HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell | None
Language | Haskell98

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

newtype Octonion k Source

Constructors

O [(Int, k)] |

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

i0 :: Octonion Q Source

i1 :: Octonion Q Source

i2 :: Octonion Q Source

i3 :: Octonion Q Source

i4 :: Octonion Q Source

i5 :: Octonion Q Source

i6 :: Octonion Q Source

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

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

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

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

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

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

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

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

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

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

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

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

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

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

alpha3 :: [[F3]] Source

beta3 :: [[F3]] Source

gamma3s :: [Octonion F3] Source

gamma3 :: [[F3]] 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 :: [[F4]] Source

beta4 :: [[F4]] Source

gamma4s :: [Octonion F4] Source

gamma4 :: [[F4]] Source

alpha4' :: Permutation (Octonion F4) Source

beta4' :: Permutation (Octonion F4) Source

gamma4' :: Permutation (Octonion F4) Source