Math.Singular.Factory.Expr

Polynomial expressions (used for parsing)

Types

data Sign

Constructors

Plus

Minus

Instances

Eq Sign

Defined in Math.Singular.Factory.Expr

Methods

(==) :: Sign -> Sign -> Bool

(/=) :: Sign -> Sign -> Bool

Ord Sign

Defined in Math.Singular.Factory.Expr

Methods

compare :: Sign -> Sign -> Ordering

(<) :: Sign -> Sign -> Bool

(<=) :: Sign -> Sign -> Bool

(>) :: Sign -> Sign -> Bool

(>=) :: Sign -> Sign -> Bool

max :: Sign -> Sign -> Sign

min :: Sign -> Sign -> Sign

Show Sign

Defined in Math.Singular.Factory.Expr

Methods

showsPrec :: Int -> Sign -> ShowS

show :: Sign -> String

showList :: [Sign] -> ShowS

negateIfMinus :: Num a => Sign -> a -> a

newtype Monom var

Monomials

Constructors

Monom [(var, Int)]

Instances

Functor Monom

Defined in Math.Singular.Factory.Expr

Methods

fmap :: (a -> b) -> Monom a -> Monom b

(<$) :: a -> Monom b -> Monom a

Foldable Monom

Defined in Math.Singular.Factory.Expr

Methods

fold :: Monoid m => Monom m -> m

foldMap :: Monoid m => (a -> m) -> Monom a -> m

foldr :: (a -> b -> b) -> b -> Monom a -> b

foldr' :: (a -> b -> b) -> b -> Monom a -> b

foldl :: (b -> a -> b) -> b -> Monom a -> b

foldl' :: (b -> a -> b) -> b -> Monom a -> b

foldr1 :: (a -> a -> a) -> Monom a -> a

foldl1 :: (a -> a -> a) -> Monom a -> a

toList :: Monom a -> [a]

null :: Monom a -> Bool

length :: Monom a -> Int

elem :: Eq a => a -> Monom a -> Bool

maximum :: Ord a => Monom a -> a

minimum :: Ord a => Monom a -> a

sum :: Num a => Monom a -> a

product :: Num a => Monom a -> a

Traversable Monom

Defined in Math.Singular.Factory.Expr

Methods

traverse :: Applicative f => (a -> f b) -> Monom a -> f (Monom b)

sequenceA :: Applicative f => Monom (f a) -> f (Monom a)

mapM :: Monad m => (a -> m b) -> Monom a -> m (Monom b)

sequence :: Monad m => Monom (m a) -> m (Monom a)

Eq var => Eq (Monom var)

Defined in Math.Singular.Factory.Expr

Methods

(==) :: Monom var -> Monom var -> Bool

(/=) :: Monom var -> Monom var -> Bool

Ord var => Ord (Monom var)

Defined in Math.Singular.Factory.Expr

Methods

compare :: Monom var -> Monom var -> Ordering

(<) :: Monom var -> Monom var -> Bool

(<=) :: Monom var -> Monom var -> Bool

(>) :: Monom var -> Monom var -> Bool

(>=) :: Monom var -> Monom var -> Bool

max :: Monom var -> Monom var -> Monom var

min :: Monom var -> Monom var -> Monom var

Show var => Show (Monom var)

Defined in Math.Singular.Factory.Expr

Methods

showsPrec :: Int -> Monom var -> ShowS

show :: Monom var -> String

showList :: [Monom var] -> ShowS

data Term coeff var

A monomial multiplied by a constant

Constructors

Term !coeff !(Monom var)

Instances

Functor (Term coeff)

Defined in Math.Singular.Factory.Expr

Methods

fmap :: (a -> b) -> Term coeff a -> Term coeff b

(<$) :: a -> Term coeff b -> Term coeff a

Foldable (Term coeff)

Defined in Math.Singular.Factory.Expr

Methods

fold :: Monoid m => Term coeff m -> m

foldMap :: Monoid m => (a -> m) -> Term coeff a -> m

foldr :: (a -> b -> b) -> b -> Term coeff a -> b

foldr' :: (a -> b -> b) -> b -> Term coeff a -> b

foldl :: (b -> a -> b) -> b -> Term coeff a -> b

foldl' :: (b -> a -> b) -> b -> Term coeff a -> b

foldr1 :: (a -> a -> a) -> Term coeff a -> a

foldl1 :: (a -> a -> a) -> Term coeff a -> a

toList :: Term coeff a -> [a]

null :: Term coeff a -> Bool

length :: Term coeff a -> Int

elem :: Eq a => a -> Term coeff a -> Bool

maximum :: Ord a => Term coeff a -> a

minimum :: Ord a => Term coeff a -> a

sum :: Num a => Term coeff a -> a

product :: Num a => Term coeff a -> a

Traversable (Term coeff)

Defined in Math.Singular.Factory.Expr

Methods

traverse :: Applicative f => (a -> f b) -> Term coeff a -> f (Term coeff b)

sequenceA :: Applicative f => Term coeff (f a) -> f (Term coeff a)

mapM :: Monad m => (a -> m b) -> Term coeff a -> m (Term coeff b)

sequence :: Monad m => Term coeff (m a) -> m (Term coeff a)

(Eq coeff, Eq var) => Eq (Term coeff var)

Defined in Math.Singular.Factory.Expr

Methods

(==) :: Term coeff var -> Term coeff var -> Bool

(/=) :: Term coeff var -> Term coeff var -> Bool

(Ord coeff, Ord var) => Ord (Term coeff var)

Defined in Math.Singular.Factory.Expr

Methods

compare :: Term coeff var -> Term coeff var -> Ordering

(<) :: Term coeff var -> Term coeff var -> Bool

(<=) :: Term coeff var -> Term coeff var -> Bool

(>) :: Term coeff var -> Term coeff var -> Bool

(>=) :: Term coeff var -> Term coeff var -> Bool

max :: Term coeff var -> Term coeff var -> Term coeff var

min :: Term coeff var -> Term coeff var -> Term coeff var

(Show coeff, Show var) => Show (Term coeff var)

Defined in Math.Singular.Factory.Expr

Methods

showsPrec :: Int -> Term coeff var -> ShowS

show :: Term coeff var -> String

showList :: [Term coeff var] -> ShowS

newtype GenPoly coeff var

Polynomials as linear combination of monomials

Constructors

GenPoly [Term coeff var]

Instances

Functor (GenPoly coeff)

Defined in Math.Singular.Factory.Expr

Methods

fmap :: (a -> b) -> GenPoly coeff a -> GenPoly coeff b

(<$) :: a -> GenPoly coeff b -> GenPoly coeff a

Foldable (GenPoly coeff)

Defined in Math.Singular.Factory.Expr

Methods

fold :: Monoid m => GenPoly coeff m -> m

foldMap :: Monoid m => (a -> m) -> GenPoly coeff a -> m

foldr :: (a -> b -> b) -> b -> GenPoly coeff a -> b

foldr' :: (a -> b -> b) -> b -> GenPoly coeff a -> b

foldl :: (b -> a -> b) -> b -> GenPoly coeff a -> b

foldl' :: (b -> a -> b) -> b -> GenPoly coeff a -> b

foldr1 :: (a -> a -> a) -> GenPoly coeff a -> a

foldl1 :: (a -> a -> a) -> GenPoly coeff a -> a

toList :: GenPoly coeff a -> [a]

null :: GenPoly coeff a -> Bool

length :: GenPoly coeff a -> Int

elem :: Eq a => a -> GenPoly coeff a -> Bool

maximum :: Ord a => GenPoly coeff a -> a

minimum :: Ord a => GenPoly coeff a -> a

sum :: Num a => GenPoly coeff a -> a

product :: Num a => GenPoly coeff a -> a

Traversable (GenPoly coeff)

Defined in Math.Singular.Factory.Expr

Methods

traverse :: Applicative f => (a -> f b) -> GenPoly coeff a -> f (GenPoly coeff b)

sequenceA :: Applicative f => GenPoly coeff (f a) -> f (GenPoly coeff a)

mapM :: Monad m => (a -> m b) -> GenPoly coeff a -> m (GenPoly coeff b)

sequence :: Monad m => GenPoly coeff (m a) -> m (GenPoly coeff a)

(Eq coeff, Eq var) => Eq (GenPoly coeff var)

Defined in Math.Singular.Factory.Expr

Methods

(==) :: GenPoly coeff var -> GenPoly coeff var -> Bool

(/=) :: GenPoly coeff var -> GenPoly coeff var -> Bool

(Ord coeff, Ord var) => Ord (GenPoly coeff var)

Defined in Math.Singular.Factory.Expr

Methods

compare :: GenPoly coeff var -> GenPoly coeff var -> Ordering

(<) :: GenPoly coeff var -> GenPoly coeff var -> Bool

(<=) :: GenPoly coeff var -> GenPoly coeff var -> Bool

(>) :: GenPoly coeff var -> GenPoly coeff var -> Bool

(>=) :: GenPoly coeff var -> GenPoly coeff var -> Bool

max :: GenPoly coeff var -> GenPoly coeff var -> GenPoly coeff var

min :: GenPoly coeff var -> GenPoly coeff var -> GenPoly coeff var

(Show coeff, Show var) => Show (GenPoly coeff var)

Defined in Math.Singular.Factory.Expr

Methods

showsPrec :: Int -> GenPoly coeff var -> ShowS

show :: GenPoly coeff var -> String

showList :: [GenPoly coeff var] -> ShowS

data Expr v

Polynomial expressions

Constructors

VarE !v

KstE !Integer

NegE (Expr v)

LinE [(Sign, Expr v)]

MulE [Expr v]

PowE (Expr v) !Int

Instances

Functor Expr

Defined in Math.Singular.Factory.Expr

Methods

fmap :: (a -> b) -> Expr a -> Expr b

(<$) :: a -> Expr b -> Expr a

Foldable Expr

Defined in Math.Singular.Factory.Expr

Methods

fold :: Monoid m => Expr m -> m

foldMap :: Monoid m => (a -> m) -> Expr a -> m

foldr :: (a -> b -> b) -> b -> Expr a -> b

foldr' :: (a -> b -> b) -> b -> Expr a -> b

foldl :: (b -> a -> b) -> b -> Expr a -> b

foldl' :: (b -> a -> b) -> b -> Expr a -> b

foldr1 :: (a -> a -> a) -> Expr a -> a

foldl1 :: (a -> a -> a) -> Expr a -> a

toList :: Expr a -> [a]

null :: Expr a -> Bool

length :: Expr a -> Int

elem :: Eq a => a -> Expr a -> Bool

maximum :: Ord a => Expr a -> a

minimum :: Ord a => Expr a -> a

sum :: Num a => Expr a -> a

product :: Num a => Expr a -> a

Traversable Expr

Defined in Math.Singular.Factory.Expr

Methods

traverse :: Applicative f => (a -> f b) -> Expr a -> f (Expr b)

sequenceA :: Applicative f => Expr (f a) -> f (Expr a)

mapM :: Monad m => (a -> m b) -> Expr a -> m (Expr b)

sequence :: Monad m => Expr (m a) -> m (Expr a)

Eq v => Eq (Expr v)

Defined in Math.Singular.Factory.Expr

Methods

(==) :: Expr v -> Expr v -> Bool

(/=) :: Expr v -> Expr v -> Bool

Ord v => Ord (Expr v)

Defined in Math.Singular.Factory.Expr

Methods

compare :: Expr v -> Expr v -> Ordering

(<) :: Expr v -> Expr v -> Bool

(<=) :: Expr v -> Expr v -> Bool

(>) :: Expr v -> Expr v -> Bool

(>=) :: Expr v -> Expr v -> Bool

max :: Expr v -> Expr v -> Expr v

min :: Expr v -> Expr v -> Expr v

Show v => Show (Expr v)

Defined in Math.Singular.Factory.Expr

Methods

showsPrec :: Int -> Expr v -> ShowS

show :: Expr v -> String

showList :: [Expr v] -> ShowS

Evaluation to Num

evalSign :: Num c => Sign -> c -> c

evalMonom :: Num c => (var -> c) -> Monom var -> c

evalTerm :: Num c => (coeff -> c) -> (var -> c) -> Term coeff var -> c

evalGenPoly :: Num c => (coeff -> c) -> (var -> c) -> GenPoly coeff var -> c

evalExpr :: Num c => (var -> c) -> Expr var -> c