Package edu.jas.fd

Class GreatestCommonDivisorSimple<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.fd.GreatestCommonDivisorAbstract<C>

edu.jas.fd.GreatestCommonDivisorSimple<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GreatestCommonDivisor<C>, java.io.Serializable

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

(Non-unique) factorization domain greatest common divisor common 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(RingFactory<C> cf)	Constructor.

Method Summary

Modifier and Type	Method	Description
GenSolvablePolynomial<C>	leftBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Univariate 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)	Univariate 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, leftGcd, leftGcdCofactors, leftLcm, leftOreCond, leftOreCond, leftPrimitivePart, leftRecursiveContent, leftRecursiveGcd, leftRecursivePrimitivePart, recursiveContent, rightBaseContent, rightBasePrimitivePart, rightContent, rightDivide, rightGcd, 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

GreatestCommonDivisorSimple

public GreatestCommonDivisorSimple(RingFactory<C> cf)

Constructor.

Parameters:

cf - coefficient ring.

Method Detail

leftBaseGcd

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

Univariate GenSolvablePolynomial greatest common divisor. Uses pseudoRemainder for remainder.

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)

Univariate GenSolvablePolynomial right greatest common divisor. Uses pseudoRemainder for remainder.

Specified by:

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

Parameters:

P - univariate GenSolvablePolynomial.

S - univariate 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. Uses pseudoRemainder for remainder.

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. Uses pseudoRemainder for remainder.

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.