HaskellForMaths-0.4.8: 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 This module has been partially superceded by Math.Algebras.TensorAlgebra, which should be used in preference.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 # |
Methods (==) :: Basis -> Basis -> Bool # (/=) :: Basis -> Basis -> Bool #
Ord Basis Source # |
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 # |
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 t 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 # |
Methods (==) :: WeylGens -> WeylGens -> Bool # (/=) :: WeylGens -> WeylGens -> Bool #
Ord WeylGens Source # |
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 # |
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 :: (Num t, Eq a) => a -> a -> t Source #

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

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

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