HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellNone
LanguageHaskell98

Math.QuantumAlgebra.QuantumPlane

Description

A module defining the quantum plane and its symmetries

Documentation

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

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

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

newtype Aq20 v Source #

Constructors

Aq20 (NonComMonomial v) 

Instances

Monomial Aq20 Source # 

Methods

var :: v -> Vect Q (Aq20 v) Source #

powers :: Eq v => Aq20 v -> [(v, Int)] Source #

Eq v => Eq (Aq20 v) Source # 

Methods

(==) :: Aq20 v -> Aq20 v -> Bool #

(/=) :: Aq20 v -> Aq20 v -> Bool #

Ord v => Ord (Aq20 v) Source # 

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 # 

Methods

showsPrec :: Int -> Aq20 v -> ShowS #

show :: Aq20 v -> String #

showList :: [Aq20 v] -> ShowS #

Algebra (LaurentPoly Q) (Aq20 String) Source # 
Comodule (LaurentPoly Q) (M2q String) (Aq20 String) Source # 

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

newtype Aq02 v Source #

Constructors

Aq02 (NonComMonomial v) 

Instances

Monomial Aq02 Source # 

Methods

var :: v -> Vect Q (Aq02 v) Source #

powers :: Eq v => Aq02 v -> [(v, Int)] Source #

Eq v => Eq (Aq02 v) Source # 

Methods

(==) :: Aq02 v -> Aq02 v -> Bool #

(/=) :: Aq02 v -> Aq02 v -> Bool #

Ord v => Ord (Aq02 v) Source # 

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 # 

Methods

showsPrec :: Int -> Aq02 v -> ShowS #

show :: Aq02 v -> String #

showList :: [Aq02 v] -> ShowS #

Algebra (LaurentPoly Q) (Aq02 String) Source # 

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

newtype M2q v Source #

Constructors

M2q (NonComMonomial v) 

Instances

Monomial M2q Source # 

Methods

var :: v -> Vect Q (M2q v) Source #

powers :: Eq v => M2q v -> [(v, Int)] Source #

Eq v => Eq (M2q v) Source # 

Methods

(==) :: M2q v -> M2q v -> Bool #

(/=) :: M2q v -> M2q v -> Bool #

Ord v => Ord (M2q v) Source # 

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 # 

Methods

showsPrec :: Int -> M2q v -> ShowS #

show :: M2q v -> String #

showList :: [M2q v] -> ShowS #

Bialgebra (LaurentPoly Q) (M2q String) Source # 
Coalgebra (LaurentPoly Q) (M2q String) Source # 
Algebra (LaurentPoly Q) (M2q String) Source # 
Comodule (LaurentPoly Q) (M2q String) (Aq20 String) Source # 

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

newtype SL2q v Source #

Constructors

SL2q (NonComMonomial v) 

Instances

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