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

Language | Haskell98 |

## 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 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)]
- alpha4 :: [[F4]]
- beta4 :: [[F4]]
- gamma4s :: [Octonion F4]
- gamma4 :: [[F4]]
- alpha4' :: Permutation (Octonion F4)
- beta4' :: Permutation (Octonion F4)
- gamma4' :: Permutation (Octonion F4)

# Documentation

## Instances

Eq k => Eq (Octonion k) Source # | |

(Ord k, Num k, Fractional k) => Fractional (Octonion k) Source # | |

(Ord k, Num k) => Num (Octonion k) Source # | |

Defined in Math.Projects.ChevalleyGroup.Exceptional | |

Ord k => Ord (Octonion k) Source # | |

Defined in Math.Projects.ChevalleyGroup.Exceptional | |

Show k => Show (Octonion k) Source # | |