edu.jas.fd

Interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

GreatestCommonDivisorAbstract, GreatestCommonDivisorPrimitive, GreatestCommonDivisorSimple

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

(Non-unique) factorization domain greatest common divisor algorithm interface.

Method Summary

Modifier and Type	Method and Description
GenSolvablePolynomial<C>	content(GenSolvablePolynomial<C> P) GenSolvablePolynomial content.
java.util.List<GenSolvablePolynomial<C>>	coPrime(java.util.List<GenSolvablePolynomial<C>> A) GenSolvablePolynomial co-prime list.
GenSolvablePolynomial<C>	gcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S) GenSolvablePolynomial greatest comon divisor.
boolean	isCoPrime(java.util.List<GenSolvablePolynomial<C>> A) GenSolvablePolynomial test for co-prime list.
GenSolvablePolynomial<C>	lcm(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S) GenSolvablePolynomial least comon multiple.
GenSolvablePolynomial<C>	primitivePart(GenSolvablePolynomial<C> P) GenSolvablePolynomial primitive part.

Method Detail

content

GenSolvablePolynomial<C> content(GenSolvablePolynomial<C> P)

GenSolvablePolynomial content.

Parameters:

P - GenSolvablePolynomial.

Returns:

cont(P).

primitivePart

GenSolvablePolynomial<C> primitivePart(GenSolvablePolynomial<C> P)

GenSolvablePolynomial primitive part.

Parameters:

P - GenSolvablePolynomial.

Returns:

pp(P).

gcd

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

GenSolvablePolynomial greatest comon divisor.

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

gcd(P,S).

lcm

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

GenSolvablePolynomial least comon multiple.

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

lcm(P,S).

coPrime

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

GenSolvablePolynomial co-prime list.

Parameters:

A - list of GenSolvablePolynomials.

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(java.util.List<GenSolvablePolynomial<C>> A)

GenSolvablePolynomial test for co-prime list.

Parameters:

A - list of GenSolvablePolynomials.

Returns:

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