HaskellForMaths-0.4.8: 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

Eq k => Eq (Octonion k) Source 
(Ord k, Num k, Fractional k) => Fractional (Octonion k) Source 
(Ord k, Num k) => Num (Octonion k) Source 
Ord k => Ord (Octonion k) Source 
Show k => Show (Octonion k) Source 

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

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

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

nf :: (Num t1, Ord t, Ord t1) => [(t, t1)] -> [(t, t1)] Source

m :: (Integral a, Num t) => (a, t) -> (a, t) -> (a, t) 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 :: (Num a, Ord a) => Octonion a -> Octonion a -> Octonion a -> [[a]] Source

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

beta3 :: [[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

beta4 :: [[F4]] Source