HaskellForMaths-0.4.8: 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 # |
Methods (==) :: Oriented -> Oriented -> Bool # (/=) :: Oriented -> Oriented -> Bool #
Ord Oriented Source # |
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 # |
Methods showsPrec :: Int -> Oriented -> ShowS # show :: Oriented -> String # showList :: [Oriented] -> ShowS #

data HorizDir Source #

Constructors

ToL |
ToR |

Instances

Eq HorizDir Source # |
Methods (==) :: HorizDir -> HorizDir -> Bool # (/=) :: HorizDir -> HorizDir -> Bool #
Ord HorizDir Source # |
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 # |
Methods showsPrec :: Int -> HorizDir -> ShowS # show :: HorizDir -> String # showList :: [HorizDir] -> ShowS #

data OrientedTangle Source #

Instances

Monoidal OrientedTangle Source # |
Methods tunit :: Ob OrientedTangle Source # tob :: Ob OrientedTangle -> Ob OrientedTangle -> Ob OrientedTangle Source # tar :: Ar OrientedTangle -> Ar OrientedTangle -> Ar OrientedTangle Source #
MCategory OrientedTangle Source # |
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 # |
Methods (==) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool # (/=) :: Ob OrientedTangle -> Ob OrientedTangle -> Bool #
Eq (Ar OrientedTangle) Source # |
Methods (==) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool # (/=) :: Ar OrientedTangle -> Ar OrientedTangle -> Bool #
Ord (Ob OrientedTangle) Source # |

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 # |

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 # |
Methods showsPrec :: Int -> Ob OrientedTangle -> ShowS # show :: Ob OrientedTangle -> String # showList :: [Ob OrientedTangle] -> ShowS #
Show (Ar OrientedTangle) Source # |
Methods showsPrec :: Int -> Ar OrientedTangle -> ShowS # show :: Ar OrientedTangle -> String # showList :: [Ar OrientedTangle] -> ShowS #
data Ob OrientedTangle Source # |
data Ob OrientedTangle = OT [Oriented]
data Ar OrientedTangle Source # |

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

coevalV' :: (Num k, Eq 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 #