cc.redberry.rings.poly.multivar

Class MultivariateResultants

java.lang.Object

cc.redberry.rings.poly.multivar.MultivariateResultants

public final class MultivariateResultants
extends Object

Polynomial resultants.

Method Summary

Modifier and Type	Method and Description
static <E> MultivariatePolynomial<E>	BrownResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Brown's algorithm for resultant with dense interpolation
static MultivariatePolynomialZp64	BrownResultant(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b, int variable) Brown's algorithm for resultant with dense interpolation
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	ClassicalResultant(Poly a, Poly b, int variable) Computes resultant via subresultant sequences
static <Poly extends AMultivariatePolynomial> Poly	Discriminant(Poly a, int variable) Computes discriminant of polynomial
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	ModularResultantInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, int variable) Modular resultant in simple number field
static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>	ModularResultantInRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over rings of integers
static MultivariatePolynomial<BigInteger>	ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over Z
static <Poly extends AMultivariatePolynomial> Poly	Resultant(Poly a, Poly b, int variable) Calculates polynomial resultant of two given polynomials with respect to specified variable
static <Poly extends AMultivariatePolynomial> Poly	ResultantInGF(Poly a, Poly b, int variable) Computes polynomial resultant of two polynomials over finite field
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	ResultantInSmallCharacteristic(Poly a, Poly b, int variable) Resultant in small characteristic
static MultivariatePolynomial<BigInteger>	ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Computes polynomial resultant of two polynomials over Z
static <E> MultivariatePolynomial<E>	ZippelResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Zippel's algorithm for resultant with sparse interpolation
static MultivariatePolynomialZp64	ZippelResultant(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b, int variable) Zippel's algorithm for resultant with sparse interpolation

Methods inherited from class java.lang.Object

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

Method Detail

Discriminant

public static <Poly extends AMultivariatePolynomial> Poly Discriminant(Poly a,
                                                                       int variable)

Computes discriminant of polynomial

Resultant

public static <Poly extends AMultivariatePolynomial> Poly Resultant(Poly a,
                                                                    Poly b,
                                                                    int variable)

Calculates polynomial resultant of two given polynomials with respect to specified variable

Parameters:

a - the first poly

b - the second poly

Returns:

the resultant

ResultantInGF

public static <Poly extends AMultivariatePolynomial> Poly ResultantInGF(Poly a,
                                                                        Poly b,
                                                                        int variable)

Computes polynomial resultant of two polynomials over finite field

ResultantInZ

public static MultivariatePolynomial<BigInteger> ResultantInZ(MultivariatePolynomial<BigInteger> a,
                                                              MultivariatePolynomial<BigInteger> b,
                                                              int variable)

Computes polynomial resultant of two polynomials over Z

ClassicalResultant

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly ClassicalResultant(Poly a,
                                                                                                                     Poly b,
                                                                                                                     int variable)

Computes resultant via subresultant sequences

ResultantInSmallCharacteristic

public static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly ResultantInSmallCharacteristic(Poly a,
                                                                                                                                 Poly b,
                                                                                                                                 int variable)

Resultant in small characteristic

ModularResultantInZ

public static MultivariatePolynomial<BigInteger> ModularResultantInZ(MultivariatePolynomial<BigInteger> a,
                                                                     MultivariatePolynomial<BigInteger> b,
                                                                     int variable)

Modular algorithm with Zippel sparse interpolation for resultant over Z

ModularResultantInNumberField

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

Modular resultant in simple number field

ModularResultantInRingOfIntegersOfNumberField

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

Modular algorithm with Zippel sparse interpolation for resultant over rings of integers

BrownResultant

public static MultivariatePolynomialZp64 BrownResultant(MultivariatePolynomialZp64 a,
                                                        MultivariatePolynomialZp64 b,
                                                        int variable)

Brown's algorithm for resultant with dense interpolation

BrownResultant

public static <E> MultivariatePolynomial<E> BrownResultant(MultivariatePolynomial<E> a,
                                                           MultivariatePolynomial<E> b,
                                                           int variable)

Brown's algorithm for resultant with dense interpolation

ZippelResultant

public static MultivariatePolynomialZp64 ZippelResultant(MultivariatePolynomialZp64 a,
                                                         MultivariatePolynomialZp64 b,
                                                         int variable)

Zippel's algorithm for resultant with sparse interpolation

ZippelResultant

public static <E> MultivariatePolynomial<E> ZippelResultant(MultivariatePolynomial<E> a,
                                                            MultivariatePolynomial<E> b,
                                                            int variable)

Zippel's algorithm for resultant with sparse interpolation