HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra
Safe HaskellNone
LanguageHaskell98

Math.Projects.ChevalleyGroup.Exceptional

Synopsis

Documentation

newtype Octonion k Source #

Constructors

O [(Int, k)] 

Instances

Instances details
Eq k => Eq (Octonion k) Source # 
Instance details

Defined in Math.Projects.ChevalleyGroup.Exceptional

Methods

(==) :: Octonion k -> Octonion k -> Bool

(/=) :: Octonion k -> Octonion k -> Bool

(Ord k, Num k, Fractional k) => Fractional (Octonion k) Source # 
Instance details

Defined in Math.Projects.ChevalleyGroup.Exceptional

Methods

(/) :: Octonion k -> Octonion k -> Octonion k

recip :: Octonion k -> Octonion k

fromRational :: Rational -> Octonion k

(Ord k, Num k) => Num (Octonion k) Source # 
Instance details

Defined in Math.Projects.ChevalleyGroup.Exceptional

Methods

(+) :: Octonion k -> Octonion k -> Octonion k

(-) :: Octonion k -> Octonion k -> Octonion k

(*) :: Octonion k -> Octonion k -> Octonion k

negate :: Octonion k -> Octonion k

abs :: Octonion k -> Octonion k

signum :: Octonion k -> Octonion k

fromInteger :: Integer -> Octonion k

Ord k => Ord (Octonion k) Source # 
Instance details

Defined in Math.Projects.ChevalleyGroup.Exceptional

Methods

compare :: Octonion k -> Octonion k -> Ordering

(<) :: Octonion k -> Octonion k -> Bool

(<=) :: Octonion k -> Octonion k -> Bool

(>) :: Octonion k -> Octonion k -> Bool

(>=) :: Octonion k -> Octonion k -> Bool

max :: Octonion k -> Octonion k -> Octonion k

min :: Octonion k -> Octonion k -> Octonion k

Show k => Show (Octonion k) Source # 
Instance details

Defined in Math.Projects.ChevalleyGroup.Exceptional

Methods

showsPrec :: Int -> Octonion k -> ShowS

show :: Octonion k -> String

showList :: [Octonion k] -> ShowS

fromList :: (Eq k, Num k) => [k] -> Octonion k Source #

toList :: Num a => Octonion a -> [a] Source #

expose :: Octonion k -> [(Int, k)] Source #

nf :: forall a b. (Num b, Ord a, Ord b) => [(a, b)] -> [(a, b)] Source #

m :: forall a1 a2. (Num a2, Integral a1) => (a1, a2) -> (a1, a2) -> (a1, a2) Source #

conj :: Num k => Octonion k -> Octonion k Source #

sqnorm :: Num a => Octonion a -> a Source #

isOrthogonal :: (Eq a, Num a) => Octonion a -> Octonion a -> Bool Source #

antiCommutes :: (Eq a, Num a) => a -> a -> Bool Source #

octonions :: (Eq k, Num k) => [k] -> [Octonion k] Source #

isUnit :: (Eq a, Num a) => Octonion a -> Bool Source #

unitImagOctonions :: (Eq a, Num a) => [a] -> [Octonion a] Source #

autFrom :: (Ord a, Num a) => Octonion a -> Octonion a -> Octonion a -> [[a]] Source #

(%^) :: (Eq k, Num k) => Octonion k -> [[k]] -> Octonion k Source #

alpha3 :: [[F3]] Source #

beta3 :: [[F3]] Source #

gamma3 :: [[F3]] Source #

g2_3 :: [Permutation (Octonion F3)] Source #

Generators for G2(3), a finite simple group of order 4245696, as a permutation group on the 702 unit imaginary octonions over F3

alpha4 :: [[F4]] Source #

beta4 :: [[F4]] Source #

gamma4 :: [[F4]] Source #