Multivariate polynomial rings.

Multivariate and univariate polynomial rings, with several different representations

polynomial-algebra Haskell library

This is a Haskell library to compute with multivariate polynomials.

Polynomials are implemented as free modules (with a coefficient ring) over the monoid of monomials. The free module implementation is basically a map from monomials to coefficients, with the invariant that zero coefficients should be never present. Different implementations of monomials are available with different speed and usability tradeoffs:

• generic monomial over a variable set given by inhabitants of a type
• monomials over x1, x2 ... xn (two different in-memory representations)
• monomials over an infinite number of variables x1, x2, ...
• univariate monomial (basically, an integer exponent)
• exterior monomial (for exterior algebra)

Type level parameters are used for the variable names (used for pretty-printing) and number of variables where possible.

A type class interface allows the user to work uniformly over different implementations.