HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

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

Instances details

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

Instances details

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

Instances details

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 :: forall k m. (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 :: forall k m. (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 #