Math.Algebra.Polynomial.Multivariate.Generic

Multivariate polynomial algebra where the set of variables is given by the inhabitants of a type

Documentation

newtype Poly (coeff :: *) (var :: *)

Constructors

Poly (FreeMod coeff (Monom var))

Instances

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

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

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

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

(Ring c, Ord v, Pretty v) => Num (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

(+) :: Poly c v -> Poly c v -> Poly c v

(-) :: Poly c v -> Poly c v -> Poly c v

(*) :: Poly c v -> Poly c v -> Poly c v

negate :: Poly c v -> Poly c v

abs :: Poly c v -> Poly c v

signum :: Poly c v -> Poly c v

fromInteger :: Integer -> Poly c v

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

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

compare :: Poly coeff var -> Poly coeff var -> Ordering

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

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

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

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

max :: Poly coeff var -> Poly coeff var -> Poly coeff var

min :: Poly coeff var -> Poly coeff var -> Poly coeff var

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

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

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

show :: Poly coeff var -> String

showList :: [Poly coeff var] -> ShowS

Ord v => FreeModule (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Associated Types

type BaseF (Poly c v) :: Type

type CoeffF (Poly c v) :: Type

Methods

toFreeModule :: Poly c v -> FreeMod (CoeffF (Poly c v)) (BaseF (Poly c v))

fromFreeModule :: FreeMod (CoeffF (Poly c v)) (BaseF (Poly c v)) -> Poly c v

IsSigned (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

signOf :: Poly c v -> Maybe Sign

(Ring c, Ord v, Pretty v, Pretty (Monom v)) => Pretty (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

pretty :: Poly c v -> String

prettyInParens :: Poly c v -> String

(Ring c, Ord v, Pretty v) => Polynomial (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

evalP :: Num d => (CoeffP (Poly c v) -> d) -> (VarP (Poly c v) -> d) -> Poly c v -> d

varSubsP :: (VarP (Poly c v) -> VarP (Poly c v)) -> Poly c v -> Poly c v

coeffSubsP :: (VarP (Poly c v) -> Maybe (CoeffP (Poly c v))) -> Poly c v -> Poly c v

subsP :: (VarP (Poly c v) -> Poly c v) -> Poly c v -> Poly c v

(Ring c, Ord v, Pretty v) => AlmostPolynomial (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Associated Types

type CoeffP (Poly c v) :: Type

type MonomP (Poly c v) :: Type

type VarP (Poly c v) :: Type

Methods

fromListP :: [(MonomP (Poly c v), CoeffP (Poly c v))] -> Poly c v

toListP :: Poly c v -> [(MonomP (Poly c v), CoeffP (Poly c v))]

zeroP :: Poly c v

isZeroP :: Poly c v -> Bool

oneP :: Poly c v

variableP :: VarP (Poly c v) -> Poly c v

singletonP :: VarP (Poly c v) -> Int -> Poly c v

monomP :: MonomP (Poly c v) -> Poly c v

monomP' :: MonomP (Poly c v) -> CoeffP (Poly c v) -> Poly c v

scalarP :: CoeffP (Poly c v) -> Poly c v

addP :: Poly c v -> Poly c v -> Poly c v

subP :: Poly c v -> Poly c v -> Poly c v

negP :: Poly c v -> Poly c v

sumP :: [Poly c v] -> Poly c v

mulP :: Poly c v -> Poly c v -> Poly c v

productP :: [Poly c v] -> Poly c v

coeffOfP :: MonomP (Poly c v) -> Poly c v -> CoeffP (Poly c v)

mulByMonomP :: MonomP (Poly c v) -> Poly c v -> Poly c v

scaleP :: CoeffP (Poly c v) -> Poly c v -> Poly c v

(Ring c, Variable v) => Ring (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

Methods

isZeroR :: Poly c v -> Bool

signumR :: Poly c v -> Maybe Sign

absR :: Poly c v -> Poly c v

isSignedR :: Proxy (Poly c v) -> Bool

isAtomicR :: Proxy (Poly c v) -> Bool

type BaseF (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

type BaseF (Poly c v) = Monom v

type CoeffF (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

type CoeffF (Poly c v) = c

type CoeffP (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

type CoeffP (Poly c v) = c

type MonomP (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

type MonomP (Poly c v) = Monom v

type VarP (Poly c v)

Defined in Math.Algebra.Polynomial.Multivariate.Generic

type VarP (Poly c v) = v

unPoly :: Poly c v -> FreeMod c (Monom v)

type ZPoly = Poly Integer

type QPoly = Poly Rational

fromZPoly :: (Ring c, Variable v) => Poly Integer v -> Poly c v

Change the coefficient ring (from integers)

fromQPoly :: (Field c, Variable v) => Poly Rational v -> Poly c v

Change the coefficient ring (from rationals)