Math.Algebras.AffinePlane

A module defining the affine plane and its symmetries

Documentation

data XY

Constructors

X

Y

Instances

Eq XY

Defined in Math.Algebras.AffinePlane

Methods

(==) :: XY -> XY -> Bool

(/=) :: XY -> XY -> Bool

Ord XY

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

Defined in Math.Algebras.AffinePlane

Methods

showsPrec :: Int -> XY -> ShowS

show :: XY -> String

showList :: [XY] -> ShowS

x :: GlexPoly Q XY

y :: GlexPoly Q XY

data ABCD

Constructors

A

B

C

D

Instances

Eq ABCD

Defined in Math.Algebras.AffinePlane

Methods

(==) :: ABCD -> ABCD -> Bool

(/=) :: ABCD -> ABCD -> Bool

Ord ABCD

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

Defined in Math.Algebras.AffinePlane

Methods

showsPrec :: Int -> ABCD -> ShowS

show :: ABCD -> String

showList :: [ABCD] -> ShowS

HopfAlgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

antipode :: Vect Q (SL2 ABCD) -> Vect Q (SL2 ABCD)

Bialgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Coalgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

counit :: Vect Q (SL2 ABCD) -> Q

comult :: Vect Q (SL2 ABCD) -> Vect Q (Tensor (SL2 ABCD) (SL2 ABCD))

Algebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

unit :: Q -> Vect Q (SL2 ABCD)

mult :: Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) -> Vect Q (SL2 ABCD)

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

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

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

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

newtype SL2 v

Constructors

SL2 (GlexMonomial v)

Instances

Monomial SL2

Defined in Math.Algebras.AffinePlane

Methods

var :: v -> Vect Q (SL2 v)

powers :: SL2 v -> [(v, Int)]

HopfAlgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

antipode :: Vect Q (SL2 ABCD) -> Vect Q (SL2 ABCD)

Bialgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Coalgebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

counit :: Vect Q (SL2 ABCD) -> Q

comult :: Vect Q (SL2 ABCD) -> Vect Q (Tensor (SL2 ABCD) (SL2 ABCD))

Algebra Q (SL2 ABCD)

Defined in Math.Algebras.AffinePlane

Methods

unit :: Q -> Vect Q (SL2 ABCD)

mult :: Vect Q (Tensor (SL2 ABCD) (SL2 ABCD)) -> Vect Q (SL2 ABCD)

Eq v => Eq (SL2 v)

Defined in Math.Algebras.AffinePlane

Methods

(==) :: SL2 v -> SL2 v -> Bool

(/=) :: SL2 v -> SL2 v -> Bool

Ord v => Ord (SL2 v)

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)

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)