Find All Factors in Imaginary Quadratic Rings which are UFDs

This page has demonstrations of the Find All Factors algorithm applied to the imaginary quadratic rings Z[i] and Z[w].  The number of factors is similar to the formula for Z, except one has to consider the number of units in the ring... or, that one wishes to consider multiplication by to generate 'unique' factors. (perhaps I'll put this together in a sequel)

The algorithm should work for any imaginary quadratic ring that is a UFD (Unique Factorization Domain).  It may also be adaptable to domains lacking unique factorization by using the ideals... I'm not sure, haven't thought about this enough.

Anyway... there are probably much more efficient ways of generating all these factors, but this is simple to understand.