Math.Projects.ChevalleyGroup.Exceptional

Synopsis

• newtype Octonion k = O [(Int, k)]
• 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 t -> [(Int, t)]
• nf :: (Num t1, Ord t, Ord t1) => [(t, t1)] -> [(t, t1)]
• m :: (Integral a, Num t) => (a, t) -> (a, t) -> (a, t)
• 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 :: (Num a, Ord 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)]
• alpha4 :: [[F4]]
• beta4 :: [[F4]]
• gamma4s :: [Octonion F4]
• gamma4 :: [[F4]]
• alpha4' :: Permutation (Octonion F4)
• beta4' :: Permutation (Octonion F4)
• gamma4' :: Permutation (Octonion F4)

Documentation