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We have different behavior between AsIdealOfNumericalSemigroup and AsNumericalSemigroup the first returns fail if it is not an ideal ("sometimes") and the second raises an error.
Also, if we want to have the same behavior as for numerical sets, the first should no longer be a function and should become an operation.
Notice that AsIdealOfNumericalSemigroup is declared on contributions and will only work for integral ideals ...
Thus, I am really in the mood of changing the existing function; we can probably use the new machinery of arithmetic of numerical sets.
AsIdealOfNumericalSemigroup could simply be i->IdealOfNumericalSemigroupBySmallElements(SmallElements(i),s)
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