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] 

class Monomial m where Source #

Minimal complete definition

var, powers

Methods

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

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

Instances

Monomial NonComMonomial Source # 

Methods

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

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

Monomial SL2q Source # 

Methods

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

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

Monomial M2q Source # 

Methods

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

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

Monomial Aq02 Source # 

Methods

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

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

Monomial Aq20 Source # 

Methods

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

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

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

class DivisionBasis m where Source #

Minimal complete definition

divM

Methods

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

lm :: Vect t t1 -> t1 Source #

lc :: Vect t1 t -> t1 Source #

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

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

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

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