Package edu.jas.fd

Class GreatestCommonDivisorLR<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.fd.GreatestCommonDivisorAbstract<C>

edu.jas.fd.GreatestCommonDivisorLR<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GreatestCommonDivisor<C>, java.io.Serializable

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

(Non-unique) factorization domain greatest common divisor common algorithms with monic polynomial remainder sequence. Fake implementation always returns 1 for any gcds.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
GreatestCommonDivisorLR(RingFactory<C> cf)	Constructor.
GreatestCommonDivisorLR(RingFactory<C> cf, SolvableSyzygyAbstract<C> s)	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.
GCDcoFactors<C>	leftRightBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Univariate GenSolvablePolynomial greatest common divisor.
GenSolvablePolynomial<C>	rightBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Univariate GenSolvablePolynomial greatest common divisor.
GCDcoFactors<C>	rightLeftBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)	Univariate GenSolvablePolynomial 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, leftBaseContent, leftBasePrimitivePart, leftContent, leftCoPrime, leftCoPrime, leftCoPrimeRec, leftGcd, leftGcd, leftLcm, leftOreCond, leftOreCond, leftPrimitivePart, leftRecursiveContent, leftRecursiveGcd, leftRecursivePrimitivePart, recursiveContent, rightBaseContent, rightBasePrimitivePart, rightContent, rightGcd, 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

GreatestCommonDivisorLR

public GreatestCommonDivisorLR(RingFactory<C> cf)

Constructor.

Parameters:

cf - coefficient ring.

GreatestCommonDivisorLR

public GreatestCommonDivisorLR(RingFactory<C> cf,
                               SolvableSyzygyAbstract<C> s)

Constructor.

Parameters:

cf - coefficient ring.

s - algorithm for SolvableSyzygy computation.

Method Detail

leftRightBaseGcd

public GCDcoFactors<C> leftRightBaseGcd(GenSolvablePolynomial<C> P,
                                        GenSolvablePolynomial<C> S)

Univariate GenSolvablePolynomial greatest common divisor. Uses pseudoRemainder for remainder.

Parameters:

P - univariate GenSolvablePolynomial.

S - univariate GenSolvablePolynomial.

Returns:

[P,S,coP,coS,left,right] with left * coP * right = P and left * coS * right = S.

rightLeftBaseGcd

public GCDcoFactors<C> rightLeftBaseGcd(GenSolvablePolynomial<C> P,
                                        GenSolvablePolynomial<C> S)

Univariate GenSolvablePolynomial greatest common divisor. Uses pseudoRemainder for remainder.

Parameters:

P - univariate GenSolvablePolynomial.

S - univariate GenSolvablePolynomial.

Returns:

[P,S,coP,coS,left,right] with left * coP * right = P and left * coS * right = S.

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:

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

rightBaseGcd

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

Univariate GenSolvablePolynomial 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:

r = gcd(P,S) with P = P'*gcd(P,S) and S = S'*gcd(P,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:

1 = 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:

1 = 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.