ToySolver.Data.Polynomial

Contents

• Polynomial type
• Conversion
• Query
• Operations
• Univariate polynomials
• Term
• Monic monomial
• Monomial order
• Pretty Printing

Description

Synopsis

• data Polynomial r v
• class Vars a v => Var a v | a -> v where
  • var :: v -> a
• constant :: (Eq k, Num k, Ord v) => k -> Polynomial k v
• terms :: Polynomial k v -> [Term k v]
• fromTerms :: (Eq k, Num k, Ord v) => [Term k v] -> Polynomial k v
• coeffMap :: Polynomial r v -> Map (Monomial v) r
• fromCoeffMap :: (Eq k, Num k, Ord v) => Map (Monomial v) k -> Polynomial k v
• fromTerm :: (Eq k, Num k, Ord v) => Term k v -> Polynomial k v
• class Degree t where
  • deg :: t -> Integer
• class Ord v => Vars a v | a -> v where
  • vars :: a -> Set v
• lt :: (Eq k, Num k, Ord v) => MonomialOrder v -> Polynomial k v -> Term k v
• lc :: (Eq k, Num k, Ord v) => MonomialOrder v -> Polynomial k v -> k
• lm :: (Eq k, Num k, Ord v) => MonomialOrder v -> Polynomial k v -> Monomial v
• coeff :: (Num k, Ord v) => Monomial v -> Polynomial k v -> k
• lookupCoeff :: Ord v => Monomial v -> Polynomial k v -> Maybe k
• isPrimitive :: (Eq k, Num k, ContPP k, Ord v) => Polynomial k v -> Bool
• class Factor a where
  • factor :: a -> [(a, Integer)]
• class SQFree a where
  • sqfree :: a -> [(a, Integer)]
• class ContPP k where
  • cont :: Ord v => Polynomial k v -> k
  • pp :: Ord v => Polynomial k v -> Polynomial k v
• deriv :: (Eq k, Num k, Ord v) => Polynomial k v -> v -> Polynomial k v
• integral :: (Eq k, Fractional k, Ord v) => Polynomial k v -> v -> Polynomial k v
• eval :: (Num k, Ord v) => (v -> k) -> Polynomial k v -> k
• subst :: (Eq k, Num k, Ord v1, Ord v2) => Polynomial k v1 -> (v1 -> Polynomial k v2) -> Polynomial k v2
• mapCoeff :: (Eq k1, Num k1, Ord v) => (k -> k1) -> Polynomial k v -> Polynomial k1 v
• toMonic :: (Eq r, Fractional r, Ord v) => MonomialOrder v -> Polynomial r v -> Polynomial r v
• toUPolynomialOf :: (Ord k, Num k, Ord v) => Polynomial k v -> v -> UPolynomial (Polynomial k v)
• divModMP :: forall k v. (Eq k, Fractional k, Ord v) => MonomialOrder v -> Polynomial k v -> [Polynomial k v] -> ([Polynomial k v], Polynomial k v)
• reduce :: (Eq k, Fractional k, Ord v) => MonomialOrder v -> Polynomial k v -> [Polynomial k v] -> Polynomial k v
• type UPolynomial r = Polynomial r X
• data X = X
• type UTerm k = Term k X
• type UMonomial = Monomial X
• div :: (Eq k, Fractional k) => UPolynomial k -> UPolynomial k -> UPolynomial k
• mod :: (Eq k, Fractional k) => UPolynomial k -> UPolynomial k -> UPolynomial k
• divMod :: (Eq k, Fractional k) => UPolynomial k -> UPolynomial k -> (UPolynomial k, UPolynomial k)
• divides :: (Eq k, Fractional k) => UPolynomial k -> UPolynomial k -> Bool
• gcd :: (Eq k, Fractional k) => UPolynomial k -> UPolynomial k -> UPolynomial k
• lcm :: (Eq k, Fractional k) => UPolynomial k -> UPolynomial k -> UPolynomial k
• exgcd :: (Eq k, Fractional k) => UPolynomial k -> UPolynomial k -> (UPolynomial k, UPolynomial k, UPolynomial k)
• pdivMod :: (Eq r, Num r) => UPolynomial r -> UPolynomial r -> (r, UPolynomial r, UPolynomial r)
• pdiv :: (Eq r, Num r) => UPolynomial r -> UPolynomial r -> UPolynomial r
• pmod :: (Eq r, Num r) => UPolynomial r -> UPolynomial r -> UPolynomial r
• gcd' :: (Eq r, Integral r) => UPolynomial r -> UPolynomial r -> UPolynomial r
• isRootOf :: (Eq k, Num k) => k -> UPolynomial k -> Bool
• isSquareFree :: (Eq k, Fractional k) => UPolynomial k -> Bool
• nat :: MonomialOrder X
• type Term k v = (k, Monomial v)
• tdeg :: Term k v -> Integer
• tscale :: (Num k, Ord v) => k -> Term k v -> Term k v
• tmult :: (Num k, Ord v) => Term k v -> Term k v -> Term k v
• tdivides :: (Fractional k, Ord v) => Term k v -> Term k v -> Bool
• tdiv :: (Fractional k, Ord v) => Term k v -> Term k v -> Term k v
• tderiv :: (Eq k, Num k, Ord v) => Term k v -> v -> Term k v
• tintegral :: (Eq k, Fractional k, Ord v) => Term k v -> v -> Term k v
• data Monomial v
• mone :: Monomial v
• mfromIndices :: Ord v => [(v, Integer)] -> Monomial v
• mfromIndicesMap :: Ord v => Map v Integer -> Monomial v
• mindices :: Ord v => Monomial v -> [(v, Integer)]
• mindicesMap :: Monomial v -> Map v Integer
• mmult :: Ord v => Monomial v -> Monomial v -> Monomial v
• mpow :: Ord v => Monomial v -> Integer -> Monomial v
• mdivides :: Ord v => Monomial v -> Monomial v -> Bool
• mdiv :: Ord v => Monomial v -> Monomial v -> Monomial v
• mderiv :: Ord v => Monomial v -> v -> (Integer, Monomial v)
• mintegral :: Ord v => Monomial v -> v -> (Rational, Monomial v)
• mlcm :: Ord v => Monomial v -> Monomial v -> Monomial v
• mgcd :: Ord v => Monomial v -> Monomial v -> Monomial v
• mcoprime :: Ord v => Monomial v -> Monomial v -> Bool
• type MonomialOrder v = Monomial v -> Monomial v -> Ordering
• lex :: Ord v => MonomialOrder v
• revlex :: Ord v => Monomial v -> Monomial v -> Ordering
• grlex :: Ord v => MonomialOrder v
• grevlex :: Ord v => MonomialOrder v
• data PrintOptions k v = PrintOptions {
  • pOptPrintVar :: PrettyLevel -> Rational -> v -> Doc
  • pOptPrintCoeff :: PrettyLevel -> Rational -> k -> Doc
  • pOptIsNegativeCoeff :: k -> Bool
  • pOptMonomialOrder :: MonomialOrder v
  }
• defaultPrintOptions :: (PrettyCoeff k, PrettyVar v, Ord v) => PrintOptions k v
• prettyPrint :: (Ord k, Num k, Ord v) => PrintOptions k v -> PrettyLevel -> Rational -> Polynomial k v -> Doc
• class PrettyCoeff a where
  • pPrintCoeff :: PrettyLevel -> Rational -> a -> Doc
  • isNegativeCoeff :: a -> Bool
• class PrettyVar a where
  • pPrintVar :: PrettyLevel -> Rational -> a -> Doc

Polynomial type

Conversion

Query

Operations

reduce cmp f gs = snd (divModMP cmp f gs)

Univariate polynomials

Term

Monic monomial

Monomial order

Pretty Printing