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 This module has been partially superceded by Math.Algebras.TensorAlgebra, which should be used in preference.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

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

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 Source # (/=) :: WeylGens -> WeylGens -> Bool Source #
Ord WeylGens Source # |

Instance details

Defined in Math.Algebra.NonCommutative.TensorAlgebra

Methods

compare :: WeylGens -> WeylGens -> Ordering Source #

(<) :: WeylGens -> WeylGens -> Bool Source #

(<=) :: WeylGens -> WeylGens -> Bool Source #

(>) :: WeylGens -> WeylGens -> Bool Source #

(>=) :: WeylGens -> WeylGens -> Bool Source #

max :: WeylGens -> WeylGens -> WeylGens Source #

min :: WeylGens -> WeylGens -> WeylGens Source #

Show WeylGens Source # |
Instance details Defined in Math.Algebra.NonCommutative.TensorAlgebra Methods showsPrec :: Int -> WeylGens -> ShowS Source # show :: WeylGens -> String Source # showList :: [WeylGens] -> ShowS Source #

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 #