemigroup(6, 2);;
gap> IsSelfDualSemigroup(S);
false

The correct answer seems to be the one returned by Smallsemi, since:

gap> S := SmallSemigroup(6, 2);;
gap> T := DualSemigroup(S);;
gap> IsIsomorphicSemigroup(S, T);
true

The issue is that the generators don't have to be mapped by the identity function from T to Range(map) in:

T := AsSemigroup(IsFpSemigroup, S);
map := AntiIsomorphismDualFpSemigroup(T);
return SemigroupIsomorphismByImages(T,
Range(map),
GeneratorsOfSemigroup(T),
List(GeneratorsOfSemigroup(T),
x -> x ^ map)) <> fail;

gap> S := SmallSemigroup(6, 2);;
gap> OnTuples(GeneratorsOfSemigroup(S), map); 
[ m1, m2, m3, m4, m6, m5 ]
@james-d-mitchell james-d-mitchell added the bug Label for issues or PR which report or fix bugs label May 20, 2024
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