HaskellForMaths-0.4.5: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellSafe-Infered

Math.Algebras.NonCommutative

Description

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

Documentation

data NonComMonomial v Source

Constructors

NCM Int [v] 

Instances

class Monomial m whereSource

Methods

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

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

Instances

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

type NCPoly v = Vect Q (NonComMonomial v)Source

class DivisionBasis m whereSource

Methods

divM :: m -> m -> Maybe (m, m)Source

Instances

ncm :: [v] -> NonComMonomial vSource

lm :: Vect t t1 -> t1Source

lc :: Vect t t1 -> tSource

lt :: Vect k b -> Vect k bSource

quotRemNP :: (Eq k, Fractional k, Ord b, Show b, Algebra k b, DivisionBasis b) => Vect k b -> [Vect k b] -> ([(Vect k b, Vect k b)], Vect k b)Source

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

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