GreatestCommonDivisorAbstract

java.lang.Object
- edu.jas.fd.GreatestCommonDivisorAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GreatestCommonDivisor<C>, java.io.Serializable

Direct Known Subclasses:

GreatestCommonDivisorFake, GreatestCommonDivisorLR, GreatestCommonDivisorPrimitive, GreatestCommonDivisorSimple, GreatestCommonDivisorSyzygy, SGCDParallelProxy
```
public abstract class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>
extends java.lang.Object
implements GreatestCommonDivisor<C>
```
(Non-unique) factorization domain greatest common divisor common algorithms.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor and Description
`GreatestCommonDivisorAbstract(RingFactory<C> cf)` Constructor.
`GreatestCommonDivisorAbstract(RingFactory<C> cf, SolvableSyzygyAbstract<C> s)` Constructor.

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method and Description
`GenSolvablePolynomial<C>[]`	`baseExtendedGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` Univariate GenSolvablePolynomial extended greatest common divisor.
`GenSolvablePolynomial<C>[]`	`baseGcdDiophant(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S, GenSolvablePolynomial<C> c)` Univariate GenSolvablePolynomial greatest common divisor diophantine version.
`GenSolvablePolynomial<C>[]`	`baseHalfExtendedGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` Univariate GenSolvablePolynomial half extended greatest comon divisor.
`C`	`baseRecursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial base recursive content.
`GenSolvablePolynomial<GenPolynomial<C>>`	`baseRecursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial base recursive primitive part.
`GenSolvablePolynomial<C>`	`divide(GenSolvablePolynomial<C> a, C b)` GenSolvablePolynomial division.
`C`	`gcd(C a, C b)` Coefficient greatest common divisor.
`boolean`	`isLeftCoPrime(java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial test for co-prime list.
`boolean`	`isLeftCoPrime(java.util.List<GenSolvablePolynomial<C>> P, java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial test for left co-prime list of given list.
`C`	`leftBaseContent(GenSolvablePolynomial<C> P)` GenSolvablePolynomial base coefficient content.
`abstract GenSolvablePolynomial<C>`	`leftBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` Univariate GenSolvablePolynomial greatest common divisor.
`GenSolvablePolynomial<C>`	`leftBasePrimitivePart(GenSolvablePolynomial<C> P)` GenSolvablePolynomial base coefficient primitive part.
`GenSolvablePolynomial<C>`	`leftContent(GenSolvablePolynomial<C> P)` GenSolvablePolynomial left content.
`java.util.List<GenSolvablePolynomial<C>>`	`leftCoPrime(GenSolvablePolynomial<C> a, java.util.List<GenSolvablePolynomial<C>> P)` GenSolvablePolynomial left co-prime list.
`java.util.List<GenSolvablePolynomial<C>>`	`leftCoPrime(java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial co-prime list.
`java.util.List<GenSolvablePolynomial<C>>`	`leftCoPrimeRec(java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial left co-prime list.
`GenSolvablePolynomial<C>`	`leftGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` GenSolvablePolynomial greatest common divisor.
`GenSolvablePolynomial<C>`	`leftGcd(java.util.List<GenSolvablePolynomial<C>> A)` List of GenSolvablePolynomials left greatest common divisor.
`GenSolvablePolynomial<C>`	`leftLcm(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` GenSolvablePolynomial left least common multiple.
`C[]`	`leftOreCond(C a, C b)` Coefficient left Ore condition.
`GenSolvablePolynomial<C>[]`	`leftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)` Left Ore condition.
`GenSolvablePolynomial<C>`	`leftPrimitivePart(GenSolvablePolynomial<C> P)` GenSolvablePolynomial left primitive part.
`GenSolvablePolynomial<C>`	`leftRecursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial left recursive content.
`GenSolvablePolynomial<GenPolynomial<C>>`	`leftRecursiveGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)` GenSolvablePolynomial left recursive greatest common divisor.
`GenSolvablePolynomial<GenPolynomial<C>>`	`leftRecursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial left recursive primitive part.
`abstract GenSolvablePolynomial<GenPolynomial<C>>`	`leftRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)` Univariate GenSolvablePolynomial recursive greatest common divisor.
`GenSolvablePolynomial<C>`	`recursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial commuting recursive content.
`C`	`rightBaseContent(GenSolvablePolynomial<C> P)` GenSolvablePolynomial right base coefficient content.
`abstract GenSolvablePolynomial<C>`	`rightBaseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` Univariate GenSolvablePolynomial right greatest common divisor.
`GenSolvablePolynomial<C>`	`rightBasePrimitivePart(GenSolvablePolynomial<C> P)` GenSolvablePolynomial right base coefficient 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.
`C[]`	`rightOreCond(C a, C b)` Coefficient rigth Ore condition.
`GenSolvablePolynomial<C>[]`	`rightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)` Right Ore condition.
`GenSolvablePolynomial<C>`	`rightPrimitivePart(GenSolvablePolynomial<C> P)` GenSolvablePolynomial right primitive part.
`GenSolvablePolynomial<C>`	`rightRecursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial right recursive content.
`GenSolvablePolynomial<GenPolynomial<C>>`	`rightRecursiveGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)` GenSolvablePolynomial right recursive greatest common divisor.
`GenSolvablePolynomial<GenPolynomial<C>>`	`rightRecursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial right recursive primitive part.
`abstract GenSolvablePolynomial<GenPolynomial<C>>`	`rightRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)` Univariate GenSolvablePolynomial right recursive greatest common divisor.
`java.lang.String`	`toString()` Get the String representation.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - GreatestCommonDivisorAbstract
```
public GreatestCommonDivisorAbstract(RingFactory<C> cf)
```
    Constructor.
    
    Parameters:
    
    cf - coefficient ring.
  - GreatestCommonDivisorAbstract
```
public GreatestCommonDivisorAbstract(RingFactory<C> cf,
                                     SolvableSyzygyAbstract<C> s)
```
    Constructor.
    
    Parameters:
    
    cf - coefficient ring.
    
    s - algorithm for SolvableSyzygy computation.
- Method Detail
  - toString
```
public java.lang.String toString()
```
    Get the String representation.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - leftBaseContent
```
public C leftBaseContent(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial base coefficient content.
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    cont(P) with pp(P)*cont(P) = P.
  - rightBaseContent
```
public C rightBaseContent(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial right base coefficient content.
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    cont(P) with cont(P)*pp(P) = P.
  - leftBasePrimitivePart
```
public GenSolvablePolynomial<C> leftBasePrimitivePart(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial base coefficient primitive part.
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    pp(P) with pp(P)*cont(P) = P.
  - rightBasePrimitivePart
```
public GenSolvablePolynomial<C> rightBasePrimitivePart(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial right base coefficient primitive part.
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    pp(P) with cont(P)*pp(P) = P.
  - leftBaseGcd
```
public abstract GenSolvablePolynomial<C> leftBaseGcd(GenSolvablePolynomial<C> P,
                                                     GenSolvablePolynomial<C> S)
```
    Univariate GenSolvablePolynomial greatest common divisor. Uses sparse pseudoRemainder for remainder.
    
    Parameters:
    
    P - univariate GenSolvablePolynomial.
    
    S - univariate GenSolvablePolynomial.
    
    Returns:
    
    gcd(P,S) with P = P'*gcd(P,S) and S = S'*gcd(P,S).
  - rightBaseGcd
```
public abstract GenSolvablePolynomial<C> rightBaseGcd(GenSolvablePolynomial<C> P,
                                                      GenSolvablePolynomial<C> S)
```
    Univariate GenSolvablePolynomial right greatest common divisor. Uses sparse pseudoRemainder for remainder.
    
    Parameters:
    
    P - univariate GenSolvablePolynomial.
    
    S - univariate GenSolvablePolynomial.
    
    Returns:
    
    gcd(P,S) with P = gcd(P,S)*P' and S = gcd(P,S)*S'.
  - recursiveContent
```
public GenSolvablePolynomial<C> recursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial commuting recursive content.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial with commuting main and coefficient variables.
    
    Returns:
    
    cont(P) with cont(P)*pp(P) = pp(P)*cont(P).
  - rightRecursiveContent
```
public GenSolvablePolynomial<C> rightRecursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial right recursive content.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    cont(P) with pp(P)*cont(P) = P.
  - rightRecursivePrimitivePart
```
public GenSolvablePolynomial<GenPolynomial<C>> rightRecursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial right recursive primitive part.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    pp(P) with pp(P)*cont(P) = P.
  - leftRecursiveContent
```
public GenSolvablePolynomial<C> leftRecursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial left recursive content.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    cont(P) with cont(P)*pp(P) = P.
  - leftRecursivePrimitivePart
```
public GenSolvablePolynomial<GenPolynomial<C>> leftRecursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial left recursive primitive part.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    pp(P) with cont(P)*pp(P) = P.
  - baseRecursiveContent
```
public C baseRecursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial base recursive content.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    baseCont(P) with pp(P)*cont(P) = P.
  - baseRecursivePrimitivePart
```
public GenSolvablePolynomial<GenPolynomial<C>> baseRecursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial base recursive primitive part.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    basePP(P) with pp(P)*cont(P) = P.
  - leftRecursiveGcd
```
public GenSolvablePolynomial<GenPolynomial<C>> leftRecursiveGcd(GenSolvablePolynomial<GenPolynomial<C>> P,
                                                                GenSolvablePolynomial<GenPolynomial<C>> S)
```
    GenSolvablePolynomial left recursive greatest common divisor. Uses pseudoRemainder for remainder.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    S - recursive 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.
  - rightRecursiveGcd
```
public GenSolvablePolynomial<GenPolynomial<C>> rightRecursiveGcd(GenSolvablePolynomial<GenPolynomial<C>> P,
                                                                 GenSolvablePolynomial<GenPolynomial<C>> S)
```
    GenSolvablePolynomial right recursive greatest common divisor. Uses pseudoRemainder for remainder.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    S - recursive 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.
  - leftRecursiveUnivariateGcd
```
public abstract GenSolvablePolynomial<GenPolynomial<C>> leftRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P,
                                                                                   GenSolvablePolynomial<GenPolynomial<C>> S)
```
    Univariate GenSolvablePolynomial recursive greatest common divisor. Uses pseudoRemainder for remainder.
    
    Parameters:
    
    P - univariate recursive GenSolvablePolynomial.
    
    S - univariate recursive 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.
  - rightRecursiveUnivariateGcd
```
public abstract GenSolvablePolynomial<GenPolynomial<C>> rightRecursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P,
                                                                                    GenSolvablePolynomial<GenPolynomial<C>> S)
```
    Univariate GenSolvablePolynomial right recursive greatest common divisor. Uses pseudoRemainder for remainder.
    
    Parameters:
    
    P - univariate recursive GenSolvablePolynomial.
    
    S - univariate recursive 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.
  - rightContent
```
public GenSolvablePolynomial<C> rightContent(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial right content.
    
    Specified by:
    
    rightContent in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    cont(P) with pp(P)*cont(P) = P.
  - rightPrimitivePart
```
public GenSolvablePolynomial<C> rightPrimitivePart(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial right primitive part.
    
    Specified by:
    
    rightPrimitivePart in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    pp(P) with pp(P)*cont(P) = P.
  - leftContent
```
public GenSolvablePolynomial<C> leftContent(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial left content.
    
    Specified by:
    
    leftContent in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    cont(P) with cont(P)*pp(P) = P.
  - leftPrimitivePart
```
public GenSolvablePolynomial<C> leftPrimitivePart(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial left primitive part.
    
    Specified by:
    
    leftPrimitivePart in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    pp(P) with cont(P)*pp(P) = P.
  - divide
```
public GenSolvablePolynomial<C> divide(GenSolvablePolynomial<C> a,
                                       C b)
```
    GenSolvablePolynomial division. Indirection to GenSolvablePolynomial method.
    
    Parameters:
    
    a - GenSolvablePolynomial.
    
    b - coefficient.
    
    Returns:
    
    a' = a/b with a = a'*b.
  - gcd
```
public C gcd(C a,
             C b)
```
    Coefficient greatest common divisor. Indirection to coefficient method.
    
    Parameters:
    
    a - coefficient.
    
    b - coefficient.
    
    Returns:
    
    gcd(a,b) with a = a'*gcd(a,b) and b = b'*gcd(a,b).
  - leftGcd
```
public GenSolvablePolynomial<C> leftGcd(GenSolvablePolynomial<C> P,
                                        GenSolvablePolynomial<C> S)
```
    GenSolvablePolynomial greatest common divisor.
    
    Specified by:
    
    leftGcd in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    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
```
public GenSolvablePolynomial<C> leftLcm(GenSolvablePolynomial<C> P,
                                        GenSolvablePolynomial<C> S)
```
    GenSolvablePolynomial left least common multiple.
    
    Specified by:
    
    leftLcm in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    S - GenSolvablePolynomial.
    
    Returns:
    
    lcm(P,S) with lcm(P,S) = P'*P = S'*S.
  - rightGcd
```
public GenSolvablePolynomial<C> rightGcd(GenSolvablePolynomial<C> P,
                                         GenSolvablePolynomial<C> S)
```
    GenSolvablePolynomial right greatest common divisor.
    
    Specified by:
    
    rightGcd in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    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.
  - rightLcm
```
public GenSolvablePolynomial<C> rightLcm(GenSolvablePolynomial<C> P,
                                         GenSolvablePolynomial<C> S)
```
    GenSolvablePolynomial right least common multiple.
    
    Specified by:
    
    rightLcm in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    S - GenSolvablePolynomial.
    
    Returns:
    
    lcm(P,S) with lcm(P,S) = P*P' = S*S'.
  - leftGcd
```
public GenSolvablePolynomial<C> leftGcd(java.util.List<GenSolvablePolynomial<C>> A)
```
    List of GenSolvablePolynomials left greatest common divisor.
    
    Parameters:
    
    A - non empty list of GenSolvablePolynomials.
    
    Returns:
    
    gcd(A_i) with A_i = A'_i*gcd(A_i)*a_i, where deg_main(a_i) == 0.
  - leftCoPrime
```
public java.util.List<GenSolvablePolynomial<C>> leftCoPrime(java.util.List<GenSolvablePolynomial<C>> A)
```
    GenSolvablePolynomial co-prime list.
    
    Specified by:
    
    leftCoPrime in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    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.
  - leftCoPrimeRec
```
public java.util.List<GenSolvablePolynomial<C>> leftCoPrimeRec(java.util.List<GenSolvablePolynomial<C>> A)
```
    GenSolvablePolynomial left 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.
  - leftCoPrime
```
public java.util.List<GenSolvablePolynomial<C>> leftCoPrime(GenSolvablePolynomial<C> a,
                                                            java.util.List<GenSolvablePolynomial<C>> P)
```
    GenSolvablePolynomial left co-prime list.
    
    Parameters:
    
    a - GenSolvablePolynomial.
    
    P - co-prime list of GenSolvablePolynomials.
    
    Returns:
    
    B with gcd(b,c) = 1 for all b != c in B and for non-constant a there exists b in P with b|a. B does not contain zero or constant polynomials.
  - isLeftCoPrime
```
public boolean isLeftCoPrime(java.util.List<GenSolvablePolynomial<C>> A)
```
    GenSolvablePolynomial test for co-prime list.
    
    Specified by:
    
    isLeftCoPrime in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    A - list of GenSolvablePolynomials.
    
    Returns:
    
    true if gcd(b,c) = 1 for all b != c in B, else false.
  - isLeftCoPrime
```
public boolean isLeftCoPrime(java.util.List<GenSolvablePolynomial<C>> P,
                             java.util.List<GenSolvablePolynomial<C>> A)
```
    GenSolvablePolynomial test for left co-prime list of given list.
    
    Parameters:
    
    A - list of GenSolvablePolynomials.
    
    P - list of co-prime GenSolvablePolynomials.
    
    Returns:
    
    true if isCoPrime(P) and for all a in A exists p in P with p | a, else false.
  - baseExtendedGcd
```
public GenSolvablePolynomial<C>[] baseExtendedGcd(GenSolvablePolynomial<C> P,
                                                  GenSolvablePolynomial<C> S)
```
    Univariate GenSolvablePolynomial extended greatest common divisor. Uses sparse pseudoRemainder for remainder.
    
    Parameters:
    
    P - univariate GenSolvablePolynomial.
    
    S - univariate GenSolvablePolynomial.
    
    Returns:
    
    [ gcd(P,S), a, b ] with a*P + b*S = gcd(P,S).
  - baseHalfExtendedGcd
```
public GenSolvablePolynomial<C>[] baseHalfExtendedGcd(GenSolvablePolynomial<C> P,
                                                      GenSolvablePolynomial<C> S)
```
    Univariate GenSolvablePolynomial half extended greatest comon divisor. Uses sparse pseudoRemainder for remainder.
    
    Parameters:
    
    S - GenSolvablePolynomial.
    
    Returns:
    
    [ gcd(P,S), a ] with a*P + b*S = gcd(P,S).
  - baseGcdDiophant
```
public GenSolvablePolynomial<C>[] baseGcdDiophant(GenSolvablePolynomial<C> P,
                                                  GenSolvablePolynomial<C> S,
                                                  GenSolvablePolynomial<C> c)
```
    Univariate GenSolvablePolynomial greatest common divisor diophantine version.
    
    Parameters:
    
    P - univariate GenSolvablePolynomial.
    
    S - univariate GenSolvablePolynomial.
    
    c - univariate GenSolvablePolynomial.
    
    Returns:
    
    [ a, b ] with a*P + b*S = c and deg(a) < deg(S).
  - leftOreCond
```
public C[] leftOreCond(C a,
                       C b)
```
    Coefficient left Ore condition. Generators for the left Ore condition of two coefficients.
    
    Parameters:
    
    a - coefficient.
    
    b - coefficient.
    
    Returns:
    
    [oa, ob] = leftOreCond(a,b), with oa*a == ob*b.
  - leftOreCond
```
public GenSolvablePolynomial<C>[] leftOreCond(GenSolvablePolynomial<C> a,
                                              GenSolvablePolynomial<C> b)
```
    Left Ore condition. Generators for the left Ore condition of two solvable polynomials.
    
    Parameters:
    
    a - solvable polynomial
    
    b - solvable polynomial
    
    Returns:
    
    [p,q] with p*a = q*b
  - rightOreCond
```
public C[] rightOreCond(C a,
                        C b)
```
    Coefficient rigth Ore condition. Generators for the right Ore condition of two coefficients.
    
    Parameters:
    
    a - coefficient.
    
    b - coefficient.
    
    Returns:
    
    [oa, ob] = rightOreCond(a,b), with a*oa == b*ob.
  - rightOreCond
```
public GenSolvablePolynomial<C>[] rightOreCond(GenSolvablePolynomial<C> a,
                                               GenSolvablePolynomial<C> b)
```
    Right Ore condition. Generators for the right Ore condition of two solvable polynomials.
    
    Parameters:
    
    a - solvable polynomial
    
    b - solvable polynomial
    
    Returns:
    
    [p,q] with a*p = b*q

Class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

GreatestCommonDivisorAbstract

GreatestCommonDivisorAbstract

Method Detail

toString

leftBaseContent

rightBaseContent

leftBasePrimitivePart

rightBasePrimitivePart

leftBaseGcd

rightBaseGcd

recursiveContent

rightRecursiveContent

rightRecursivePrimitivePart

leftRecursiveContent

leftRecursivePrimitivePart

baseRecursiveContent

baseRecursivePrimitivePart

leftRecursiveGcd

rightRecursiveGcd

leftRecursiveUnivariateGcd

rightRecursiveUnivariateGcd

rightContent

rightPrimitivePart

leftContent

leftPrimitivePart

divide

gcd

leftGcd

leftLcm

rightGcd

rightLcm

leftGcd

leftCoPrime

leftCoPrimeRec

leftCoPrime

isLeftCoPrime

isLeftCoPrime

baseExtendedGcd

baseHalfExtendedGcd

baseGcdDiophant

leftOreCond

leftOreCond

rightOreCond

rightOreCond