cc.redberry.rings.poly.univar

Class UnivariateResultants

java.lang.Object

cc.redberry.rings.poly.univar.UnivariateResultants

public final class UnivariateResultants
extends Object

Various algorithms to compute (sub)resultants via Euclidean algorithm. Implementation is based on Gathen & Lücking, "Subresultants revisited", https://doi.org/10.1016/S0304-3975(02)00639-4

Since:

2.5

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	UnivariateResultants.APolynomialRemainderSequence<Poly extends IUnivariatePolynomial<Poly>> Polynomial remainder sequence (PRS).
static class	UnivariateResultants.PolynomialRemainderSequence<E> Polynomial remainder sequence (PRS).
static class	UnivariateResultants.PolynomialRemainderSequenceZp64 Classical division rule for polynomials over Zp

Method Summary

Modifier and Type	Method and Description
static <E> UnivariateResultants.PolynomialRemainderSequence<E>	ClassicalPRS(UnivariatePolynomial<E> a, UnivariatePolynomial<E> b) Computes polynomial remainder sequence using classical division algorithm
static UnivariateResultants.PolynomialRemainderSequenceZp64	ClassicalPRS(UnivariatePolynomialZp64 a, UnivariatePolynomialZp64 b) Computes polynomial remainder sequence using classical division algorithm
static <E> E	Discriminant(UnivariatePolynomial<E> a) Computes discriminant of polynomial
static long	Discriminant(UnivariatePolynomialZp64 a) Computes discriminant of polynomial
static <Poly extends IUnivariatePolynomial<Poly>> Poly	DiscriminantAsPoly(Poly a) Computes discriminant of polynomial and returns the result as a constant poly
static BigInteger	ModularResultant(UnivariatePolynomial<BigInteger> a, UnivariatePolynomial<BigInteger> b) Modular algorithm for computing resultants over Z
static UnivariatePolynomial<Rational<BigInteger>>	ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Modular resultant in simple number field
static UnivariatePolynomial<BigInteger>	ModularResultantInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a, UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b) Modular resultant in the ring of integers of number field
static BigInteger	polyPowNumFieldCfBound(BigInteger maxCf, BigInteger maxMinPolyCf, int minPolyDeg, int exponent)
static <E> UnivariateResultants.PolynomialRemainderSequence<E>	PrimitivePRS(UnivariatePolynomial<E> a, UnivariatePolynomial<E> b) Computes polynomial remainder sequence using primitive division algorithm
static <E> UnivariateResultants.PolynomialRemainderSequence<E>	PseudoPRS(UnivariatePolynomial<E> a, UnivariatePolynomial<E> b) Computes polynomial remainder sequence using pseudo division algorithm
static <E> UnivariateResultants.PolynomialRemainderSequence<E>	ReducedPRS(UnivariatePolynomial<E> a, UnivariatePolynomial<E> b) Computes polynomial remainder sequence using reduced division algorithm
static <E> E	Resultant(UnivariatePolynomial<E> a, UnivariatePolynomial<E> b) Computes resultant of two polynomials
static long	Resultant(UnivariatePolynomialZp64 a, UnivariatePolynomialZp64 b) Computes resultant of two polynomials
static <Poly extends IUnivariatePolynomial<Poly>> Poly	ResultantAsPoly(Poly a, Poly b) Computes resultant of two polynomials and returns the result as a constant poly
static <E> UnivariateResultants.PolynomialRemainderSequence<E>	SubresultantPRS(UnivariatePolynomial<E> a, UnivariatePolynomial<E> b) Computes subresultant polynomial remainder sequence
static <E> List<E>	Subresultants(UnivariatePolynomial<E> a, UnivariatePolynomial<E> b) Computes sequence of scalar subresultants.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

DiscriminantAsPoly

public static <Poly extends IUnivariatePolynomial<Poly>> Poly DiscriminantAsPoly(Poly a)

Computes discriminant of polynomial and returns the result as a constant poly

Discriminant

public static <E> E Discriminant(UnivariatePolynomial<E> a)

Computes discriminant of polynomial

Discriminant

public static long Discriminant(UnivariatePolynomialZp64 a)

Computes discriminant of polynomial

ResultantAsPoly

public static <Poly extends IUnivariatePolynomial<Poly>> Poly ResultantAsPoly(Poly a,
                                                                              Poly b)

Computes resultant of two polynomials and returns the result as a constant poly

Resultant

public static <E> E Resultant(UnivariatePolynomial<E> a,
                              UnivariatePolynomial<E> b)

Computes resultant of two polynomials

Resultant

public static long Resultant(UnivariatePolynomialZp64 a,
                             UnivariatePolynomialZp64 b)

Computes resultant of two polynomials

Subresultants

public static <E> List<E> Subresultants(UnivariatePolynomial<E> a,
                                        UnivariatePolynomial<E> b)

Computes sequence of scalar subresultants.

ModularResultant

public static BigInteger ModularResultant(UnivariatePolynomial<BigInteger> a,
                                          UnivariatePolynomial<BigInteger> b)

Modular algorithm for computing resultants over Z

ModularResultantInNumberField

public static UnivariatePolynomial<Rational<BigInteger>> ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a,
                                                                                       UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)

Modular resultant in simple number field

polyPowNumFieldCfBound

public static BigInteger polyPowNumFieldCfBound(BigInteger maxCf,
                                                BigInteger maxMinPolyCf,
                                                int minPolyDeg,
                                                int exponent)

ModularResultantInRingOfIntegersOfNumberField

public static UnivariatePolynomial<BigInteger> ModularResultantInRingOfIntegersOfNumberField(UnivariatePolynomial<UnivariatePolynomial<BigInteger>> a,
                                                                                             UnivariatePolynomial<UnivariatePolynomial<BigInteger>> b)

Modular resultant in the ring of integers of number field

ClassicalPRS

public static UnivariateResultants.PolynomialRemainderSequenceZp64 ClassicalPRS(UnivariatePolynomialZp64 a,
                                                                                UnivariatePolynomialZp64 b)

Computes polynomial remainder sequence using classical division algorithm

ClassicalPRS

public static <E> UnivariateResultants.PolynomialRemainderSequence<E> ClassicalPRS(UnivariatePolynomial<E> a,
                                                                                   UnivariatePolynomial<E> b)

Computes polynomial remainder sequence using classical division algorithm

PseudoPRS

public static <E> UnivariateResultants.PolynomialRemainderSequence<E> PseudoPRS(UnivariatePolynomial<E> a,
                                                                                UnivariatePolynomial<E> b)

Computes polynomial remainder sequence using pseudo division algorithm

PrimitivePRS

public static <E> UnivariateResultants.PolynomialRemainderSequence<E> PrimitivePRS(UnivariatePolynomial<E> a,
                                                                                   UnivariatePolynomial<E> b)

Computes polynomial remainder sequence using primitive division algorithm

ReducedPRS

public static <E> UnivariateResultants.PolynomialRemainderSequence<E> ReducedPRS(UnivariatePolynomial<E> a,
                                                                                 UnivariatePolynomial<E> b)

Computes polynomial remainder sequence using reduced division algorithm

SubresultantPRS

public static <E> UnivariateResultants.PolynomialRemainderSequence<E> SubresultantPRS(UnivariatePolynomial<E> a,
                                                                                      UnivariatePolynomial<E> b)

Computes subresultant polynomial remainder sequence