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

Safe Haskell | None
Language | Haskell98

Math.Algebras.LaurentPoly

# Documentation

data LaurentMonomial Source #

Constructors

LM Int [(String, Int)] |

#### Instances

Instances details

Eq LaurentMonomial Source # |
Instance details Defined in Math.Algebras.LaurentPoly Methods (==) :: LaurentMonomial -> LaurentMonomial -> Bool (/=) :: LaurentMonomial -> LaurentMonomial -> Bool
Ord LaurentMonomial Source # |

Instance details

Defined in Math.Algebras.LaurentPoly

Methods

compare :: LaurentMonomial -> LaurentMonomial -> Ordering

(<) :: LaurentMonomial -> LaurentMonomial -> Bool

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

(>) :: LaurentMonomial -> LaurentMonomial -> Bool

(>=) :: LaurentMonomial -> LaurentMonomial -> Bool

max :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial

min :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial

Show LaurentMonomial Source # |
Instance details Defined in Math.Algebras.LaurentPoly Methods showsPrec :: Int -> LaurentMonomial -> ShowS show :: LaurentMonomial -> String showList :: [LaurentMonomial] -> ShowS
Mon LaurentMonomial Source # |
Instance details Defined in Math.Algebras.LaurentPoly Methods munit :: LaurentMonomial Source # mmult :: LaurentMonomial -> LaurentMonomial -> LaurentMonomial Source #
(Eq k, Num k) => Algebra k LaurentMonomial Source # |
Instance details Defined in Math.Algebras.LaurentPoly Methods unit :: k -> Vect k LaurentMonomial Source # mult :: Vect k (Tensor LaurentMonomial LaurentMonomial) -> Vect k LaurentMonomial Source #
(Eq k, Fractional k) => Fractional (LaurentPoly k) Source # |
Instance details Defined in Math.Algebras.LaurentPoly Methods (/) :: LaurentPoly k -> LaurentPoly k -> LaurentPoly k recip :: LaurentPoly k -> LaurentPoly k fromRational :: Rational -> LaurentPoly k
HopfAlgebra (LaurentPoly Q) (SL2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods antipode :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (SL2q String) Source #
Bialgebra (LaurentPoly Q) (SL2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane
Bialgebra (LaurentPoly Q) (M2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane
Coalgebra (LaurentPoly Q) (SL2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods counit :: Vect (LaurentPoly Q) (SL2q String) -> LaurentPoly Q Source # comult :: Vect (LaurentPoly Q) (SL2q String) -> Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String)) Source #
Coalgebra (LaurentPoly Q) (M2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods counit :: Vect (LaurentPoly Q) (M2q String) -> LaurentPoly Q Source # comult :: Vect (LaurentPoly Q) (M2q String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String)) Source #
Algebra (LaurentPoly Q) (SL2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (SL2q String) Source # mult :: Vect (LaurentPoly Q) (Tensor (SL2q String) (SL2q String)) -> Vect (LaurentPoly Q) (SL2q String) Source #
Algebra (LaurentPoly Q) (M2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (M2q String) Source # mult :: Vect (LaurentPoly Q) (Tensor (M2q String) (M2q String)) -> Vect (LaurentPoly Q) (M2q String) Source #
Algebra (LaurentPoly Q) (Aq02 String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq02 String) Source # mult :: Vect (LaurentPoly Q) (Tensor (Aq02 String) (Aq02 String)) -> Vect (LaurentPoly Q) (Aq02 String) Source #
Algebra (LaurentPoly Q) (Aq20 String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods unit :: LaurentPoly Q -> Vect (LaurentPoly Q) (Aq20 String) Source # mult :: Vect (LaurentPoly Q) (Tensor (Aq20 String) (Aq20 String)) -> Vect (LaurentPoly Q) (Aq20 String) Source #
Comodule (LaurentPoly Q) (M2q String) (Aq20 String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods coaction :: Vect (LaurentPoly Q) (Aq20 String) -> Vect (LaurentPoly Q) (Tensor (M2q String) (Aq20 String)) Source #

type LaurentPoly k = Vect k LaurentMonomial Source #

lvar :: String -> LaurentPoly Q Source #

q :: LaurentPoly Q Source #

q' :: LaurentPoly Q Source #