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

Safe Haskell | None
Language | Haskell98

Math.Algebras.AffinePlane

Description

A module defining the affine plane and its symmetries

# Documentation

data XY Source #

Constructors

X |
Y |

Instances

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

x :: GlexPoly Q XY Source #

y :: GlexPoly Q XY Source #

data ABCD Source #

Constructors

A |
B |
C |
D |

Instances

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

a :: Monomial m => Vect Q (m ABCD) Source #

b :: Monomial m => Vect Q (m ABCD) Source #

c :: Monomial m => Vect Q (m ABCD) Source #

d :: Monomial m => Vect Q (m ABCD) Source #

newtype SL2 v Source #

Constructors

SL2 (GlexMonomial v) |

Instances

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 Source # (/=) :: SL2 v -> SL2 v -> Bool Source #
Ord v => Ord (SL2 v) Source # |
Instance details Defined in Math.Algebras.AffinePlane Methods compare :: SL2 v -> SL2 v -> Ordering Source # (<) :: SL2 v -> SL2 v -> Bool Source # (<=) :: SL2 v -> SL2 v -> Bool Source # (>) :: SL2 v -> SL2 v -> Bool Source # (>=) :: SL2 v -> SL2 v -> Bool Source # max :: SL2 v -> SL2 v -> SL2 v Source # min :: SL2 v -> SL2 v -> SL2 v Source #
Show v => Show (SL2 v) Source # |
Instance details Defined in Math.Algebras.AffinePlane Methods showsPrec :: Int -> SL2 v -> ShowS Source # show :: SL2 v -> String Source # showList :: [SL2 v] -> ShowS Source #

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