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

Safe HaskellNone
LanguageHaskell98

Math.Projects.ChevalleyGroup.Exceptional

Synopsis

Documentation

newtype Octonion k Source #

Constructors

O [(Int, k)] 

Instances

Eq k => Eq (Octonion k) Source # 

Methods

(==) :: Octonion k -> Octonion k -> Bool #

(/=) :: Octonion k -> Octonion k -> Bool #

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

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) Source # 

Methods

showsPrec :: Int -> Octonion k -> ShowS #

show :: Octonion k -> String #

showList :: [Octonion k] -> ShowS #

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

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

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

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

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

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

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

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

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

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

isUnit :: (Num a, Eq 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 #

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

alpha3 :: [[F3]] Source #

beta3 :: [[F3]] Source #

gamma3 :: [[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 #

gamma4 :: [[F4]] Source #