[NumericPrelude] multivariate polynomials

[Henning Thielemann]

On Sat, 19 Jun 2010, Lewis-Sandy, Darrell wrote:

> Henning,
>
> In my polynomial library I did not have a function fromCoeffs because all my polynomials were multivariate.  Instead, I had a function fromTerms:
>
> fromTerms :: (Ring a, Ord symbol) => [(ring,Bag symbol)] -> Poly symbol ring
>
> where a term was represented as a coefficient/monomial pair, and Bag was 
> my monoidial mononomial type.

That is you do not only want a sparse polynomial representation but also a 
sparse representation of the monomial exponents using Bags, right? 
Nonetheless this would be just an instance of MathObj.Algebra, where (Bag 
symbol) with mempty=Bag.empty and mappend=Bag.union (occurrences of all 
bag elements are added) is the Monoid of monomials.