More efficient factorizations in UFDs

UFD factorizations are all stored as unordered vectors of pairs (irreducible : Ring::Set, power : Natural). This leads to slow algorithms for multiplying factorizations are comparing them for equality.

I want to allow a different representation for cases where an ordering on the ring elements is provided. Factorizations will still be represented by vectors of the pairs (irreducible : Ring::Set, power : Natural), but there will be a requirement that they are ordered with respect to the irreducibles and that no powers are zero.

I also want to allow different factorization representations for the same ring. Then a blank slow implementation will work for all rings, while a faster implementation can be used in cerain cases. This will require decoupling the factorization structure from the ring structure.

Start by reviewing the existing UFD factorization representation and how it is coupled to the ring structure. Determine the design needed for ordered and alternative representations, then verify that a generic slow implementation and faster specialized cases can coexist.