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

Instances details

Eq Oriented Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods (==) :: Oriented -> Oriented -> Bool (/=) :: Oriented -> Oriented -> Bool
Ord Oriented Source # |
Instance details 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 Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods showsPrec :: Int -> Oriented -> ShowS show :: Oriented -> String showList :: [Oriented] -> ShowS

data HorizDir Source #

Constructors

ToL |
ToR |

#### Instances

Instances details

Eq HorizDir Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods (==) :: HorizDir -> HorizDir -> Bool (/=) :: HorizDir -> HorizDir -> Bool
Ord HorizDir Source # |
Instance details 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 Source # |
Instance details Defined in Math.QuantumAlgebra.OrientedTangle Methods showsPrec :: Int -> HorizDir -> ShowS show :: HorizDir -> String showList :: [HorizDir] -> ShowS

data OrientedTangle Source #

#### Instances

Instances details

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

Instance details

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) Source # |

Instance details

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