[NumericPrelude] Progress toward UFD implementation

[Lewis-Sandy, Darrell]

On Jun3 29, lemming at henning-thielemann.de wrote:
> Is the basis always a single element?

The defining property of principal ideal domains is that for any ideal, the basis consists of a single element.  I have been considering implementing Noetherian domains as well to provide an interface for finite ideals which have finite, but not necessarily singleton bases.   

On Jun3 29, lemming at henning-thielemann.de wrote:
> Great! Would you provide automated tests for the non-trivial algorithms?

I think one of the most beautiful things about the numeric-prelude was that you had integrated quick check tests into your class libraries to facilitate testing of essential class properties.  I will be following your example and extending the automated test set as appropriate for these new classes.

On Jun3 29, lemming at henning-thielemann.de wrote:
> Yes, there is no perfect solution, thus I decided to implement the 
> basic functionality without fitting into any numeric type class as in
>   http://hackage.haskell.org/packages/archive/numeric-prelude/0.1.3.4/doc/html/Number-ResidueClass.html
>  and then I provide different interfaces to those functions in modules in 
> a sub-directory. Maybe I should split also modules like Polynomial this 
> way, since the basic polynomial operations are also needed somewhere else, 
> without the need to refer to polynomials explicitly.

Thank you!  That is very helpful - I hadn't realized that there were concrete implementations in the sub-directories.