Math.QuantumAlgebra.OrientedTangle

Documentation

data Oriented

Constructors

Plus

Minus

Instances

Eq Oriented

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

(==) :: Oriented -> Oriented -> Bool

(/=) :: Oriented -> Oriented -> Bool

Ord Oriented

Defined in Math.QuantumAlgebra.OrientedTangle

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

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

showsPrec :: Int -> Oriented -> ShowS

show :: Oriented -> String

showList :: [Oriented] -> ShowS

data HorizDir

Constructors

ToL

ToR

Instances

Eq HorizDir

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

(==) :: HorizDir -> HorizDir -> Bool

(/=) :: HorizDir -> HorizDir -> Bool

Ord HorizDir

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

compare :: HorizDir -> HorizDir -> Ordering

(<) :: HorizDir -> HorizDir -> Bool

(<=) :: HorizDir -> HorizDir -> Bool

(>) :: HorizDir -> HorizDir -> Bool

(>=) :: HorizDir -> HorizDir -> Bool

max :: HorizDir -> HorizDir -> HorizDir

min :: HorizDir -> HorizDir -> HorizDir

Show HorizDir

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

showsPrec :: Int -> HorizDir -> ShowS

show :: HorizDir -> String

showList :: [HorizDir] -> ShowS

data OrientedTangle

Instances

Monoidal OrientedTangle

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

tunit :: Ob OrientedTangle

tob :: Ob OrientedTangle -> Ob OrientedTangle -> Ob OrientedTangle

tar :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle

MCategory OrientedTangle

Defined in Math.QuantumAlgebra.OrientedTangle

Associated Types

data Ob OrientedTangle :: Type

data Ar OrientedTangle :: Type

Methods

id_ :: Ob OrientedTangle -> Ar OrientedTangle

source :: Ar OrientedTangle -> Ob OrientedTangle

target :: Ar OrientedTangle -> Ob OrientedTangle

(>>>) :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle

Eq (Ob OrientedTangle)

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

(==) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool

(/=) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool

Eq (Ar OrientedTangle)

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

(==) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool

(/=) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool

Ord (Ob OrientedTangle)

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

compare :: Ob OrientedTangle -> Ob OrientedTangle -> Ordering

(<) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool

(<=) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool

(>) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool

(>=) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool

max :: Ob OrientedTangle -> Ob OrientedTangle -> Ob OrientedTangle

min :: Ob OrientedTangle -> Ob OrientedTangle -> Ob OrientedTangle

Ord (Ar OrientedTangle)

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

compare :: Ar OrientedTangle -> Ar OrientedTangle -> Ordering

(<) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool

(<=) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool

(>) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool

(>=) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool

max :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle

min :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle

Show (Ob OrientedTangle)

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

showsPrec :: Int -> Ob OrientedTangle -> ShowS

show :: Ob OrientedTangle -> String

showList :: [Ob OrientedTangle] -> ShowS

Show (Ar OrientedTangle)

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

showsPrec :: Int -> Ar OrientedTangle -> ShowS

show :: Ar OrientedTangle -> String

showList :: [Ar OrientedTangle] -> ShowS

data Ob OrientedTangle

Defined in Math.QuantumAlgebra.OrientedTangle

data Ob OrientedTangle = OT [Oriented]

data Ar OrientedTangle

Defined in Math.QuantumAlgebra.OrientedTangle

data Ar OrientedTangle

• = IdT [Oriented]
• | CapT HorizDir
• | CupT HorizDir
• | XPlus
• | XMinus
• | SeqT [Ar OrientedTangle]
• | ParT [Ar OrientedTangle]

idV :: a -> a

idV' :: a -> a

evalV :: (EBasis, EBasis) -> Vect (LaurentPoly Q) ()

evalV' :: (EBasis, EBasis) -> Vect (LaurentPoly Q) ()

coevalV :: (Eq k, Num k) => Int -> Vect k (Tensor EBasis EBasis)

coevalV' :: (Eq k, Num k) => Int -> Vect k (Tensor EBasis EBasis)

lambda :: Integral b => b -> LaurentPoly Q

c :: Integral b => b -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

c' :: Integral b => b -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

testcc' :: Integral b => b -> Vect (LaurentPoly Q) (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

mu :: Integral b => b -> EBasis -> Vect (LaurentPoly Q) EBasis

mu' :: Integral b => b -> EBasis -> Vect (LaurentPoly Q) EBasis

capRL :: (Eq k, Num k) => Int -> Vect k (Tensor EBasis EBasis)

capLR :: Int -> Vect (LaurentPoly Q) (EBasis, EBasis)

cupRL :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) ()

cupLR :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) ()

xplus :: Integral b => b -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

xminus :: Integral b => b -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

yplus :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

yminus :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

tplus :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

tminus :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

zplus :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

zminus :: Int -> (EBasis, EBasis) -> Vect (LaurentPoly Q) (EBasis, EBasis)

oloop :: Int -> Vect (LaurentPoly Q) ()

otrefoil :: Int -> Vect (LaurentPoly Q) ()

otrefoil' :: Int -> Vect (LaurentPoly Q) ()