Safe Haskell	None
Language	Haskell98

Math.QuantumAlgebra.Tangle

Contents

Orphan instances

Description

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

Documentation

data Tangle Source #

Instances

Monoidal Tangle Source #
Instance details Defined in Math.QuantumAlgebra.Tangle Methods tunit :: Ob Tangle Source # tob :: Ob Tangle -> Ob Tangle -> Ob Tangle Source # tar :: Ar Tangle -> Ar Tangle -> Ar Tangle Source #
MCategory Tangle Source #
Instance details Defined in Math.QuantumAlgebra.Tangle Associated Types data Ob Tangle :: Type Source # data Ar Tangle :: Type Source # Methods id_ :: Ob Tangle -> Ar Tangle Source # source :: Ar Tangle -> Ob Tangle Source # target :: Ar Tangle -> Ob Tangle Source # (>>>) :: Ar Tangle -> Ar Tangle -> 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 Ar Tangle = IdT Int \| CapT \| CupT \| OverT \| UnderT \| SeqT [Ar Tangle] \| ParT [Ar Tangle]

data Oriented Source #

Constructors

Plus
Minus

Instances

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 #

type TangleRep b = Vect (LaurentPoly Q) b Source #

cap :: [Oriented] -> TangleRep [Oriented] Source #

cup :: [Oriented] -> TangleRep [Oriented] Source #

over :: [Oriented] -> TangleRep [Oriented] Source #

under :: [Oriented] -> TangleRep [Oriented] Source #

loop :: Vect (LaurentPoly Q) [Oriented] Source #

kauffman :: Ar Tangle -> TangleRep [Oriented] -> TangleRep [Oriented] Source #

loopT :: Ar Tangle Source #

trefoilT :: Ar Tangle Source #

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 #