Safe Haskell	None
Language	Haskell2010

Polynomial.Prelude

Contents

Types
Classes
Functions

Synopsis

newtype Polynomial k ord n = Polynomial {
- getTerms :: Map (Monomial ord n) k
}
class (CoeffRig (Coeff poly), KnownNat (Arity poly)) => IsPolynomial poly where
- type Coeff poly :: *
- type Arity poly :: Nat
class (IsMonomialOrder (MonOrder poly), IsPolynomial poly) => IsOrderedPolynomial poly where
- type MonOrder poly :: *
polytope2 :: IsOrderedPolynomial poly => poly -> [Point2D]
(!*) :: Num k => k -> Polynomial k ord n -> Polynomial k ord n

Types

newtype Polynomial k ord n Source #

Polynomial requires just the type of the coefficient and the monomial ordering. | Arity is given when defining variables with variable function

Constructors

Polynomial
Fields getTerms :: Map (Monomial ord n) k

Instances

(Additive (Polynomial k2 ord n), Semiring k2, Num k2) => LeftModule k2 (Polynomial k2 ord n) Source #
Instance details Defined in Polynomial.Prelude Methods (.*) :: k2 -> Polynomial k2 ord n -> Polynomial k2 ord n #
(Additive (Polynomial k2 ord n), Semiring k2, Num k2) => RightModule k2 (Polynomial k2 ord n) Source #
Instance details Defined in Polynomial.Prelude Methods (*.) :: Polynomial k2 ord n -> k2 -> Polynomial k2 ord n #
Eq k1 => Eq (Polynomial k1 ord n) Source #
Instance details Defined in Polynomial.Prelude Methods (==) :: Polynomial k1 ord n -> Polynomial k1 ord n -> Bool # (/=) :: Polynomial k1 ord n -> Polynomial k1 ord n -> Bool #
(IsMonomialOrder ord, KnownNat n) => Fractional (Polynomial (Tropical Integer) ord n) Source #
Instance details Defined in Polynomial.Prelude Methods (/) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # recip :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # fromRational :: Rational -> Polynomial (Tropical Integer) ord n #
(IsMonomialOrder ord, KnownNat n) => Num (Polynomial (Tropical Integer) ord n) Source #
Instance details Defined in Polynomial.Prelude Methods (+) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # (-) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # (*) :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # negate :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # abs :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # signum :: Polynomial (Tropical Integer) ord n -> Polynomial (Tropical Integer) ord n # fromInteger :: Integer -> Polynomial (Tropical Integer) ord n #
(KnownNat n, Unital k, Show k, Eq k) => Show (Polynomial k Revlex n) Source #
Instance details Defined in Polynomial.Prelude Methods showsPrec :: Int -> Polynomial k Revlex n -> ShowS # show :: Polynomial k Revlex n -> String # showList :: [Polynomial k Revlex n] -> ShowS #
(Unital k, Show k, Eq k) => Show (Polynomial k Lex n) Source #
Instance details Defined in Polynomial.Prelude Methods showsPrec :: Int -> Polynomial k Lex n -> ShowS # show :: Polynomial k Lex n -> String # showList :: [Polynomial k Lex n] -> ShowS #
(Num k, IsMonomialOrder ord) => Additive (Polynomial k ord n) Source #
Instance details Defined in Polynomial.Prelude Methods (+) :: Polynomial k ord n -> Polynomial k ord n -> Polynomial k ord n # sinnum1p :: Natural -> Polynomial k ord n -> Polynomial k ord n # sumWith1 :: Foldable1 f => (a -> Polynomial k ord n) -> f a -> Polynomial k ord n #
(KnownNat n, CoeffRig k, IsMonomialOrder ord) => IsOrderedPolynomial (Polynomial k ord n) Source #
Instance details Defined in Polynomial.Prelude Associated Types type MonOrder (Polynomial k ord n) :: * Source # Methods terms :: Polynomial k ord n -> Map (Monomial (MonOrder (Polynomial k ord n)) (Arity (Polynomial k ord n))) (Coeff (Polynomial k ord n)) Source # leadingTerm :: Polynomial k ord n -> (Coeff (Polynomial k ord n), Monomial (MonOrder (Polynomial k ord n)) (Arity (Polynomial k ord n))) Source # leadingMonomial :: Polynomial k ord n -> Monomial (MonOrder (Polynomial k ord n)) (Arity (Polynomial k ord n)) Source # leadingCoeff :: Polynomial k ord n -> Coeff (Polynomial k ord n) Source #
(KnownNat n, IsMonomialOrder ord, CoeffRig k) => IsPolynomial (Polynomial k ord n) Source #
Instance details Defined in Polynomial.Prelude Associated Types type Coeff (Polynomial k ord n) :: * Source # type Arity (Polynomial k ord n) :: Nat Source # Methods arity :: Polynomial k ord n -> SNat (Arity (Polynomial k ord n)) Source # toPolynomial :: (Mon (Arity (Polynomial k ord n)), Coeff (Polynomial k ord n)) -> Polynomial k ord n Source # fromMonomial :: Mon (Arity (Polynomial k ord n)) -> Polynomial k ord n Source # variable :: Ordinal (Arity (Polynomial k ord n)) -> Polynomial k ord n Source #
type MonOrder (Polynomial k ord n) Source #
Instance details Defined in Polynomial.Prelude type MonOrder (Polynomial k ord n) = ord
type Coeff (Polynomial k ord n) Source #
Instance details Defined in Polynomial.Prelude type Coeff (Polynomial k ord n) = k
type Arity (Polynomial k ord n) Source #
Instance details Defined in Polynomial.Prelude type Arity (Polynomial k ord n) = n

Classes

class (CoeffRig (Coeff poly), KnownNat (Arity poly)) => IsPolynomial poly where Source #

Every polynomial must implement this class

Minimal complete definition

arity, toPolynomial

Associated Types

type Coeff poly :: * Source #

type Arity poly :: Nat Source #

Methods

arity :: poly -> SNat (Arity poly) Source #

toPolynomial :: (Mon (Arity poly), Coeff poly) -> poly Source #

fromMonomial :: Mon (Arity poly) -> poly Source #

variable :: Ordinal (Arity poly) -> poly Source #

Instances

(KnownNat n, IsMonomialOrder ord, CoeffRig k) => IsPolynomial (Polynomial k ord n) Source #

Instance details

Defined in Polynomial.Prelude

Associated Types

type Coeff (Polynomial k ord n) :: * Source #

type Arity (Polynomial k ord n) :: Nat Source #

Methods

arity :: Polynomial k ord n -> SNat (Arity (Polynomial k ord n)) Source #

toPolynomial :: (Mon (Arity (Polynomial k ord n)), Coeff (Polynomial k ord n)) -> Polynomial k ord n Source #

fromMonomial :: Mon (Arity (Polynomial k ord n)) -> Polynomial k ord n Source #

variable :: Ordinal (Arity (Polynomial k ord n)) -> Polynomial k ord n Source #

class (IsMonomialOrder (MonOrder poly), IsPolynomial poly) => IsOrderedPolynomial poly where Source #

Minimal complete definition

terms

Associated Types

type MonOrder poly :: * Source #

Methods

terms :: poly -> Map (Monomial (MonOrder poly) (Arity poly)) (Coeff poly) Source #

leadingTerm :: poly -> (Coeff poly, Monomial (MonOrder poly) (Arity poly)) Source #

leadingMonomial :: poly -> Monomial (MonOrder poly) (Arity poly) Source #

leadingCoeff :: poly -> Coeff poly Source #

Instances

(KnownNat n, CoeffRig k, IsMonomialOrder ord) => IsOrderedPolynomial (Polynomial k ord n) Source #

Instance details

Defined in Polynomial.Prelude

Associated Types

type MonOrder (Polynomial k ord n) :: * Source #

Methods

terms :: Polynomial k ord n -> Map (Monomial (MonOrder (Polynomial k ord n)) (Arity (Polynomial k ord n))) (Coeff (Polynomial k ord n)) Source #

leadingTerm :: Polynomial k ord n -> (Coeff (Polynomial k ord n), Monomial (MonOrder (Polynomial k ord n)) (Arity (Polynomial k ord n))) Source #

leadingMonomial :: Polynomial k ord n -> Monomial (MonOrder (Polynomial k ord n)) (Arity (Polynomial k ord n)) Source #

leadingCoeff :: Polynomial k ord n -> Coeff (Polynomial k ord n) Source #

Functions

polytope2 :: IsOrderedPolynomial poly => poly -> [Point2D] Source #

(!*) :: Num k => k -> Polynomial k ord n -> Polynomial k ord n Source #