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

Math.Algebras.TensorProduct

Description

A module defining tensor products of vector spaces

Synopsis

# Documentation

data Tensor a b Source

Constructors

 T a b

Instances

 (Num k, Ord a, Ord m, Ord n, Bialgebra k a, Comodule k a m, Comodule k a n) => Comodule k a (Tensor m n) (Num k, Ord a, Ord u, Ord v, Bialgebra k a, Module k a u, Module k a v) => Module k a (Tensor u v) (Num k, Ord a, Ord b, Coalgebra k a, Coalgebra k b) => Coalgebra k (Tensor a b) (Num k, Ord a, Ord b, Algebra k a, Algebra k b) => Algebra k (Tensor a b) (Num k, Ord a, Ord u, Ord v, Algebra k a, Module k a u, Module k a v) => Module k (Tensor a a) (Tensor u v) (Eq a, Eq b) => Eq (Tensor a b) (Ord a, Ord b) => Ord (Tensor a b) (Show a, Show b) => Show (Tensor a b)

te :: Num k => Vect k a -> Vect k b -> Vect k (Tensor a b)Source

Tensor product of two elements

tf :: (Num k, Ord a', Ord b') => (Vect k a -> Vect k a') -> (Vect k b -> Vect k b') -> Vect k (Tensor a b) -> Vect k (Tensor a' b')Source

Tensor product of two (linear) functions

assocL :: Vect k (Tensor u (Tensor v w)) -> Vect k (Tensor (Tensor u v) w)Source

assocR :: Vect k (Tensor (Tensor u v) w) -> Vect k (Tensor u (Tensor v w))Source