Safe Haskell	None
Language	Haskell98

Math.Algebras.AffinePlane

Description

A module defining the affine plane and its symmetries

Documentation

Constructors

X
Y

Instances details

Eq XY Source #
Instance details Defined in Math.Algebras.AffinePlane Methods (==) :: XY -> XY -> Bool (/=) :: XY -> XY -> Bool
Ord XY Source #
Instance details Defined in Math.Algebras.AffinePlane Methods compare :: XY -> XY -> Ordering (<) :: XY -> XY -> Bool (<=) :: XY -> XY -> Bool (>) :: XY -> XY -> Bool (>=) :: XY -> XY -> Bool max :: XY -> XY -> XY min :: XY -> XY -> XY
Show XY Source #
Instance details Defined in Math.Algebras.AffinePlane Methods showsPrec :: Int -> XY -> ShowS show :: XY -> String showList :: [XY] -> ShowS

Constructors

Instances details

Eq ABCD Source #
Instance details Defined in Math.Algebras.AffinePlane Methods (==) :: ABCD -> ABCD -> Bool (/=) :: ABCD -> ABCD -> Bool
Ord ABCD Source #
Instance details Defined in Math.Algebras.AffinePlane Methods compare :: ABCD -> ABCD -> Ordering (<) :: ABCD -> ABCD -> Bool (<=) :: ABCD -> ABCD -> Bool (>) :: ABCD -> ABCD -> Bool (>=) :: ABCD -> ABCD -> Bool max :: ABCD -> ABCD -> ABCD min :: ABCD -> ABCD -> ABCD
Show ABCD Source #
Instance details Defined in Math.Algebras.AffinePlane Methods showsPrec :: Int -> ABCD -> ShowS show :: ABCD -> String showList :: [ABCD] -> ShowS
HopfAlgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods antipode :: Vect Q (SL2 ABCD) -> Vect Q (SL2 ABCD) Source #
Bialgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane
Coalgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods counit :: Vect Q (SL2 ABCD) -> Q Source # comult :: Vect Q (SL2 ABCD) -> Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) Source #
Algebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods unit :: Q -> Vect Q (SL2 ABCD) Source # mult :: Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) -> Vect Q (SL2 ABCD) Source #

newtype SL2 v Source #

Constructors

Instances details

Monomial SL2 Source #
Instance details Defined in Math.Algebras.AffinePlane Methods var :: v -> Vect Q (SL2 v) Source # powers :: SL2 v -> [(v, Int)] Source #
HopfAlgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods antipode :: Vect Q (SL2 ABCD) -> Vect Q (SL2 ABCD) Source #
Bialgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane
Coalgebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods counit :: Vect Q (SL2 ABCD) -> Q Source # comult :: Vect Q (SL2 ABCD) -> Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) Source #
Algebra Q (SL2 ABCD) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods unit :: Q -> Vect Q (SL2 ABCD) Source # mult :: Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) -> Vect Q (SL2 ABCD) Source #
Eq v => Eq (SL2 v) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods (==) :: SL2 v -> SL2 v -> Bool (/=) :: SL2 v -> SL2 v -> Bool
Ord v => Ord (SL2 v) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods compare :: SL2 v -> SL2 v -> Ordering (<) :: SL2 v -> SL2 v -> Bool (<=) :: SL2 v -> SL2 v -> Bool (>) :: SL2 v -> SL2 v -> Bool (>=) :: SL2 v -> SL2 v -> Bool max :: SL2 v -> SL2 v -> SL2 v min :: SL2 v -> SL2 v -> SL2 v
Show v => Show (SL2 v) Source #
Instance details Defined in Math.Algebras.AffinePlane Methods showsPrec :: Int -> SL2 v -> ShowS show :: SL2 v -> String showList :: [SL2 v] -> ShowS

sl2Var :: Num k => v -> Vect k (SL2 v) Source #