Class GreatestCommonDivisorHensel<MOD extends GcdRingElem<MOD> & Modular>

java.lang.Object

edu.jas.ufd.GreatestCommonDivisorAbstract<BigInteger>

edu.jas.ufd.GreatestCommonDivisorHensel<MOD>

All Implemented Interfaces:

GreatestCommonDivisor<BigInteger>, Serializable

public class GreatestCommonDivisorHensel<MOD extends GcdRingElem<MOD> & Modular>
extends GreatestCommonDivisorAbstract<BigInteger>

Greatest common divisor algorithms with subresultant polynomial remainder sequence and univariate Hensel lifting.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
final GreatestCommonDivisorAbstract<BigInteger>	iufd	Fall back gcd algorithm.
final boolean	quadratic	Flag for linear or quadratic Hensel lift.

Constructor Summary

Constructors

Constructor	Description
GreatestCommonDivisorHensel()	Constructor.
GreatestCommonDivisorHensel(boolean quadratic)	Constructor.

Method Summary

Modifier and Type	Method	Description
GenPolynomial<BigInteger>	baseGcd(GenPolynomial<BigInteger> P, GenPolynomial<BigInteger> S)	Univariate GenPolynomial greatest common divisor.
GenPolynomial<GenPolynomial<BigInteger>>	recursiveUnivariateGcd(GenPolynomial<GenPolynomial<BigInteger>> P, GenPolynomial<GenPolynomial<BigInteger>> S)	Univariate GenPolynomial recursive greatest common divisor.

Methods inherited from class GreatestCommonDivisorAbstract

baseContent, baseExtendedGcd, baseGcdDiophant, baseHalfExtendedGcd, basePartialFraction, basePartialFraction, basePartialFraction, basePartialFractionValue, basePrimitivePart, basePrimitivePart, baseRecursiveContent, baseRecursivePrimitivePart, baseResultant, content, contentPrimitivePart, coPrime, coPrime, coPrimeRec, divide, gcd, gcd, gcd, isBasePartialFraction, isBasePartialFraction, isCoPrime, isCoPrime, lcm, primitivePart, recursiveContent, recursiveGcd, recursivePrimitivePart, recursivePrimitivePart, recursiveResultant, recursiveUnivariateResultant, resultant, toString

Methods inherited from class Object

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

Field Details

quadratic

public final boolean quadratic

Flag for linear or quadratic Hensel lift.

iufd

public final GreatestCommonDivisorAbstract<BigInteger> iufd

Fall back gcd algorithm.

Constructor Details

GreatestCommonDivisorHensel

public GreatestCommonDivisorHensel()

Constructor.

GreatestCommonDivisorHensel

public GreatestCommonDivisorHensel(boolean quadratic)

Constructor.

Parameters:

quadratic - use quadratic Hensel lift.

Method Details

baseGcd

public GenPolynomial<BigInteger> baseGcd(GenPolynomial<BigInteger> P,
 GenPolynomial<BigInteger> S)

Univariate GenPolynomial greatest common divisor. Uses univariate Hensel lifting.

Specified by:

baseGcd in class GreatestCommonDivisorAbstract<BigInteger>

Parameters:

P - univariate GenPolynomial.

S - univariate GenPolynomial.

Returns:

gcd(P,S).

recursiveUnivariateGcd

public GenPolynomial<GenPolynomial<BigInteger>> recursiveUnivariateGcd(GenPolynomial<GenPolynomial<BigInteger>> P,
 GenPolynomial<GenPolynomial<BigInteger>> S)

Univariate GenPolynomial recursive greatest common divisor. Uses multivariate Hensel list.

Specified by:

recursiveUnivariateGcd in class GreatestCommonDivisorAbstract<BigInteger>

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

gcd(P,S).