Math.Projects.ChevalleyGroup.Exceptional

Documentation

newtype Octonion k

Constructors

O [(Int, k)]

Instances

Eq k => Eq (Octonion k)

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)

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)

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)

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)

Defined in Math.Projects.ChevalleyGroup.Exceptional

Methods

showsPrec :: Int -> Octonion k -> ShowS

show :: Octonion k -> String

showList :: [Octonion k] -> ShowS

i0 :: Octonion Q

i1 :: Octonion Q

i2 :: Octonion Q

i3 :: Octonion Q

i4 :: Octonion Q

i5 :: Octonion Q

i6 :: Octonion Q

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

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

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

nf :: (Num b, Ord a, Ord b) => [(a, b)] -> [(a, b)]

m :: (Num a2, Integral a1) => (a1, a2) -> (a1, a2) -> (a1, a2)

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

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

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

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

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

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

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

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

(%^) :: (Eq k, Num 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)