Math.Singular.Factory.Polynomial

High-level bindings to singular-factory

Polynomials

newtype Polynomial varset domain

A multivariate polynomial over a base domain.

Typically, you want to fix your variable set (see the module Math.Singular.Factory.Variables), make a type synonym, and use that; for example:

type Poly domain = Polynomial (VarN "x") domain

Constructors

Poly

Fields

• unPoly :: CF

Instances

Eq (Polynomial vars domain)

Defined in Math.Singular.Factory.Polynomial

Methods

(==) :: Polynomial vars domain -> Polynomial vars domain -> Bool

(/=) :: Polynomial vars domain -> Polynomial vars domain -> Bool

BaseDomain domain => Num (Polynomial vars domain)

Defined in Math.Singular.Factory.Polynomial

Methods

(+) :: Polynomial vars domain -> Polynomial vars domain -> Polynomial vars domain

(-) :: Polynomial vars domain -> Polynomial vars domain -> Polynomial vars domain

(*) :: Polynomial vars domain -> Polynomial vars domain -> Polynomial vars domain

negate :: Polynomial vars domain -> Polynomial vars domain

abs :: Polynomial vars domain -> Polynomial vars domain

signum :: Polynomial vars domain -> Polynomial vars domain

fromInteger :: Integer -> Polynomial vars domain

VariableSet vars => Show (Polynomial vars domain)

Defined in Math.Singular.Factory.Polynomial

Methods

showsPrec :: Int -> Polynomial vars domain -> ShowS

show :: Polynomial vars domain -> String

showList :: [Polynomial vars domain] -> ShowS

polyIsZero :: Polynomial vars domain -> Bool

polyIsOne :: Polynomial vars domain -> Bool

inBaseDomain :: Polynomial vars domain -> Bool

Returns true if the polynomial is a constant

mbConstant :: BaseDomain domain => Polynomial vars domain -> Maybe domain

If it is a constant, returns the value

konst :: BaseDomain domain => domain -> Polynomial vars domain

A constant polynomial

var :: VarIdx -> Polynomial vars domain

A variable as a polynomial

varPow :: VarIdx -> Int -> Polynomial vars domain

A power of a variable

Operations on polynomials

mapIntoDomain :: forall domain1 domain2 vars. (BaseDomain domain1, BaseDomain domain2) => Polynomial vars domain1 -> Polynomial vars domain2

pow :: BaseDomain domain => Polynomial vars domain -> Int -> Polynomial vars domain

polyGCD :: BaseDomain domain => Polynomial vars domain -> Polynomial vars domain -> Polynomial vars domain

Polynomial GCD

polyReduce :: BaseDomain domain => Polynomial vars domain -> Polynomial vars domain -> Polynomial vars domain

Polynomial reduction

factorize :: BaseDomain domain => Polynomial vars domain -> [(Polynomial vars domain, Int)]

Polynomial factorization

substitute1 :: BaseDomain domain => VarIdx -> Polynomial vars domain -> Polynomial vars domain -> Polynomial vars domain

Substitution

evaluate :: BaseDomain domain => (VarIdx -> domain) -> Polynomial vars domain -> domain

Evaluate a polynomial at the given point

Parsing

parsePolynomial :: forall vars. VariableSet vars => Text -> Maybe (Polynomial vars Integer)

Parse a polynomial in expanded form

parsePolyExpr :: forall vars. VariableSet vars => Text -> Maybe (Polynomial vars Integer)

Parse a polynomial expression (for example the product of two polynomials)

parsePolynomialStr :: forall vars. VariableSet vars => String -> Maybe (Polynomial vars Integer)

parsePolyExprStr :: forall vars. VariableSet vars => String -> Maybe (Polynomial vars Integer)