Package edu.jas.fd

Class GreatestCommonDivisorSyzygy<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.fd.GreatestCommonDivisorAbstract<C>

edu.jas.fd.GreatestCommonDivisorSyzygy<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GreatestCommonDivisor<C>, java.io.Serializable

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

(Non-unique) factorization domain greatest common divisor common algorithms with syzygy computation. The implementation uses solvable syzygy gcd computation.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
GreatestCommonDivisorSyzygy(RingFactory<C> cf)	Constructor.

Method Summary

Modifier and Type	Method	Description
GenSolvablePolynomial<C>	leftBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Left univariate GenSolvablePolynomial greatest common divisor.
GenSolvablePolynomial<C>	leftGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Left GenSolvablePolynomial greatest common divisor.
GenSolvablePolynomial<GenPolynomial<C>>	leftRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)	Univariate GenSolvablePolynomial left recursive greatest common divisor.
GenSolvablePolynomial<C>	rightBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Right univariate GenSolvablePolynomial greatest common divisor.
GenSolvablePolynomial<C>	rightGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Right GenSolvablePolynomial right greatest common divisor.
GenSolvablePolynomial<GenPolynomial<C>>	rightRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)	Univariate GenSolvablePolynomial right recursive greatest common divisor.

Methods inherited from class edu.jas.fd.GreatestCommonDivisorAbstract

baseExtendedGcd, baseGcdDiophant, baseHalfExtendedGcd, baseRecursiveContent, baseRecursivePrimitivePart, divide, gcd, isLeftCoPrime, isLeftCoPrime, isLeftOreCond, isRightOreCond, leftBaseContent, leftBasePrimitivePart, leftContent, leftCoPrime, leftCoPrime, leftCoPrimeRec, leftGcd, leftGcd, leftGcdCofactors, leftLcm, leftOreCond, leftOreCond, leftPrimitivePart, leftRecursiveContent, leftRecursiveGcd, leftRecursivePrimitivePart, recursiveContent, rightBaseContent, rightBasePrimitivePart, rightContent, rightDivide, rightGcd, rightGcdCofactors, rightLcm, rightOreCond, rightOreCond, rightPrimitivePart, rightRecursiveContent, rightRecursiveGcd, rightRecursivePrimitivePart, toString

Methods inherited from class java.lang.Object

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

Constructor Detail

GreatestCommonDivisorSyzygy

public GreatestCommonDivisorSyzygy(RingFactory<C> cf)

Constructor.

Parameters:

cf - coefficient ring.

Method Detail

leftBaseGcd

public GenSolvablePolynomial<C> leftBaseGcd(GenSolvablePolynomial<C> P,
                                            GenSolvablePolynomial<C> S)

Left univariate GenSolvablePolynomial greatest common divisor.

Specified by:

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

Parameters:

P - univariate GenSolvablePolynomial.

S - univariate GenSolvablePolynomial.

Returns:

gcd(P,S) with P = P'*gcd(P,S) and S = S'*gcd(P,S).

rightBaseGcd

public GenSolvablePolynomial<C> rightBaseGcd(GenSolvablePolynomial<C> P,
                                             GenSolvablePolynomial<C> S)

Right univariate GenSolvablePolynomial greatest common divisor.

Specified by:

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

Parameters:

P - univariate GenSolvablePolynomial.

S - univariate GenSolvablePolynomial.

Returns:

gcd(P,S) with P = P'*gcd(P,S) and S = S'*gcd(P,S).

leftGcd

public GenSolvablePolynomial<C> leftGcd(GenSolvablePolynomial<C> P,
                                        GenSolvablePolynomial<C> S)

Left GenSolvablePolynomial greatest common divisor.

Specified by:

leftGcd in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Overrides:

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

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

gcd(P,S) with P = P'*gcd(P,S) and S = S'*gcd(P,S).

rightGcd

public GenSolvablePolynomial<C> rightGcd(GenSolvablePolynomial<C> P,
                                         GenSolvablePolynomial<C> S)

Right GenSolvablePolynomial right greatest common divisor.

Specified by:

rightGcd in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Overrides:

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

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

gcd(P,S) with P = gcd(P,S)*P' and S = gcd(P,S)*S'.

leftRecursiveUnivariateGcd

public GenSolvablePolynomial<GenPolynomial<C>> leftRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P,
                                                                          GenSolvablePolynomial<GenPolynomial<C>> S)

Univariate GenSolvablePolynomial left recursive greatest common divisor.

Specified by:

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

Parameters:

P - univariate recursive GenSolvablePolynomial.

S - univariate recursive GenSolvablePolynomial.

Returns:

gcd(P,S) with P = P'*gcd(P,S)*p and S = S'*gcd(P,S)*s, where deg_main(p) = deg_main(s) == 0.

rightRecursiveUnivariateGcd

public GenSolvablePolynomial<GenPolynomial<C>> rightRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P,
                                                                           GenSolvablePolynomial<GenPolynomial<C>> S)

Univariate GenSolvablePolynomial right recursive greatest common divisor.

Specified by:

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

Parameters:

P - univariate recursive GenSolvablePolynomial.

S - univariate recursive GenSolvablePolynomial.

Returns:

gcd(P,S) with P = p*gcd(P,S)*P' and S = s*gcd(P,S)*S', where deg_main(p) = deg_main(s) == 0.