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>, 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.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static final boolean	debug
private static final org.apache.logging.log4j.Logger	logger

Fields inherited from class GreatestCommonDivisorAbstract

coFac, syz

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 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 Object

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

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

debug

private static final boolean debug

See Also:

• Constant Field Values

Constructor Details

GreatestCommonDivisorSyzygy

public GreatestCommonDivisorSyzygy(RingFactory<C> cf)

Constructor.

Parameters:

cf - coefficient ring.

Method Details

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.