Package edu.jas.fd
Interface GreatestCommonDivisor<C extends GcdRingElem<C>>
- Type Parameters:
C
- coefficient type
- All Superinterfaces:
Serializable
- All Known Implementing Classes:
GreatestCommonDivisorAbstract
,GreatestCommonDivisorFake
,GreatestCommonDivisorPrimitive
,GreatestCommonDivisorSimple
,GreatestCommonDivisorSyzygy
,SGCDParallelProxy
(Non-unique) factorization domain greatest common divisor algorithm
interface.
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Method Summary
Modifier and TypeMethodDescriptionboolean
GenSolvablePolynomial test for left co-prime list.GenSolvablePolynomial left content.GenSolvablePolynomial left co-prime list.GenSolvablePolynomial left greatest common divisor.GenSolvablePolynomial left least common multiple.GenSolvablePolynomial left primitive part.GenSolvablePolynomial right content.GenSolvablePolynomial right greatest common divisor.GenSolvablePolynomial right least common multiple.GenSolvablePolynomial right primitive part.
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Method Details
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leftGcd
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 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 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 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 right content.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- cont(P) with pp(P)*cont(P) = P.
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rightPrimitivePart
GenSolvablePolynomial right primitive part.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- pp(P) with pp(P)*cont(P) = P.
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leftContent
GenSolvablePolynomial left content.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- cont(P) with cont(P)*pp(P) = P.
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leftPrimitivePart
GenSolvablePolynomial left primitive part.- Parameters:
P
- GenSolvablePolynomial.- Returns:
- pp(P) with cont(P)*pp(P) = P.
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leftCoPrime
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
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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