Safe Haskell	None
Language	Haskell98

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

Monomial NonComMonomial Source #
Instance details Defined in Math.Algebras.NonCommutative Methods var :: v -> Vect Q (NonComMonomial v) Source # powers :: Eq v => NonComMonomial v -> [(v, Int)] Source #
(Eq k, Num k, Ord v) => Algebra k (NonComMonomial v) Source #
Instance details Defined in Math.Algebras.NonCommutative Methods unit :: k -> Vect k (NonComMonomial v) Source # mult :: Vect k (Tensor (NonComMonomial v) (NonComMonomial v)) -> Vect k (NonComMonomial v) Source #
Eq v => Eq (NonComMonomial v) Source #
Instance details Defined in Math.Algebras.NonCommutative Methods (==) :: NonComMonomial v -> NonComMonomial v -> Bool # (/=) :: NonComMonomial v -> NonComMonomial v -> Bool #
Ord v => Ord (NonComMonomial v) Source #
Instance details Defined in Math.Algebras.NonCommutative Methods compare :: NonComMonomial v -> NonComMonomial v -> Ordering # (<) :: NonComMonomial v -> NonComMonomial v -> Bool # (<=) :: NonComMonomial v -> NonComMonomial v -> Bool # (>) :: NonComMonomial v -> NonComMonomial v -> Bool # (>=) :: NonComMonomial v -> NonComMonomial v -> Bool # max :: NonComMonomial v -> NonComMonomial v -> NonComMonomial v # min :: NonComMonomial v -> NonComMonomial v -> NonComMonomial v #
(Eq v, Show v) => Show (NonComMonomial v) Source #
Instance details Defined in Math.Algebras.NonCommutative Methods showsPrec :: Int -> NonComMonomial v -> ShowS # show :: NonComMonomial v -> String # showList :: [NonComMonomial v] -> ShowS #
Mon (NonComMonomial v) Source #
Instance details Defined in Math.Algebras.NonCommutative Methods munit :: NonComMonomial v Source # mmult :: NonComMonomial v -> NonComMonomial v -> NonComMonomial v Source #
Eq v => DivisionBasis (NonComMonomial v) Source #
Instance details Defined in Math.Algebras.NonCommutative Methods divM :: NonComMonomial v -> NonComMonomial v -> Maybe (NonComMonomial v, NonComMonomial v) Source #

class Monomial m where Source #

Methods

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

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

Instances

Monomial NonComMonomial Source #
Instance details Defined in Math.Algebras.NonCommutative Methods var :: v -> Vect Q (NonComMonomial v) Source # powers :: Eq v => NonComMonomial v -> [(v, Int)] Source #
Monomial SL2q Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (SL2q v) Source # powers :: Eq v => SL2q v -> [(v, Int)] Source #
Monomial M2q Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (M2q v) Source # powers :: Eq v => M2q v -> [(v, Int)] Source #
Monomial Aq02 Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (Aq02 v) Source # powers :: Eq v => Aq02 v -> [(v, Int)] Source #
Monomial Aq20 Source #
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (Aq20 v) Source # powers :: Eq v => Aq20 v -> [(v, Int)] Source #

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

Eq v => DivisionBasis (NonComMonomial v) Source #
Instance details Defined in Math.Algebras.NonCommutative Methods divM :: NonComMonomial v -> NonComMonomial v -> Maybe (NonComMonomial v, NonComMonomial v) Source #

ncm :: [v] -> NonComMonomial v Source #

lm :: Vect k b -> b Source #

lc :: Vect k b -> k Source #

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

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

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

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