isArf -- test whether a numerical semigroup is Arf

A numerical semigroup S is \emph{Arf} if for every triple of elements x \geq y \geq z in S, the element x+y-z also lies in S. Equivalently, S is Arf if and only if every semigroup in the sequence of blowups (the infinitely near semigroups of S) has minimal multiplicity, that is, has multiplicity equal to its embedding dimension. The latter characterization is what isArf actually checks.

The input L is interpreted as a generating set of a semigroup; it need not be the minimal generating set, and isArf works with the semigroup it generates.

The trivial semigroup (all of N) is Arf: