Safe Haskell	None
Language	Haskell2010

Haskell4Maths

Documentation

data F2 :: * #

Instances

Eq F2
Methods (==) :: F2 -> F2 -> Bool # (/=) :: F2 -> F2 -> Bool #
Fractional F2
Methods (/) :: F2 -> F2 -> F2 # recip :: F2 -> F2 # fromRational :: Rational -> F2 #
Num F2
Methods (+) :: F2 -> F2 -> F2 # (-) :: F2 -> F2 -> F2 # (*) :: F2 -> F2 -> F2 # negate :: F2 -> F2 # abs :: F2 -> F2 # signum :: F2 -> F2 # fromInteger :: Integer -> F2 #
Ord F2
Methods compare :: F2 -> F2 -> Ordering # (<) :: F2 -> F2 -> Bool # (<=) :: F2 -> F2 -> Bool # (>) :: F2 -> F2 -> Bool # (>=) :: F2 -> F2 -> Bool # max :: F2 -> F2 -> F2 # min :: F2 -> F2 -> F2 #
Show F2
Methods showsPrec :: Int -> F2 -> ShowS # show :: F2 -> String # showList :: [F2] -> ShowS #
FinSet F2
Methods elts :: [F2]

data MonImpl v :: * -> * #

Constructors

M Int [(v, Int)]

Instances

Functor MonImpl
Methods fmap :: (a -> b) -> MonImpl a -> MonImpl b # (<$) :: a -> MonImpl b -> MonImpl a #
MonomialConstructor MonImpl
Methods mvar :: v -> MonImpl v mindices :: MonImpl v -> [(v, Int)] #
Eq v => Eq (MonImpl v)
Methods (==) :: MonImpl v -> MonImpl v -> Bool # (/=) :: MonImpl v -> MonImpl v -> Bool #
Show v => Show (MonImpl v)
Methods showsPrec :: Int -> MonImpl v -> ShowS # show :: MonImpl v -> String # showList :: [MonImpl v] -> ShowS #
Ord v => Mon (MonImpl v)
Methods munit :: MonImpl v mmult :: MonImpl v -> MonImpl v -> MonImpl v
(Ord v, Show v) => Monomial (MonImpl v)
Methods mdivides :: MonImpl v -> MonImpl v -> Bool mdiv :: MonImpl v -> MonImpl v -> MonImpl v mgcd :: MonImpl v -> MonImpl v -> MonImpl v mlcm :: MonImpl v -> MonImpl v -> MonImpl v mcoprime :: MonImpl v -> MonImpl v -> Bool mdeg :: MonImpl v -> Int

newtype Vect k b :: * -> * -> * #

Constructors

V [(b, k)]

Instances

Num k => Monad (Vect k)
Methods (>>=) :: Vect k a -> (a -> Vect k b) -> Vect k b # (>>) :: Vect k a -> Vect k b -> Vect k b # return :: a -> Vect k a # fail :: String -> Vect k a #
Functor (Vect k)
Methods fmap :: (a -> b) -> Vect k a -> Vect k b # (<$) :: a -> Vect k b -> Vect k a #
Num k => Applicative (Vect k)
Methods pure :: a -> Vect k a # (<>) :: Vect k (a -> b) -> Vect k a -> Vect k b # liftA2 :: (a -> b -> c) -> Vect k a -> Vect k b -> Vect k c # (>) :: Vect k a -> Vect k b -> Vect k b # (<*) :: Vect k a -> Vect k b -> Vect k a #
(Eq k, Eq b) => Eq (Vect k b)
Methods (==) :: Vect k b -> Vect k b -> Bool # (/=) :: Vect k b -> Vect k b -> Bool #
(Ord k, Ord b) => Ord (Vect k b)
Methods compare :: Vect k b -> Vect k b -> Ordering # (<) :: Vect k b -> Vect k b -> Bool # (<=) :: Vect k b -> Vect k b -> Bool # (>) :: Vect k b -> Vect k b -> Bool # (>=) :: Vect k b -> Vect k b -> Bool # max :: Vect k b -> Vect k b -> Vect k b # min :: Vect k b -> Vect k b -> Vect k b #
(Show k, Eq k, Num k, Show b) => Show (Vect k b)
Methods showsPrec :: Int -> Vect k b -> ShowS # show :: Vect k b -> String # showList :: [Vect k b] -> ShowS #

linear :: (Eq k, Num k, Ord b) => (a -> Vect k b) -> Vect k a -> Vect k b #

newtype Lex v :: * -> * #

Constructors

Instances

Functor Lex
Methods fmap :: (a -> b) -> Lex a -> Lex b # (<$) :: a -> Lex b -> Lex a #
MonomialConstructor Lex
Methods mvar :: v -> Lex v mindices :: Lex v -> [(v, Int)] #
(Eq k, Num k, Ord v, Show v) => Algebra k (Lex v)
Methods unit :: k -> Vect k (Lex v) mult :: Vect k (Tensor (Lex v) (Lex v)) -> Vect k (Lex v)
Eq v => Eq (Lex v)
Methods (==) :: Lex v -> Lex v -> Bool # (/=) :: Lex v -> Lex v -> Bool #
Ord v => Ord (Lex v)
Methods compare :: Lex v -> Lex v -> Ordering # (<) :: Lex v -> Lex v -> Bool # (<=) :: Lex v -> Lex v -> Bool # (>) :: Lex v -> Lex v -> Bool # (>=) :: Lex v -> Lex v -> Bool # max :: Lex v -> Lex v -> Lex v # min :: Lex v -> Lex v -> Lex v #
Show v => Show (Lex v)
Methods showsPrec :: Int -> Lex v -> ShowS # show :: Lex v -> String # showList :: [Lex v] -> ShowS #
Ord v => Mon (Lex v)
Methods munit :: Lex v mmult :: Lex v -> Lex v -> Lex v
(Show v, Ord v) => Monomial (Lex v)
Methods mdivides :: Lex v -> Lex v -> Bool mdiv :: Lex v -> Lex v -> Lex v mgcd :: Lex v -> Lex v -> Lex v mlcm :: Lex v -> Lex v -> Lex v mcoprime :: Lex v -> Lex v -> Bool mdeg :: Lex v -> Int

data Glex v :: * -> * #

Instances

Functor Glex
Methods fmap :: (a -> b) -> Glex a -> Glex b # (<$) :: a -> Glex b -> Glex a #
MonomialConstructor Glex
Methods mvar :: v -> Glex v mindices :: Glex v -> [(v, Int)] #
(Eq k, Num k, Ord v, Show v) => Algebra k (Glex v)
Methods unit :: k -> Vect k (Glex v) mult :: Vect k (Tensor (Glex v) (Glex v)) -> Vect k (Glex v)
Eq v => Eq (Glex v)
Methods (==) :: Glex v -> Glex v -> Bool # (/=) :: Glex v -> Glex v -> Bool #
Ord v => Ord (Glex v)
Methods compare :: Glex v -> Glex v -> Ordering # (<) :: Glex v -> Glex v -> Bool # (<=) :: Glex v -> Glex v -> Bool # (>) :: Glex v -> Glex v -> Bool # (>=) :: Glex v -> Glex v -> Bool # max :: Glex v -> Glex v -> Glex v # min :: Glex v -> Glex v -> Glex v #
Show v => Show (Glex v)
Methods showsPrec :: Int -> Glex v -> ShowS # show :: Glex v -> String # showList :: [Glex v] -> ShowS #
Ord v => Mon (Glex v)
Methods munit :: Glex v mmult :: Glex v -> Glex v -> Glex v
(Show v, Ord v) => Monomial (Glex v)
Methods mdivides :: Glex v -> Glex v -> Bool mdiv :: Glex v -> Glex v -> Glex v mgcd :: Glex v -> Glex v -> Glex v mlcm :: Glex v -> Glex v -> Glex v mcoprime :: Glex v -> Glex v -> Bool mdeg :: Glex v -> Int

data Grevlex v :: * -> * #

Instances

Functor Grevlex
Methods fmap :: (a -> b) -> Grevlex a -> Grevlex b # (<$) :: a -> Grevlex b -> Grevlex a #
MonomialConstructor Grevlex
Methods mvar :: v -> Grevlex v mindices :: Grevlex v -> [(v, Int)] #
(Eq k, Num k, Ord v, Show v) => Algebra k (Grevlex v)
Methods unit :: k -> Vect k (Grevlex v) mult :: Vect k (Tensor (Grevlex v) (Grevlex v)) -> Vect k (Grevlex v)
Eq v => Eq (Grevlex v)
Methods (==) :: Grevlex v -> Grevlex v -> Bool # (/=) :: Grevlex v -> Grevlex v -> Bool #
Ord v => Ord (Grevlex v)
Methods compare :: Grevlex v -> Grevlex v -> Ordering # (<) :: Grevlex v -> Grevlex v -> Bool # (<=) :: Grevlex v -> Grevlex v -> Bool # (>) :: Grevlex v -> Grevlex v -> Bool # (>=) :: Grevlex v -> Grevlex v -> Bool # max :: Grevlex v -> Grevlex v -> Grevlex v # min :: Grevlex v -> Grevlex v -> Grevlex v #
Show v => Show (Grevlex v)
Methods showsPrec :: Int -> Grevlex v -> ShowS # show :: Grevlex v -> String # showList :: [Grevlex v] -> ShowS #
Ord v => Mon (Grevlex v)
Methods munit :: Grevlex v mmult :: Grevlex v -> Grevlex v -> Grevlex v
(Show v, Ord v) => Monomial (Grevlex v)
Methods mdivides :: Grevlex v -> Grevlex v -> Bool mdiv :: Grevlex v -> Grevlex v -> Grevlex v mgcd :: Grevlex v -> Grevlex v -> Grevlex v mlcm :: Grevlex v -> Grevlex v -> Grevlex v mcoprime :: Grevlex v -> Grevlex v -> Bool mdeg :: Grevlex v -> Int

var :: (Num k, MonomialConstructor m) => v -> Vect k (m v) #

mindices :: MonomialConstructor m => forall v. m v -> [(v, Int)] #

lm :: Vect b c -> c #

lt :: Vect k b -> (b, k) #

eval :: (Eq k, Num k, MonomialConstructor m, Eq (m v), Show v) => Vect k (m v) -> [(Vect k (m v), k)] -> k #

(%%) :: (Eq k, Fractional k, Monomial m, Ord m, Algebra k m) => Vect k m -> [Vect k m] -> Vect k m #

vars :: (Num k, Ord k, MonomialConstructor m, Ord (m v)) => Vect k (m v) -> [Vect k (m v)] #