Package edu.jas.ufd

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

java.lang.Object

edu.jas.ufd.GreatestCommonDivisorAbstract<BigInteger>

edu.jas.ufd.GreatestCommonDivisorModular<MOD>

All Implemented Interfaces:

GreatestCommonDivisor<BigInteger>, java.io.Serializable

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

Greatest common divisor algorithms with modular computation and Chinese remainder algorithm.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected GreatestCommonDivisorAbstract<BigInteger>	iufd
protected GreatestCommonDivisorAbstract<MOD>	mufd

Constructor Summary

Constructors

Constructor	Description
GreatestCommonDivisorModular()	Constructor to set recursive algorithm.
GreatestCommonDivisorModular(boolean simple)	Constructor to set recursive algorithm.

Method Summary

Modifier and Type	Method	Description
GenPolynomial<BigInteger>	baseGcd(GenPolynomial<BigInteger> P, GenPolynomial<BigInteger> S)	Univariate GenPolynomial greatest common divisor.
GenPolynomial<BigInteger>	baseResultant(GenPolynomial<BigInteger> P, GenPolynomial<BigInteger> S)	Univariate GenPolynomial resultant.
GenPolynomial<BigInteger>	gcd(GenPolynomial<BigInteger> P, GenPolynomial<BigInteger> S)	GenPolynomial greatest common divisor, modular algorithm.
GenPolynomial<GenPolynomial<BigInteger>>	recursiveUnivariateGcd(GenPolynomial<GenPolynomial<BigInteger>> P, GenPolynomial<GenPolynomial<BigInteger>> S)	Univariate GenPolynomial recursive greatest common divisor.
GenPolynomial<GenPolynomial<BigInteger>>	recursiveUnivariateResultant(GenPolynomial<GenPolynomial<BigInteger>> P, GenPolynomial<GenPolynomial<BigInteger>> S)	Univariate GenPolynomial recursive resultant.
GenPolynomial<BigInteger>	resultant(GenPolynomial<BigInteger> P, GenPolynomial<BigInteger> S)	GenPolynomial resultant, modular algorithm.

Methods inherited from class edu.jas.ufd.GreatestCommonDivisorAbstract

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

Methods inherited from class java.lang.Object

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

Field Detail

mufd

protected final GreatestCommonDivisorAbstract<MOD extends GcdRingElem<MOD> & Modular> mufd

iufd

protected final GreatestCommonDivisorAbstract<BigInteger> iufd

Constructor Detail

GreatestCommonDivisorModular

public GreatestCommonDivisorModular()

Constructor to set recursive algorithm. Use modular evaluation GCD algorithm.

GreatestCommonDivisorModular

public GreatestCommonDivisorModular(boolean simple)

Constructor to set recursive algorithm.

Parameters:

simple - , true if the simple PRS should be used.

Method Detail

baseGcd

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

Univariate GenPolynomial greatest common divisor. Delegate to subresultant baseGcd, should not be needed.

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. Delegate to subresultant recursiveGcd, should not be needed.

Specified by:

recursiveUnivariateGcd in class GreatestCommonDivisorAbstract<BigInteger>

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

gcd(P,S).

gcd

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

GenPolynomial greatest common divisor, modular algorithm.

Specified by:

gcd in interface GreatestCommonDivisor<MOD extends GcdRingElem<MOD> & Modular>

Overrides:

gcd in class GreatestCommonDivisorAbstract<BigInteger>

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

gcd(P,S).

baseResultant

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

Univariate GenPolynomial resultant.

Overrides:

baseResultant in class GreatestCommonDivisorAbstract<BigInteger>

Parameters:

P - univariate GenPolynomial.

S - univariate GenPolynomial.

Returns:

res(P,S).

recursiveUnivariateResultant

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

Univariate GenPolynomial recursive resultant.

Overrides:

recursiveUnivariateResultant in class GreatestCommonDivisorAbstract<BigInteger>

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

res(P,S).

resultant

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

GenPolynomial resultant, modular algorithm.

Specified by:

resultant in interface GreatestCommonDivisor<MOD extends GcdRingElem<MOD> & Modular>

Overrides:

resultant in class GreatestCommonDivisorAbstract<BigInteger>

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

res(P,S).

See Also:

GreatestCommonDivisorAbstract.recursiveResultant(edu.jas.poly.GenPolynomial<edu.jas.poly.GenPolynomial<C>>, edu.jas.poly.GenPolynomial<edu.jas.poly.GenPolynomial<C>>)