Safe Haskell | None |
---|---|

Language | Haskell98 |

- newtype Octonion k = O [(Int, 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)]
- alpha4 :: [[F4]]
- beta4 :: [[F4]]
- gamma4s :: [Octonion F4]
- gamma4 :: [[F4]]
- alpha4' :: Permutation (Octonion F4)
- beta4' :: Permutation (Octonion F4)
- gamma4' :: Permutation (Octonion F4)

# Documentation

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

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

alpha3' :: Permutation (Octonion F3) Source

beta3' :: Permutation (Octonion F3) Source

gamma3' :: Permutation (Octonion F3) Source

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

alpha4' :: Permutation (Octonion F4) Source

beta4' :: Permutation (Octonion F4) Source

gamma4' :: Permutation (Octonion F4) Source