HaskellForMaths-0.4.1: Combinatorics, group theory, commutative algebra, non-commutative algebra



A module defining the algebra of commutative polynomials over a field k



data GlexMonomial v Source


Glex Int [(v, Int)] 

glexVar :: Num k => v -> GlexPoly k vSource

glexVar creates a variable in the algebra of commutative polynomials with Glex term ordering. For example, the following code creates variables called x, y and z:

 [x,y,z] = map glexVar ["x","y","z"] :: GlexPoly Q String

class Monomial m whereSource


var :: v -> Vect Q (m v)Source

powers :: m v -> [(v, Int)]Source

bind :: (Monomial m, Num k, Ord b, Show b, Algebra k b) => Vect k (m v) -> (v -> Vect k b) -> Vect k bSource

In effect, we have (Num k, Monomial m) => Monad (v -> Vect k (m v)), with return = var, and (>>=) = bind. However, we can't express this directly in Haskell, firstly because of the Ord b constraint, secondly because Haskell doesn't support type functions.

class DivisionBasis b whereSource


dividesB :: b -> b -> BoolSource

divB :: b -> b -> bSource


(%%) :: (Fractional k, Ord b, Show b, Algebra k b, DivisionBasis b) => Vect k b -> [Vect k b] -> Vect k bSource

(%%) reduces a polynomial with respect to a list of polynomials.