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

Safe Haskell | None
Language | Haskell98

Math.QuantumAlgebra.OrientedTangle

# Documentation

data Oriented Source #

Constructors

Plus |
Minus |

Instances

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

Instance details

Defined in Math.QuantumAlgebra.OrientedTangle

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.OrientedTangle Methods showsPrec :: Int -> Oriented -> ShowS Source # show :: Oriented -> String Source # showList :: [Oriented] -> ShowS Source #

data HorizDir Source #

Constructors

ToL |
ToR |

Instances

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

Instance details

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

compare :: HorizDir -> HorizDir -> Ordering Source #

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

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

(>) :: HorizDir -> HorizDir -> Bool Source #

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

max :: HorizDir -> HorizDir -> HorizDir Source #

min :: HorizDir -> HorizDir -> HorizDir Source #

Show HorizDir Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods showsPrec :: Int -> HorizDir -> ShowS Source # show :: HorizDir -> String Source # showList :: [HorizDir] -> ShowS Source #

data OrientedTangle Source #

Instances

Monoidal OrientedTangle Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods tunit :: Ob OrientedTangle Source # tob :: Ob OrientedTangle -> Ob OrientedTangle -> Ob OrientedTangle Source # tar :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle Source #
MCategory OrientedTangle Source # |

Instance details

Defined in Math.QuantumAlgebra.OrientedTangle

Associated Types

data Ob OrientedTangle :: Type Source #

data Ar OrientedTangle :: Type Source #

Methods

id_ :: Ob OrientedTangle -> Ar OrientedTangle Source #

source :: Ar OrientedTangle -> Ob OrientedTangle Source #

target :: Ar OrientedTangle -> Ob OrientedTangle Source #

(>>>) :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle Source #

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

Instance details

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

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

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

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

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

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

max :: Ob OrientedTangle -> Ob OrientedTangle -> Ob OrientedTangle Source #

min :: Ob OrientedTangle -> Ob OrientedTangle -> Ob OrientedTangle Source #

Ord (Ar OrientedTangle) Source # |

Instance details

Defined in Math.QuantumAlgebra.OrientedTangle

Methods

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

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

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

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

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

max :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle Source #

min :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle Source #

Show (Ob OrientedTangle) Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods showsPrec :: Int -> Ob OrientedTangle -> ShowS Source # show :: Ob OrientedTangle -> String Source # showList :: [Ob OrientedTangle] -> ShowS Source #
Show (Ar OrientedTangle) Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods showsPrec :: Int -> Ar OrientedTangle -> ShowS Source # show :: Ar OrientedTangle -> String Source # showList :: [Ar OrientedTangle] -> ShowS Source #
data Ob OrientedTangle Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle data Ob OrientedTangle = OT [Oriented]
data Ar OrientedTangle Source # |

Instance details

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 Source #

idV' :: a -> a Source #

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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