Interface GreatestCommonDivisor<C extends GcdRingElem<C>>

All Superinterfaces:
Serializable
All Known Implementing Classes:
GCDProxy, GreatestCommonDivisorAbstract, GreatestCommonDivisorFake, GreatestCommonDivisorHensel, GreatestCommonDivisorModEval, GreatestCommonDivisorModular, GreatestCommonDivisorPrimitive, GreatestCommonDivisorSimple, GreatestCommonDivisorSubres
public interface GreatestCommonDivisor<C extends GcdRingElem<C>> extends Serializable
Greatest common divisor algorithm interface.

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);
See Also:

  • Method Details

    • 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 common divisor.
      Parameters:
      P - GenPolynomial.
      S - GenPolynomial.
      Returns:
      gcd(P,S).

    • lcm

      GenPolynomial<C> lcm(GenPolynomial<C> P, GenPolynomial<C> S)
      GenPolynomial least common 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).
      Throws:
      UnsupportedOperationException - if there is no implementation in the sub-class.

    • coPrime

      List<GenPolynomial<C>> coPrime(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.

    • isCoPrime

      boolean isCoPrime(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.