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

Safe Haskell | None
Language | Haskell98

Math.QuantumAlgebra.QuantumPlane

Description

A module defining the quantum plane and its symmetries

# Documentation

qvar :: Monomial m => v -> Vect (LaurentPoly Q) (m v) Source #

a :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

b :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

c :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

d :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

detq :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => Vect (LaurentPoly Q) (m [Char]) Source #

x :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

y :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

u :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

v :: Monomial m => Vect (LaurentPoly Q) (m [Char]) Source #

aq20 :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => [Vect (LaurentPoly Q) (m [Char])] Source #

newtype Aq20 v Source #

Constructors

Aq20 (NonComMonomial v) |

#### Instances

Instances details

Monomial Aq20 Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (Aq20 v) Source # powers :: Eq v => Aq20 v -> [(v, Int)] Source #
Eq v => Eq (Aq20 v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods (==) :: Aq20 v -> Aq20 v -> Bool (/=) :: Aq20 v -> Aq20 v -> Bool
Ord v => Ord (Aq20 v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods compare :: Aq20 v -> Aq20 v -> Ordering (<) :: Aq20 v -> Aq20 v -> Bool (<=) :: Aq20 v -> Aq20 v -> Bool (>) :: Aq20 v -> Aq20 v -> Bool (>=) :: Aq20 v -> Aq20 v -> Bool max :: Aq20 v -> Aq20 v -> Aq20 v min :: Aq20 v -> Aq20 v -> Aq20 v
(Eq v, Show v) => Show (Aq20 v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods showsPrec :: Int -> Aq20 v -> ShowS show :: Aq20 v -> String showList :: [Aq20 v] -> ShowS
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 #

aq02 :: (Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m, Ord (m [Char])) => [Vect (LaurentPoly Q) (m [Char])] Source #

newtype Aq02 v Source #

Constructors

Aq02 (NonComMonomial v) |

#### Instances

Instances details

Monomial Aq02 Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (Aq02 v) Source # powers :: Eq v => Aq02 v -> [(v, Int)] Source #
Eq v => Eq (Aq02 v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods (==) :: Aq02 v -> Aq02 v -> Bool (/=) :: Aq02 v -> Aq02 v -> Bool
Ord v => Ord (Aq02 v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods compare :: Aq02 v -> Aq02 v -> Ordering (<) :: Aq02 v -> Aq02 v -> Bool (<=) :: Aq02 v -> Aq02 v -> Bool (>) :: Aq02 v -> Aq02 v -> Bool (>=) :: Aq02 v -> Aq02 v -> Bool max :: Aq02 v -> Aq02 v -> Aq02 v min :: Aq02 v -> Aq02 v -> Aq02 v
(Eq v, Show v) => Show (Aq02 v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods showsPrec :: Int -> Aq02 v -> ShowS show :: Aq02 v -> String showList :: [Aq02 v] -> ShowS
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 #

m2q :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => [Vect (LaurentPoly Q) (m [Char])] Source #

newtype M2q v Source #

Constructors

M2q (NonComMonomial v) |

#### Instances

Instances details

Monomial M2q Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (M2q v) Source # powers :: Eq v => M2q v -> [(v, Int)] Source #
Eq v => Eq (M2q v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods (==) :: M2q v -> M2q v -> Bool (/=) :: M2q v -> M2q v -> Bool
Ord v => Ord (M2q v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods compare :: M2q v -> M2q v -> Ordering (<) :: M2q v -> M2q v -> Bool (<=) :: M2q v -> M2q v -> Bool (>) :: M2q v -> M2q v -> Bool (>=) :: M2q v -> M2q v -> Bool max :: M2q v -> M2q v -> M2q v min :: M2q v -> M2q v -> M2q v
(Eq v, Show v) => Show (M2q v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods showsPrec :: Int -> M2q v -> ShowS show :: M2q v -> String showList :: [M2q v] -> ShowS
Bialgebra (LaurentPoly Q) (M2q String) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane
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) (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 #
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 #

sl2q :: (Ord (m [Char]), Show (m [Char]), Algebra (Vect Q LaurentMonomial) (m [Char]), Monomial m) => [Vect (LaurentPoly Q) (m [Char])] Source #

newtype SL2q v Source #

Constructors

SL2q (NonComMonomial v) |

#### Instances

Instances details

Monomial SL2q Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods var :: v -> Vect Q (SL2q v) Source # powers :: Eq v => SL2q v -> [(v, Int)] Source #
Eq v => Eq (SL2q v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods (==) :: SL2q v -> SL2q v -> Bool (/=) :: SL2q v -> SL2q v -> Bool
Ord v => Ord (SL2q v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods compare :: SL2q v -> SL2q v -> Ordering (<) :: SL2q v -> SL2q v -> Bool (<=) :: SL2q v -> SL2q v -> Bool (>) :: SL2q v -> SL2q v -> Bool (>=) :: SL2q v -> SL2q v -> Bool max :: SL2q v -> SL2q v -> SL2q v min :: SL2q v -> SL2q v -> SL2q v
(Eq v, Show v) => Show (SL2q v) Source # |
Instance details Defined in Math.QuantumAlgebra.QuantumPlane Methods showsPrec :: Int -> SL2q v -> ShowS show :: SL2q v -> String showList :: [SL2q v] -> ShowS
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
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 #
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 #

yb :: (Ord b, Show b, Algebra (Vect Q LaurentMonomial) b) => Vect (LaurentPoly Q) (b, b) -> Vect (LaurentPoly Q) (b, b) Source #