edu.jas.ufd

Class GreatestCommonDivisorSubres<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.GreatestCommonDivisorAbstract<C>

edu.jas.ufd.GreatestCommonDivisorSubres<C>

All Implemented Interfaces:

GreatestCommonDivisor<C>, java.io.Serializable

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

Greatest common divisor algorithms with subresultant polynomial remainder sequence.

Author:

Heinz Kredel, Youssef Elbarbary

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
GreatestCommonDivisorSubres()

Method Summary

Modifier and Type	Method and Description
GenPolynomial<C>	baseDiscriminant(GenPolynomial<C> P) GenPolynomial base coefficient discriminant.
GenPolynomial<C>	baseGcd(GenPolynomial<C> P, GenPolynomial<C> S) Univariate GenPolynomial greatest comon divisor.
GenPolynomial<C>	basePseudoRemainder(GenPolynomial<C> P, GenPolynomial<C> S) Deprecated. Use PolyUtil.baseDensePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial) instead
GenPolynomial<C>	baseResultant(GenPolynomial<C> P, GenPolynomial<C> S) Univariate GenPolynomial resultant.
GenPolynomial<GenPolynomial<C>>	recursivePseudoRemainder(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S) Deprecated. Use PolyUtil.recursiveDensePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial) instead
GenPolynomial<GenPolynomial<C>>	recursiveUnivariateGcd(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S) Univariate GenPolynomial recursive greatest comon divisor.
GenPolynomial<GenPolynomial<C>>	recursiveUnivariateResultant(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S) Univariate GenPolynomial recursive resultant.
java.util.List<GenPolynomial<GenPolynomial<C>>>	recursiveUnivariateSubResultantList(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S) Univariate GenPolynomial recursive Subresultant list.

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

GreatestCommonDivisorSubres

public GreatestCommonDivisorSubres()

Method Detail

basePseudoRemainder

@Deprecated
public GenPolynomial<C> basePseudoRemainder(GenPolynomial<C> P,
                                                        GenPolynomial<C> S)

Deprecated. Use PolyUtil.baseDensePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial) instead

GenPolynomial pseudo remainder. For univariate polynomials.

Parameters:

P - GenPolynomial.

S - nonzero GenPolynomial.

Returns:

remainder with ldcf(S)^m P = quotient * S + remainder.

See Also:

GenPolynomial.remainder(edu.jas.poly.GenPolynomial).

recursivePseudoRemainder

@Deprecated
public GenPolynomial<GenPolynomial<C>> recursivePseudoRemainder(GenPolynomial<GenPolynomial<C>> P,
                                                                            GenPolynomial<GenPolynomial<C>> S)

Deprecated. Use PolyUtil.recursiveDensePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial) instead

GenPolynomial pseudo remainder. For recursive polynomials.

Parameters:

P - recursive GenPolynomial.

S - nonzero recursive GenPolynomial.

Returns:

remainder with ldcf(S)^m P = quotient * S + remainder.

See Also:

GenPolynomial.remainder(edu.jas.poly.GenPolynomial).

baseGcd

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

Univariate GenPolynomial greatest comon 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 comon 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. Uses pseudoRemainder for remainder.

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. Uses pseudoRemainder for remainder.

Overrides:

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

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

res(P,S).

recursiveUnivariateSubResultantList

public java.util.List<GenPolynomial<GenPolynomial<C>>> recursiveUnivariateSubResultantList(GenPolynomial<GenPolynomial<C>> P,
                                                                                           GenPolynomial<GenPolynomial<C>> S)

Univariate GenPolynomial recursive Subresultant list. Uses pseudoRemainder for remainder. Author: Youssef Elbarbary

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

subResList(P,S).

baseDiscriminant

public GenPolynomial<C> baseDiscriminant(GenPolynomial<C> P)

GenPolynomial base coefficient discriminant.

Parameters:

P - GenPolynomial.

Returns:

discriminant(P).