HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

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

Monoidal Tangle Source |
MCategory Tangle Source |
Eq (Ob Tangle) Source |
Eq (Ar Tangle) Source |
Ord (Ob Tangle) Source |
Ord (Ar Tangle) Source |
Show (Ob Tangle) Source |
Show (Ar Tangle) Source |
data Ob Tangle = OT Int Source |

data Ar Tangle

- = IdT Int
- | CapT
- | CupT
- | OverT
- | UnderT
- | SeqT [Ar Tangle]
- | ParT [Ar Tangle]

Source

data Oriented Source

Constructors

Plus |
Minus |

Instances

Eq Oriented Source |
Ord Oriented Source |
Show Oriented 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

trefoil :: Vect (LaurentPoly Q) [Oriented] Source

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

loopT :: Ar Tangle Source

trefoilT :: Ar Tangle Source