Math.Algebras.NonCommutative

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

Documentation

data NonComMonomial v

Constructors

NCM Int [v]

Instances

Monomial NonComMonomial

(Eq k, Num k, Ord v) => Algebra k (NonComMonomial v)

Eq v => Eq (NonComMonomial v)

Ord v => Ord (NonComMonomial v)

(Eq v, Show v) => Show (NonComMonomial v)

Mon (NonComMonomial v)

Eq v => DivisionBasis (NonComMonomial v)

class Monomial m where

Methods

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

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

Instances

Monomial NonComMonomial

Monomial SL2q

Monomial M2q

Monomial Aq02

Monomial Aq20

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

type NCPoly v = Vect Q (NonComMonomial v)

class DivisionBasis m where

Methods

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

Instances

Eq v => DivisionBasis (NonComMonomial v)

ncm :: [v] -> NonComMonomial v

lm :: Vect t t1 -> t1

lc :: Vect t t1 -> t

lt :: Vect k b -> Vect k b

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)

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

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