GreatestCommonDivisor

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

All Known Implementing Classes:: GCDProxy, GreatestCommonDivisorAbstract, GreatestCommonDivisorModEval, GreatestCommonDivisorModular, GreatestCommonDivisorPrimitive, GreatestCommonDivisorSimple, GreatestCommonDivisorSubres

public interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Greatest common divisor algorithm interface.

Author:

Heinz Kredel

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

Method Summary
`GenPolynomial<C>`	`content(GenPolynomial<C> P)` GenPolynomial content.
`GenPolynomial<C>`	`gcd(GenPolynomial<C> P, GenPolynomial<C> S)` GenPolynomial greatest comon divisor.
`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.
`java.util.Map<java.lang.Integer,GenPolynomial<C>>`	`squarefreeFactors(GenPolynomial<C> P)` GenPolynomial squarefree factorization.
`GenPolynomial<C>`	`squarefreePart(GenPolynomial<C> P)` GenPolynomial greatest squarefree divisor.

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.

Parameters:: P - GenPolynomial.; S - GenPolynomial.
Returns:: res(P,S).

squarefreePart

GenPolynomial<C> squarefreePart(GenPolynomial<C> P)

GenPolynomial greatest squarefree divisor.

Parameters:: P - GenPolynomial.
Returns:: squarefree(P).

squarefreeFactors

java.util.Map<java.lang.Integer,GenPolynomial<C>> squarefreeFactors(GenPolynomial<C> P)

GenPolynomial squarefree factorization.

Parameters:: P - GenPolynomial.
Returns:: squarefreeFactors(P).