Math.QuantumAlgebra.Tangle

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

Documentation

data Tangle

Instances

Monoidal Tangle

MCategory Tangle

Eq (Ob Tangle)

Eq (Ar Tangle)

Ord (Ob Tangle)

Ord (Ar Tangle)

Show (Ob Tangle)

Show (Ar Tangle)

data Ob Tangle = OT Int

data Ar Tangle

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

data Oriented

Constructors

Plus

Minus

Instances

Eq Oriented

Ord Oriented

Show Oriented

type TangleRep b = Vect (LaurentPoly Q) b

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

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

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

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

loop :: Vect (LaurentPoly Q) [Oriented]

trefoil :: Vect (LaurentPoly Q) [Oriented]

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

loopT :: Ar Tangle

trefoilT :: Ar Tangle