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

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 Source # (/=) :: Ob Tangle -> Ob Tangle -> Bool Source #
Eq (Ar Tangle) Source # |
Instance details Defined in Math.QuantumAlgebra.Tangle Methods (==) :: Ar Tangle -> Ar Tangle -> Bool Source # (/=) :: Ar Tangle -> Ar Tangle -> Bool Source #
Ord (Ob Tangle) Source # |

Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

compare :: Ob Tangle -> Ob Tangle -> Ordering Source #

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

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

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

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

max :: Ob Tangle -> Ob Tangle -> Ob Tangle Source #

min :: Ob Tangle -> Ob Tangle -> Ob Tangle Source #

Ord (Ar Tangle) Source # |

Instance details

Defined in Math.QuantumAlgebra.Tangle

Methods

compare :: Ar Tangle -> Ar Tangle -> Ordering Source #

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

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

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

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

max :: Ar Tangle -> Ar Tangle -> Ar Tangle Source #

min :: Ar Tangle -> Ar Tangle -> Ar Tangle Source #

Show (Ob Tangle) Source # |
Instance details Defined in Math.QuantumAlgebra.Tangle Methods showsPrec :: Int -> Ob Tangle -> ShowS Source # show :: Ob Tangle -> String Source # showList :: [Ob Tangle] -> ShowS Source #
Show (Ar Tangle) Source # |
Instance details Defined in Math.QuantumAlgebra.Tangle Methods showsPrec :: Int -> Ar Tangle -> ShowS Source # show :: Ar Tangle -> String Source # showList :: [Ar Tangle] -> ShowS Source #
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 Source # (/=) :: Oriented -> Oriented -> Bool Source #
Ord Oriented Source # |
Instance details Defined in Math.QuantumAlgebra.Tangle Methods compare :: Oriented -> Oriented -> Ordering Source # (<) :: Oriented -> Oriented -> Bool Source # (<=) :: Oriented -> Oriented -> Bool Source # (>) :: Oriented -> Oriented -> Bool Source # (>=) :: Oriented -> Oriented -> Bool Source # max :: Oriented -> Oriented -> Oriented Source # min :: Oriented -> Oriented -> Oriented Source #
Show Oriented Source # |
Instance details Defined in Math.QuantumAlgebra.Tangle Methods showsPrec :: Int -> Oriented -> ShowS Source # show :: Oriented -> String Source # showList :: [Oriented] -> ShowS Source #

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 #