HaskellForMaths-0.3.1: Combinatorics, group theory, commutative algebra, non-commutative algebra

Math.Algebra.NonCommutative.NCPoly

Description

A module providing a type for non-commutative polynomials.

Synopsis

Documentation

newtype Monomial v Source

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 Source

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 Source

Constructors

X 
Y 
Z 

Instances

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

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 whereSource

Methods

inv :: a -> aSource

Instances