HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra
Safe HaskellNone
LanguageHaskell98

Math.QuantumAlgebra.Tangle

Description

A module defining the category of tangles, and representations into the category of vector spaces (specifically, knot invariants).

Documentation

data Tangle Source #

Instances

Instances details
Monoidal Tangle Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

MCategory Tangle Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Associated Types

data Ob Tangle Source #

data Ar Tangle Source #

Eq (Ob Tangle) Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

(==) :: Ob Tangle -> Ob Tangle -> Bool

(/=) :: Ob Tangle -> Ob Tangle -> Bool

Eq (Ar Tangle) Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

(==) :: Ar Tangle -> Ar Tangle -> Bool

(/=) :: Ar Tangle -> Ar Tangle -> Bool

Ord (Ob Tangle) Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

compare :: Ob Tangle -> Ob Tangle -> Ordering

(<) :: Ob Tangle -> Ob Tangle -> Bool

(<=) :: Ob Tangle -> Ob Tangle -> Bool

(>) :: Ob Tangle -> Ob Tangle -> Bool

(>=) :: Ob Tangle -> Ob Tangle -> Bool

max :: Ob Tangle -> Ob Tangle -> Ob Tangle

min :: Ob Tangle -> Ob Tangle -> Ob Tangle

Ord (Ar Tangle) Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

compare :: Ar Tangle -> Ar Tangle -> Ordering

(<) :: Ar Tangle -> Ar Tangle -> Bool

(<=) :: Ar Tangle -> Ar Tangle -> Bool

(>) :: Ar Tangle -> Ar Tangle -> Bool

(>=) :: Ar Tangle -> Ar Tangle -> Bool

max :: Ar Tangle -> Ar Tangle -> Ar Tangle

min :: Ar Tangle -> Ar Tangle -> Ar Tangle

Show (Ob Tangle) Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

showsPrec :: Int -> Ob Tangle -> ShowS

show :: Ob Tangle -> String

showList :: [Ob Tangle] -> ShowS

Show (Ar Tangle) Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

showsPrec :: Int -> Ar Tangle -> ShowS

show :: Ar Tangle -> String

showList :: [Ar Tangle] -> ShowS

data Ob Tangle Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

data Ob Tangle = OT Int
data Ar Tangle Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

data Oriented Source #

Constructors

Plus 
Minus 

Instances

Instances details
Eq Oriented Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

(==) :: Oriented -> Oriented -> Bool

(/=) :: Oriented -> Oriented -> Bool

Ord Oriented Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

compare :: Oriented -> Oriented -> Ordering

(<) :: Oriented -> Oriented -> Bool

(<=) :: Oriented -> Oriented -> Bool

(>) :: Oriented -> Oriented -> Bool

(>=) :: Oriented -> Oriented -> Bool

max :: Oriented -> Oriented -> Oriented

min :: Oriented -> Oriented -> Oriented

Show Oriented Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

showsPrec :: Int -> Oriented -> ShowS

show :: Oriented -> String

showList :: [Oriented] -> ShowS

Orphan instances

(Eq k, Num k, Ord a) => Algebra k [a] Source # 
Instance details

Methods

unit :: k -> Vect k [a] Source #

mult :: Vect k (Tensor [a] [a]) -> Vect k [a] Source #

Mon [a] Source # 
Instance details

Methods

munit :: [a] Source #

mmult :: [a] -> [a] -> [a] Source #