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 This module has been partially superceded by Math.Algebras.TensorAlgebra, which should be used in preference.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

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

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 #