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

Defined in Math.Algebras.NonCommutative

Methods

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

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

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

Defined in Math.Algebras.NonCommutative

Methods

unit :: k -> Vect k (NonComMonomial v)

mult :: Vect k (Tensor (NonComMonomial v) (NonComMonomial v)) -> Vect k (NonComMonomial v)

Eq v => Eq (NonComMonomial v)

Defined in Math.Algebras.NonCommutative

Methods

(==) :: NonComMonomial v -> NonComMonomial v -> Bool

(/=) :: NonComMonomial v -> NonComMonomial v -> Bool

Ord v => Ord (NonComMonomial v)

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)

Defined in Math.Algebras.NonCommutative

Methods

showsPrec :: Int -> NonComMonomial v -> ShowS

show :: NonComMonomial v -> String

showList :: [NonComMonomial v] -> ShowS

Mon (NonComMonomial v)

Defined in Math.Algebras.NonCommutative

Methods

munit :: NonComMonomial v

mmult :: NonComMonomial v -> NonComMonomial v -> NonComMonomial v

Eq v => DivisionBasis (NonComMonomial v)

Defined in Math.Algebras.NonCommutative

Methods

divM :: NonComMonomial v -> NonComMonomial v -> Maybe (NonComMonomial v, NonComMonomial v)

class Monomial m where

Methods

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

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

Instances

Monomial NonComMonomial

Defined in Math.Algebras.NonCommutative

Methods

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

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

Monomial SL2q

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (SL2q v)

powers :: Eq v => SL2q v -> [(v, Int)]

Monomial M2q

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (M2q v)

powers :: Eq v => M2q v -> [(v, Int)]

Monomial Aq02

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (Aq02 v)

powers :: Eq v => Aq02 v -> [(v, Int)]

Monomial Aq20

Defined in Math.QuantumAlgebra.QuantumPlane

Methods

var :: v -> Vect Q (Aq20 v)

powers :: Eq v => Aq20 v -> [(v, Int)]

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

type NCPoly v = Vect Q (NonComMonomial v)

class DivisionBasis m where

Methods

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

Instances

Eq v => DivisionBasis (NonComMonomial v)

Defined in Math.Algebras.NonCommutative

Methods

divM :: NonComMonomial v -> NonComMonomial v -> Maybe (NonComMonomial v, NonComMonomial v)

ncm :: [v] -> NonComMonomial v

lm :: Vect k b -> b

lc :: Vect k b -> k

lt :: Vect k b -> Vect k b

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)

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

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