edu.jas.ufd
Interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

GCDProxy, GreatestCommonDivisorAbstract, GreatestCommonDivisorHensel, GreatestCommonDivisorModEval, GreatestCommonDivisorModular, GreatestCommonDivisorPrimitive, GreatestCommonDivisorSimple, GreatestCommonDivisorSubres

public interface GreatestCommonDivisor<C extends GcdRingElem<C>>
extends java.io.Serializable

Greatest common divisor algorithm interface.

Author:

Heinz Kredel

See Also:

GCDFactory.getImplementation(edu.jas.arith.ModLongRing)

Usage

To create classes that implement this interface use the GreatestCommonDivisorFactory. It will select an appropriate implementation based on the types of polynomial coefficients CT.

 GreatestCommonDivisor<CT> engine = GCDFactory.<CT> getImplementation(cofac);
 c = engine.gcd(a, b);
 

For example, if the coefficient type is BigInteger, the usage looks like

 BigInteger cofac = new BigInteger();
 GreatestCommonDivisor<BigInteger> engine = GCDFactory.getImplementation(cofac);
 c = engine.gcd(a, b);
 

Method Summary

GenPolynomial<C>	content(GenPolynomial<C> P) GenPolynomial content.
java.util.List<GenPolynomial<C>>	coPrime(GenPolynomial<C> a, java.util.List<GenPolynomial<C>> P) GenPolynomial co-prime list.
java.util.List<GenPolynomial<C>>	coPrime(java.util.List<GenPolynomial<C>> A) GenPolynomial co-prime list.
GenPolynomial<C>	gcd(GenPolynomial<C> P, GenPolynomial<C> S) GenPolynomial greatest comon divisor.
boolean	isCoPrime(java.util.List<GenPolynomial<C>> A) GenPolynomial test for co-prime list.
boolean	isCoPrime(java.util.List<GenPolynomial<C>> P, java.util.List<GenPolynomial<C>> A) GenPolynomial test for co-prime list of given list.
GenPolynomial<C>	lcm(GenPolynomial<C> P, GenPolynomial<C> S) GenPolynomial least comon multiple.
GenPolynomial<C>	primitivePart(GenPolynomial<C> P) GenPolynomial primitive part.
GenPolynomial<C>	resultant(GenPolynomial<C> P, GenPolynomial<C> S) GenPolynomial resultant.

Method Detail

content

GenPolynomial<C> content(GenPolynomial<C> P)

GenPolynomial content.

Parameters:

P - GenPolynomial.

Returns:

cont(P).

primitivePart

GenPolynomial<C> primitivePart(GenPolynomial<C> P)

GenPolynomial primitive part.

Parameters:

P - GenPolynomial.

Returns:

pp(P).

gcd

GenPolynomial<C> gcd(GenPolynomial<C> P,
                     GenPolynomial<C> S)

GenPolynomial greatest comon divisor.

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

gcd(P,S).

lcm

GenPolynomial<C> lcm(GenPolynomial<C> P,
                     GenPolynomial<C> S)

GenPolynomial least comon multiple.

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

lcm(P,S).

resultant

GenPolynomial<C> resultant(GenPolynomial<C> P,
                           GenPolynomial<C> S)

GenPolynomial resultant. The input polynomials are considered as univariate polynomials in the main variable.

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

res(P,S).

See Also:

GreatestCommonDivisorSubres.recursiveResultant(edu.jas.poly.GenPolynomial>, edu.jas.poly.GenPolynomial>)

coPrime

java.util.List<GenPolynomial<C>> coPrime(java.util.List<GenPolynomial<C>> A)

GenPolynomial co-prime list.

Parameters:

A - list of GenPolynomials.

Returns:

B with gcd(b,c) = 1 for all b != c in B and for all non-constant a in A there exists b in B with b|a. B does not contain zero or constant polynomials.

coPrime

java.util.List<GenPolynomial<C>> coPrime(GenPolynomial<C> a,
                                         java.util.List<GenPolynomial<C>> P)

GenPolynomial co-prime list.

Parameters:

a - GenPolynomial.

P - co-prime list of GenPolynomials.

Returns:

B with gcd(b,c) = 1 for all b != c in B and for non-constant a there exists b in P with b|a. B does not contain zero or constant polynomials.

isCoPrime

boolean isCoPrime(java.util.List<GenPolynomial<C>> A)

GenPolynomial test for co-prime list.

Parameters:

A - list of GenPolynomials.

Returns:

true if gcd(b,c) = 1 for all b != c in B, else false.

isCoPrime

boolean isCoPrime(java.util.List<GenPolynomial<C>> P,
                  java.util.List<GenPolynomial<C>> A)

GenPolynomial test for co-prime list of given list.

Parameters:

A - list of GenPolynomials.

P - list of co-prime GenPolynomials.

Returns:

true if isCoPrime(P) and for all a in A exists p in P with p | a, else false.