HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra

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

Instances details

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 Source # data Ar Tangle 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

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

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 #