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

Safe HaskellNone
LanguageHaskell98

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 #

(/=) :: 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 #

data ABCD Source #

Constructors

A 
B 
C 
D 
Instances
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

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

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 #