HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellNone
LanguageHaskell98

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 where Source

Methods

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

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

Instances

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

type NCPoly v = Vect Q (NonComMonomial v) Source

class DivisionBasis m where Source

Methods

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

Instances

ncm :: [v] -> NonComMonomial v Source

lm :: Vect t t1 -> t1 Source

lc :: Vect t t1 -> t Source

lt :: Vect k b -> Vect k b Source

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

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

(%%) :: (DivisionBasis b, Algebra k b, Show b, Ord b, Fractional k, Eq k) => Vect k b -> [Vect k b] -> Vect k b infixl 7 Source