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

Safe Haskell | None
Language | Haskell98

Math.Projects.MiniquaternionGeometry

# Documentation

data F9 Source #

Constructors

F9 F3 F3 |

Instances

Eq F9 Source # |
Methods (==) :: F9 -> F9 -> Bool # (/=) :: F9 -> F9 -> Bool #
Fractional F9 Source # |
Methods (/) :: F9 -> F9 -> F9 # recip :: F9 -> F9 # fromRational :: Rational -> F9 #
Num F9 Source # |
Methods (+) :: F9 -> F9 -> F9 # (-) :: F9 -> F9 -> F9 # (*) :: F9 -> F9 -> F9 # negate :: F9 -> F9 # abs :: F9 -> F9 # signum :: F9 -> F9 # fromInteger :: Integer -> F9 #
Ord F9 Source # |
Methods compare :: F9 -> F9 -> Ordering # (<) :: F9 -> F9 -> Bool # (<=) :: F9 -> F9 -> Bool # (>) :: F9 -> F9 -> Bool # (>=) :: F9 -> F9 -> Bool # max :: F9 -> F9 -> F9 # min :: F9 -> F9 -> F9 #
Show F9 Source # |
Methods showsPrec :: Int -> F9 -> ShowS # show :: F9 -> String # showList :: [F9] -> ShowS #
FiniteField F9 Source # |
Methods eltsFq :: F9 -> [F9] Source # basisFq :: F9 -> [F9] Source #

e :: F9 Source #

f9 :: [F9] Source #

w :: F9 Source #

conj :: F9 -> F9 Source #

norm :: F9 -> F3 Source #

data J9 Source #

Constructors

J9 F9 |

Instances

Eq J9 Source # |
Methods (==) :: J9 -> J9 -> Bool # (/=) :: J9 -> J9 -> Bool #
Fractional J9 Source # |
Methods (/) :: J9 -> J9 -> J9 # recip :: J9 -> J9 # fromRational :: Rational -> J9 #
Num J9 Source # |
Methods (+) :: J9 -> J9 -> J9 # (-) :: J9 -> J9 -> J9 # (*) :: J9 -> J9 -> J9 # negate :: J9 -> J9 # abs :: J9 -> J9 # signum :: J9 -> J9 # fromInteger :: Integer -> J9 #
Ord J9 Source # |
Methods compare :: J9 -> J9 -> Ordering # (<) :: J9 -> J9 -> Bool # (<=) :: J9 -> J9 -> Bool # (>) :: J9 -> J9 -> Bool # (>=) :: J9 -> J9 -> Bool # max :: J9 -> J9 -> J9 # min :: J9 -> J9 -> J9 #
Show J9 Source # |
Methods showsPrec :: Int -> J9 -> ShowS # show :: J9 -> String # showList :: [J9] -> ShowS #
FiniteField J9 Source # |
Methods eltsFq :: J9 -> [J9] Source # basisFq :: J9 -> [J9] Source #

squaresF9 :: [F9] Source #

i :: J9 Source #

j :: J9 Source #

k :: J9 Source #

j9 :: [J9] Source #

autJ9 :: J9 -> Permutation J9 Source #

autA :: Permutation J9 Source #

autB :: Permutation J9 Source #

autC :: Permutation J9 Source #

autsJ9 :: [Permutation J9] Source #

conj' :: J9 -> J9 Source #

isAut :: (Num a1, Num a, Eq a) => [a1] -> (a1 -> a) -> Bool Source #

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

isComplex :: J9 -> Bool Source #

ptsPG2 :: Num t => [t] -> [[t]] Source #

orthogonalLinesPG2 :: (Num a, Ord a) => [[a]] -> [[[a]]] Source #

rightLinesPG2 :: Num t => [t] -> [[[t]]] Source #

leftLinesPG2 :: Num t => [t] -> [[[t]]] Source #

phi :: Design [F9] Source #

phi' :: Design [F9] Source #

collineationsPhi :: [Permutation [F9]] Source #

liftToGraph :: Ord a => Design a -> Permutation a -> Permutation (Either a [a]) Source #

omega0 :: Design [J9] Source #

omega :: Design [J9] Source #

omega2 :: Design [J9] Source #

collineationsOmega :: [Permutation [J9]] Source #

omegaD :: Design [J9] Source #

omegaD1 :: Design Integer Source #

omegaD2 :: Design [J9] Source #

(<*) :: Num b => [b] -> b -> [b] Source #

psi :: Design [J9] Source #

psi2 :: Design [J9] Source #

collineationsPsi :: [Permutation [J9]] Source #

order :: Design a -> Int Source #

isProjectivePlane :: Eq t => Design t -> Bool Source #

collinear :: (Eq a, Foldable t) => Design a -> t a -> Bool Source #

isQuadrangle :: Eq a => Design a -> [a] -> Bool Source #

concurrent :: (Eq a, Foldable t, Foldable t1) => Design a -> t1 (t a) -> Bool Source #

isQuadrilateral :: (Foldable t, Eq a) => Design a -> [t a] -> Bool Source #

isOval :: Eq a => Design a -> [a] -> Bool Source #

findOvals1 :: Eq a => Design a -> [[a]] Source #

findQuadrangles :: Eq a => Design a -> [[a]] Source #

findOvals :: Ord a => Design a -> [[a]] Source #