Package edu.jas.fd
Interface GreatestCommonDivisor<C extends GcdRingElem<C>>
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- Type Parameters:
C
- coefficient type
- All Superinterfaces:
java.io.Serializable
- All Known Implementing Classes:
GreatestCommonDivisorAbstract
,GreatestCommonDivisorFake
,GreatestCommonDivisorPrimitive
,GreatestCommonDivisorSimple
,GreatestCommonDivisorSyzygy
,SGCDParallelProxy
public interface GreatestCommonDivisor<C extends GcdRingElem<C>> extends java.io.Serializable
(Non-unique) factorization domain greatest common divisor algorithm interface.- Author:
- Heinz Kredel
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method 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.
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Method Detail
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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.
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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.
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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.
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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'.
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rightContent
GenSolvablePolynomial<C> rightContent(GenSolvablePolynomial<C> P)
GenSolvablePolynomial right content.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- cont(P) with pp(P)*cont(P) = P.
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rightPrimitivePart
GenSolvablePolynomial<C> rightPrimitivePart(GenSolvablePolynomial<C> P)
GenSolvablePolynomial right primitive part.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- pp(P) with pp(P)*cont(P) = P.
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leftContent
GenSolvablePolynomial<C> leftContent(GenSolvablePolynomial<C> P)
GenSolvablePolynomial left content.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- cont(P) with cont(P)*pp(P) = P.
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leftPrimitivePart
GenSolvablePolynomial<C> leftPrimitivePart(GenSolvablePolynomial<C> P)
GenSolvablePolynomial left primitive part.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- pp(P) with cont(P)*pp(P) = P.
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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.
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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.
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