HaskellForMaths-0.4.7: Combinatorics, group theory, commutative algebra, non-commutative algebra

Math.Projects.ChevalleyGroup.Exceptional

Synopsis

# Documentation

newtype Octonion k Source

Constructors

 O [(Int, k)]

Instances

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

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

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

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

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

m :: (Num t, Integral a) => (a, t) -> (a, t) -> (a, t) Source

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

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

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

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

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

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

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

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

beta3 :: [[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