Signed multisets are unfamiliar to most of us, and I for one found the paper a little fast-paced. Can you put a bit more into the documentation? Just for starters, I found it confusing when the documentation talks about "an element with multiplicity zero", because in the _paper_ a value that has multiplicity zero in an mzset is NOT an element of it. For a specific example, I haven't the faintest intuition about what 'map' should do. Suppose we have {(k1)x1, (k2)x2} and f x1 == f x2 = y. Should the value of map f {...} be {(k1+k2)y} or {(k1`max`k2)y} or what? I think anyone is going to be confused that a non-empty mzset can have 'cardinality' 0, so a little more reassurance that cardinality/=size is intentional might not go amiss. Perhaps an additional name such as totalMultiplicity could make things a little easier for writers and readers, even though cardinality is correct. Are you _sure_ that the definitions of isSubmultisetOf and isProperSubmultisetOf are correct? Proper sub<thing> is normally taken as requiring that only *one* member of the larger collection occur strictly fewer times in the smaller; here you require that for *all*. At least once, "multiplicities" is spelled "multiplicites".