Math.Algebra.NonCommutative.NCPoly

A module providing a type for non-commutative polynomials.

Documentation

newtype Monomial v

Constructors

M [v]

Instances

Eq v => Eq (Monomial v)

(Eq v, Show v) => Num (Monomial v)

Ord v => Ord (Monomial v)

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

newtype NPoly r v

Constructors

NP [(Monomial v, r)]

Instances

(Eq r, Eq v) => Eq (NPoly r v)

(Ord v, Show v, Fractional r) => Fractional (NPoly r v)

(Ord v, Show v, Num r) => Num (NPoly r v)

(Ord r, Ord v) => Ord (NPoly r v)

(Show r, Eq v, Show v) => Show (NPoly r v)

Invertible (NPoly LPQ BraidGens)

Invertible (NPoly LPQ IwahoriHeckeGens)

data Var

Constructors

X

Y

Z

Instances

Eq Var

Ord Var

Show Var

var :: Num k => v -> NPoly k v

Create a non-commutative variable for use in forming non-commutative polynomials. For example, we could define x = var x, y = var y. Then x*y /= y*x.

class Invertible a where

Methods

inv :: a -> a

Instances

Invertible LPQ

Invertible (NPoly LPQ BraidGens)

Invertible (NPoly LPQ IwahoriHeckeGens)