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

Safe Haskell | None
Language | Haskell98

Math.Algebra.NonCommutative.TensorAlgebra

Description

A module defining the tensor, symmetric, and exterior algebras. This module has been partially superceded by Math.Algebras.TensorAlgebra, which should be used in preference. This module is likely to be removed at some point.

# Documentation

data Basis Source #

Constructors

E Int |

#### Instances

Instances details

Eq Basis Source # |
Instance details Defined in Math.Algebra.NonCommutative.TensorAlgebra Methods (==) :: Basis -> Basis -> Bool (/=) :: Basis -> Basis -> Bool
Ord Basis Source # |
Instance details Defined in Math.Algebra.NonCommutative.TensorAlgebra Methods compare :: Basis -> Basis -> Ordering (<) :: Basis -> Basis -> Bool (<=) :: Basis -> Basis -> Bool (>) :: Basis -> Basis -> Bool (>=) :: Basis -> Basis -> Bool max :: Basis -> Basis -> Basis min :: Basis -> Basis -> Basis
Show Basis Source # |
Instance details Defined in Math.Algebra.NonCommutative.TensorAlgebra Methods showsPrec :: Int -> Basis -> ShowS show :: Basis -> String showList :: [Basis] -> ShowS

e_ :: Int -> NPoly Q Basis Source #

e1 :: NPoly Q Basis Source #

e2 :: NPoly Q Basis Source #

e3 :: NPoly Q Basis Source #

e4 :: NPoly Q Basis Source #

dim :: NPoly r Basis -> Int Source #

tensorBasis :: Int -> [NPoly Q Basis] Source #

extRelations :: Int -> [NPoly Q Basis] Source #

extnf :: NPoly Q Basis -> NPoly Q Basis Source #

exteriorBasis :: Int -> [NPoly Q Basis] Source #

symRelations :: Int -> [NPoly Q Basis] Source #

symnf :: NPoly Q Basis -> NPoly Q Basis Source #

symmetricBasis :: Int -> [NPoly Q Basis] Source #

weylRelations :: Int -> [NPoly Q Basis] Source #

weylnf :: Int -> NPoly Q Basis -> NPoly Q Basis Source #

weylBasis :: Int -> [NPoly Q Basis] Source #

data WeylGens Source #

Constructors

X Int |
D Int |

#### Instances

Instances details

Eq WeylGens Source # |
Instance details Defined in Math.Algebra.NonCommutative.TensorAlgebra Methods (==) :: WeylGens -> WeylGens -> Bool (/=) :: WeylGens -> WeylGens -> Bool
Ord WeylGens Source # |
Instance details Defined in Math.Algebra.NonCommutative.TensorAlgebra Methods compare :: WeylGens -> WeylGens -> Ordering (<) :: WeylGens -> WeylGens -> Bool (<=) :: WeylGens -> WeylGens -> Bool (>) :: WeylGens -> WeylGens -> Bool (>=) :: WeylGens -> WeylGens -> Bool max :: WeylGens -> WeylGens -> WeylGens min :: WeylGens -> WeylGens -> WeylGens
Show WeylGens Source # |
Instance details Defined in Math.Algebra.NonCommutative.TensorAlgebra Methods showsPrec :: Int -> WeylGens -> ShowS show :: WeylGens -> String showList :: [WeylGens] -> ShowS

d_ :: Int -> NPoly Q WeylGens Source #

x_ :: Int -> NPoly Q WeylGens Source #

d1 :: NPoly Q WeylGens Source #

d2 :: NPoly Q WeylGens Source #

d3 :: NPoly Q WeylGens Source #

x1 :: NPoly Q WeylGens Source #

x2 :: NPoly Q WeylGens Source #

x3 :: NPoly Q WeylGens Source #

comm :: Num a => a -> a -> a Source #

delta :: (Eq a, Num p) => a -> a -> p Source #

weylRelations' :: Int -> [NPoly Q WeylGens] Source #

weylnf' :: NPoly Q WeylGens -> NPoly Q WeylGens Source #

weylBasis' :: Int -> [NPoly Q WeylGens] Source #