Math.Projects.ChevalleyGroup.Exceptional

Documentation

newtype Octonion k

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)

i0 :: Octonion Q

i6 :: Octonion Q

i5 :: Octonion Q

i4 :: Octonion Q

i3 :: Octonion Q

i2 :: Octonion Q

i1 :: Octonion Q

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

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

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

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

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

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

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

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

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

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

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

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

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

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

alpha3 :: [[F3]]

beta3 :: [[F3]]

gamma3s :: [Octonion F3]

gamma3 :: [[F3]]

alpha3' :: Permutation (Octonion F3)

beta3' :: Permutation (Octonion F3)

gamma3' :: Permutation (Octonion F3)

g2_3 :: [Permutation (Octonion F3)]

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]]

beta4 :: [[F4]]

gamma4s :: [Octonion F4]

gamma4 :: [[F4]]

alpha4' :: Permutation (Octonion F4)

beta4' :: Permutation (Octonion F4)

gamma4' :: Permutation (Octonion F4)