HaskellForMaths-0.4.3: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellSafe-Infered

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

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 -> aSource

antiCommutes :: (Eq a, Num a) => a -> a -> BoolSource

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

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

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

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

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

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