Package edu.jas.ufd

Class GreatestCommonDivisorSimple<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.GreatestCommonDivisorAbstract<C>

edu.jas.ufd.GreatestCommonDivisorSimple<C>

All Implemented Interfaces:

GreatestCommonDivisor<C>, java.io.Serializable

public class GreatestCommonDivisorSimple<C extends GcdRingElem<C>>
extends GreatestCommonDivisorAbstract<C>

Greatest common divisor algorithms with monic polynomial remainder sequence. If C is a field, then the monic PRS (on coefficients) is computed otherwise no simplifications in the reduction are made.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
GreatestCommonDivisorSimple()

Method Summary

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

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, gcd, isBasePartialFraction, isBasePartialFraction, isCoPrime, isCoPrime, lcm, primitivePart, recursiveContent, recursiveGcd, recursivePrimitivePart, recursivePrimitivePart, recursiveResultant, resultant, toString

Methods inherited from class java.lang.Object

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

Constructor Detail

GreatestCommonDivisorSimple

public GreatestCommonDivisorSimple()

Method Detail

baseGcd

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

Univariate GenPolynomial greatest common divisor. Uses pseudoRemainder for remainder.

Specified by:

baseGcd in class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>

Parameters:

P - univariate GenPolynomial.

S - univariate GenPolynomial.

Returns:

gcd(P,S).

recursiveUnivariateGcd

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

Univariate GenPolynomial recursive greatest common divisor. Uses pseudoRemainder for remainder.

Specified by:

recursiveUnivariateGcd in class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

gcd(P,S).

baseResultant

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

Univariate GenPolynomial resultant.

Overrides:

baseResultant in class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>

Parameters:

P - univariate GenPolynomial.

S - univariate GenPolynomial.

Returns:

res(P,S).

recursiveUnivariateResultant

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

Univariate GenPolynomial recursive resultant.

Overrides:

recursiveUnivariateResultant in class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

res(P,S).