Multilpe of a numerical sets and semigroups?

[pedritomelenas]

We have n*I which is I+...+I (n times) with I an ideal, but we do not have the same thing for numerical semigroups; we would probably want to have the same for numerical sets.

For ideals, 0*I is defined as S (the ambient semigroup of I); for semigroups or numerical sets, this is not so clear what should be the setting.
Since

gap> s:=NumericalSemigroup(3,5,7);;
gap> c:=NumericalSemigroupBySmallElements([0,Conductor(s)]);;
gap> s+c=s;
true

We could take 0*S to be {0,C(S),...}.

[pedritomelenas]

But the same thing holds for every T={0,x,...} with x larger than or equal to the conductor of S. So, here we could simply return fail for 0*S, or raise an error.

[ManuelAFDelgado]

Thank you for pointing out this possible enhancement. In my opinion, it is worth thinking about it.