java.lang.Object
- cc.redberry.rings.poly.multivar.MultivariateGCD

public final class MultivariateGCD
extends Object

Multivariate polynomial GCD

Since:: 1.0

Method Summary

Modifier and Type	Method	Description
`static <E> MultivariatePolynomial<E>`	`BrownGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b)`	Calculates GCD of two multivariate polynomials over Zp using Brown's algorithm with dense interpolation.
`static MultivariatePolynomialZp64`	`BrownGCD(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b)`	Calculates GCD of two multivariate polynomials over Zp using Brown's algorithm with dense interpolation.
`static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly`	`EEZGCD(Poly a, Poly b)`	Calculates GCD of two multivariate polynomials over Zp using enhanced EZ algorithm
`static MultivariatePolynomialZp64`	`EZGCD(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b)`	Calculates GCD of two multivariate polynomials over Zp using EZ algorithm
`static <E> MultivariatePolynomial<E>`	`KaltofenMonaganEEZModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b)`	Modular GCD algorithm for polynomials over finite fields of small cardinality.
`static MultivariatePolynomialZp64`	`KaltofenMonaganEEZModularGCDInGF(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b)`	Modular GCD algorithm for polynomials over finite fields of small cardinality.
`static MultivariatePolynomialZp64`	`KaltofenMonaganModularGCDInGF(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b, cc.redberry.rings.poly.multivar.MultivariateGCD.KaltofenMonaganAlgorithm algorithm)`	Modular GCD algorithm for polynomials over finite fields of small cardinality.
`static <E> MultivariatePolynomial<E>`	`KaltofenMonaganSparseModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b)`	Modular GCD algorithm for polynomials over finite fields of small cardinality.
`static MultivariatePolynomialZp64`	`KaltofenMonaganSparseModularGCDInGF(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b)`	Modular GCD algorithm for polynomials over finite fields of small cardinality.
`static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>`	`ModularGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)`	Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
`static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>`	`ModularGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)`	Modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
`static MultivariatePolynomial<BigInteger>`	`ModularGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, BiFunction<MultivariatePolynomialZp64,MultivariatePolynomialZp64,MultivariatePolynomialZp64> gcdInZp)`	Modular GCD algorithm for polynomials over Z.
`static <Poly extends AMultivariatePolynomial> Poly`	`PolynomialGCD(Iterable<Poly> arr)`	Calculates greatest common divisor of the array of polynomials
`static <Poly extends AMultivariatePolynomial> Poly`	`PolynomialGCD(Poly... arr)`	Calculates greatest common divisor of the array of polynomials
`static <Poly extends AMultivariatePolynomial> Poly`	`PolynomialGCD(Poly a, Poly b)`	Calculates greatest common divisor of two multivariate polynomials
`static <Poly extends AMultivariatePolynomial> Poly`	`PolynomialGCDinGF(Poly a, Poly b)`	Calculates greatest common divisor of two multivariate polynomials over finite fields
`static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>`	`PolynomialGCDinNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)`	Calculates greatest common divisor of two multivariate polynomials over Z
`static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>`	`PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b)`	Calculates greatest common divisor of two multivariate polynomials over Z
`static MultivariatePolynomial<BigInteger>`	`PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)`	Calculates greatest common divisor of two multivariate polynomials over Z
`static <E> MultivariatePolynomial<E>`	`ZippelGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b)`	Calculates GCD of two multivariate polynomials over Zp using Zippel's algorithm with sparse interpolation.
`static MultivariatePolynomialZp64`	`ZippelGCD(MultivariatePolynomialZp64 a, MultivariatePolynomialZp64 b)`	Calculates GCD of two multivariate polynomials over Zp using Zippel's algorithm with sparse interpolation.
`static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>`	`ZippelGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)`	Zippel's sparse modular interpolation algorithm for computing GCD associate for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
`static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>`	`ZippelGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b)`	Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of rational reconstruction to reconstruct the result
`static MultivariatePolynomial<BigInteger>`	`ZippelGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b)`	Sparse modular GCD algorithm for polynomials over Z.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

PolynomialGCD
```
public static <Poly extends AMultivariatePolynomial> Poly PolynomialGCD(Poly... arr)
```
Calculates greatest common divisor of the array of polynomials

Parameters:

arr - set of polynomials

Returns:

the gcd

PolynomialGCD
```
public static <Poly extends AMultivariatePolynomial> Poly PolynomialGCD(Iterable<Poly> arr)
```
Calculates greatest common divisor of the array of polynomials

Parameters:

arr - set of polynomials

Returns:

the gcd

PolynomialGCD

public static <Poly extends AMultivariatePolynomial> Poly PolynomialGCD(Poly a,
                                                                        Poly b)

Calculates greatest common divisor of two multivariate polynomials

Parameters:: a - the first poly; b - the second poly
Returns:: the gcd

PolynomialGCDinGF

public static <Poly extends AMultivariatePolynomial> Poly PolynomialGCDinGF(Poly a,
                                                                            Poly b)

Calculates greatest common divisor of two multivariate polynomials over finite fields

Parameters:: a - the first poly; b - the second poly
Returns:: the gcd

PolynomialGCDinZ

public static MultivariatePolynomial<BigInteger> PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a,
                                                                  MultivariatePolynomial<BigInteger> b)

Calculates greatest common divisor of two multivariate polynomials over Z

Parameters:: a - the first poly; b - the second poly
Returns:: the gcd

PolynomialGCDinNumberField

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

Calculates greatest common divisor of two multivariate polynomials over Z

Parameters:: a - the first poly; b - the second poly
Returns:: the gcd

PolynomialGCDinRingOfIntegersOfNumberField

public static MultivariatePolynomial<UnivariatePolynomial<BigInteger>> PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a,
                                                                                                                  MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b)

Calculates greatest common divisor of two multivariate polynomials over Z

Parameters:: a - the first poly; b - the second poly
Returns:: the gcd

ZippelGCDInZ

public static MultivariatePolynomial<BigInteger> ZippelGCDInZ(MultivariatePolynomial<BigInteger> a,
                                                              MultivariatePolynomial<BigInteger> b)

Sparse modular GCD algorithm for polynomials over Z.

Parameters:: a - the first polynomial; b - the second polynomial
Returns:: GCD of two polynomials

ModularGCDInZ

public static MultivariatePolynomial<BigInteger> ModularGCDInZ(MultivariatePolynomial<BigInteger> a,
                                                               MultivariatePolynomial<BigInteger> b,
                                                               BiFunction<MultivariatePolynomialZp64,MultivariatePolynomialZp64,MultivariatePolynomialZp64> gcdInZp)

Modular GCD algorithm for polynomials over Z.

Parameters:: a - the first polynomial; b - the second polynomial; gcdInZp - algorithm for gcd in Zp
Returns:: GCD of two polynomials

ZippelGCDInNumberFieldViaRationalReconstruction

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

Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of rational reconstruction to reconstruct the result

ZippelGCDInNumberFieldViaLangemyrMcCallum

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

Zippel's sparse modular interpolation algorithm for computing GCD associate for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction

ModularGCDInNumberFieldViaRationalReconstruction

public static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> ModularGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a,
                                                                                                                                  MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b,
                                                                                                                                  BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)

Modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction

ModularGCDInNumberFieldViaLangemyrMcCallum

public static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> ModularGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a,
                                                                                                                            MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b,
                                                                                                                            BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm)

Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction