Right now, spire has a finer grained distinction of commutative rings, namely:
the availability of gcd and lcm operations,
the availability of Euclidean division (emod, equot),
in the type classes GCDRing and EuclideanRing. As the corresponding operations are already part of the Java/Scala API for e.g. integers, it would be natural to include them in algebra. The corresponding type classes are pretty uncontroversial and map to the mathematical hierarchy.
Another step in the hierarchy, UniqueFactorizationDomain relates to the availability of factorization into prime elements. There, the API is less clear. For various reasons, this type class is present outside the ring hierarchy in Spire, and I suggest it is not included in algebra.
(There is also the story of Signed -- for abs -- and TruncatedDivision, but that should be discussed separately)
denisrosset
commented
3 years ago
Right now,
spirehas a finer grained distinction of commutative rings, namely:gcdandlcmoperations,emod,equot),in the type classes
GCDRingandEuclideanRing. As the corresponding operations are already part of the Java/Scala API for e.g. integers, it would be natural to include them inalgebra. The corresponding type classes are pretty uncontroversial and map to the mathematical hierarchy.Another step in the hierarchy,
UniqueFactorizationDomainrelates to the availability of factorization into prime elements. There, the API is less clear. For various reasons, this type class is present outside the ring hierarchy in Spire, and I suggest it is not included in algebra.(There is also the story of
Signed-- for abs -- andTruncatedDivision, but that should be discussed separately)