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.

Author:

Heinz Kredel

Method Summary

Modifier and Type	Method and Description
boolean	isLeftCoPrime(java.util.List<GenSolvablePolynomial<C>> A) GenSolvablePolynomial test for left co-prime list.
GenSolvablePolynomial<C>	leftContent(GenSolvablePolynomial<C> P) GenSolvablePolynomial left content.
java.util.List<GenSolvablePolynomial<C>>	leftCoPrime(java.util.List<GenSolvablePolynomial<C>> A) GenSolvablePolynomial left co-prime list.
GenSolvablePolynomial<C>	leftGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S) GenSolvablePolynomial left greatest common divisor.
GenSolvablePolynomial<C>	leftLcm(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S) GenSolvablePolynomial left least common multiple.
GenSolvablePolynomial<C>	leftPrimitivePart(GenSolvablePolynomial<C> P) GenSolvablePolynomial left primitive part.
GenSolvablePolynomial<C>	rightContent(GenSolvablePolynomial<C> P) GenSolvablePolynomial right content.
GenSolvablePolynomial<C>	rightGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S) GenSolvablePolynomial right greatest common divisor.
GenSolvablePolynomial<C>	rightLcm(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S) GenSolvablePolynomial right least common multiple.
GenSolvablePolynomial<C>	rightPrimitivePart(GenSolvablePolynomial<C> P) GenSolvablePolynomial right primitive part.

Method Detail

leftGcd

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

GenSolvablePolynomial left greatest common divisor.

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

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.

rightGcd

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

GenSolvablePolynomial right greatest common divisor.

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

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.

leftLcm

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

GenSolvablePolynomial left least common multiple.

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

lcm(P,S) with lcm(P,S) = P'*P = S'*S.

rightLcm

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

GenSolvablePolynomial right least common multiple.

Parameters:

P - GenSolvablePolynomial.

S - GenSolvablePolynomial.

Returns:

lcm(P,S) with lcm(P,S) = P*P' = S*S'.

rightContent

GenSolvablePolynomial<C> rightContent(GenSolvablePolynomial<C> P)

GenSolvablePolynomial right content.

Parameters:

P - GenSolvablePolynomial.

Returns:

cont(P) with pp(P)*cont(P) = P.

rightPrimitivePart

GenSolvablePolynomial<C> rightPrimitivePart(GenSolvablePolynomial<C> P)

GenSolvablePolynomial right primitive part.

Parameters:

P - GenSolvablePolynomial.

Returns:

pp(P) with pp(P)*cont(P) = P.

leftContent

GenSolvablePolynomial<C> leftContent(GenSolvablePolynomial<C> P)

GenSolvablePolynomial left content.

Parameters:

P - GenSolvablePolynomial.

Returns:

cont(P) with cont(P)*pp(P) = P.

leftPrimitivePart

GenSolvablePolynomial<C> leftPrimitivePart(GenSolvablePolynomial<C> P)

GenSolvablePolynomial left primitive part.

Parameters:

P - GenSolvablePolynomial.

Returns:

pp(P) with cont(P)*pp(P) = P.

leftCoPrime

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

GenSolvablePolynomial left co-prime list.

Parameters:

A - list of GenSolvablePolynomials.

Returns:

B with leftGcd(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.

isLeftCoPrime

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

GenSolvablePolynomial test for left co-prime list.

Parameters:

A - list of GenSolvablePolynomials.

Returns:

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