GreatestCommonDivisorAbstract

Documentation of 'edu.jas.fd.GreatestCommonDivisorAbstract' Java class GreatestCommonDivisorAbstract

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

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GreatestCommonDivisor<C>, java.io.Serializable

Direct Known Subclasses:

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

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor and Description

GreatestCommonDivisorAbstract()
Constructor.

Constructors
Constructor and Description
`GreatestCommonDivisorAbstract()` Constructor.

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method and Description
`C`	`baseContent(GenSolvablePolynomial<C> P)` GenSolvablePolynomial base coefficient content.
`GenSolvablePolynomial<C>[]`	`baseExtendedGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` Univariate GenSolvablePolynomial extended greatest common divisor.
`abstract GenSolvablePolynomial<C>`	`baseGcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` Univariate GenSolvablePolynomial 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.
`GenSolvablePolynomial<C>`	`basePrimitivePart(GenSolvablePolynomial<C> P)` GenSolvablePolynomial base coefficient primitive part.
`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>`	`content(GenSolvablePolynomial<C> P)` GenSolvablePolynomial content.
`java.util.List<GenSolvablePolynomial<C>>`	`coPrime(GenSolvablePolynomial<C> a, java.util.List<GenSolvablePolynomial<C>> P)` GenSolvablePolynomial co-prime list.
`java.util.List<GenSolvablePolynomial<C>>`	`coPrime(java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial co-prime list.
`java.util.List<GenSolvablePolynomial<C>>`	`coPrimeRec(java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial co-prime list.
`GenSolvablePolynomial<C>`	`divide(GenSolvablePolynomial<C> a, C b)` GenSolvablePolynomial division.
`C`	`gcd(C a, C b)` Coefficient greatest common divisor.
`GenSolvablePolynomial<C>`	`gcd(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` GenSolvablePolynomial greatest common divisor.
`GenSolvablePolynomial<C>`	`gcd(java.util.List<GenSolvablePolynomial<C>> A)` List of GenSolvablePolynomials greatest common divisor.
`boolean`	`isCoPrime(java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial test for co-prime list.
`boolean`	`isCoPrime(java.util.List<GenSolvablePolynomial<C>> P, java.util.List<GenSolvablePolynomial<C>> A)` GenSolvablePolynomial test for co-prime list of given list.
`GenSolvablePolynomial<C>`	`lcm(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)` GenSolvablePolynomial 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>`	`primitivePart(GenSolvablePolynomial<C> P)` GenSolvablePolynomial primitive part.
`GenSolvablePolynomial<C>`	`recursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial recursive content.
`GenSolvablePolynomial<GenPolynomial<C>>`	`recursiveGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)` GenSolvablePolynomial recursive greatest common divisor.
`GenSolvablePolynomial<GenPolynomial<C>>`	`recursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)` GenSolvablePolynomial recursive primitive part.
`abstract GenSolvablePolynomial<GenPolynomial<C>>`	`recursiveUnivariateGcd(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)` Univariate GenSolvablePolynomial recursive greatest common divisor.
`java.lang.String`	`toString()` Get the String representation.

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

- Constructor Detail
  - GreatestCommonDivisorAbstract
```
public GreatestCommonDivisorAbstract()
```
    Constructor.
- Method Detail
  - toString
```
public java.lang.String toString()
```
    Get the String representation.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - baseContent
```
public C baseContent(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial base coefficient content.
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    cont(P).
  - basePrimitivePart
```
public GenSolvablePolynomial<C> basePrimitivePart(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial base coefficient primitive part.
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    pp(P).
  - baseGcd
```
public abstract GenSolvablePolynomial<C> baseGcd(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).
  - recursiveContent
```
public GenSolvablePolynomial<C> recursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial recursive content.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    cont(P).
  - recursivePrimitivePart
```
public GenSolvablePolynomial<GenPolynomial<C>> recursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial recursive primitive part.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    pp(P).
  - baseRecursiveContent
```
public C baseRecursiveContent(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial base recursive content.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    baseCont(P).
  - baseRecursivePrimitivePart
```
public GenSolvablePolynomial<GenPolynomial<C>> baseRecursivePrimitivePart(GenSolvablePolynomial<GenPolynomial<C>> P)
```
    GenSolvablePolynomial base recursive primitive part.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    Returns:
    
    basePP(P).
  - recursiveGcd
```
public GenSolvablePolynomial<GenPolynomial<C>> recursiveGcd(GenSolvablePolynomial<GenPolynomial<C>> P,
                                                            GenSolvablePolynomial<GenPolynomial<C>> S)
```
    GenSolvablePolynomial recursive greatest common divisor. Uses pseudoRemainder for remainder.
    
    Parameters:
    
    P - recursive GenSolvablePolynomial.
    
    S - recursive GenSolvablePolynomial.
    
    Returns:
    
    gcd(P,S).
  - recursiveUnivariateGcd
```
public abstract GenSolvablePolynomial<GenPolynomial<C>> recursiveUnivariateGcd(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).
  - content
```
public GenSolvablePolynomial<C> content(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial content.
    
    Specified by:
    
    content in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    cont(P).
  - primitivePart
```
public GenSolvablePolynomial<C> primitivePart(GenSolvablePolynomial<C> P)
```
    GenSolvablePolynomial primitive part.
    
    Specified by:
    
    primitivePart in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    Returns:
    
    pp(P).
  - divide
```
public GenSolvablePolynomial<C> divide(GenSolvablePolynomial<C> a,
                                       C b)
```
    GenSolvablePolynomial division. Indirection to GenSolvablePolynomial method.
    
    Parameters:
    
    a - GenSolvablePolynomial.
    
    b - coefficient.
    
    Returns:
    
    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).
  - gcd
```
public GenSolvablePolynomial<C> gcd(GenSolvablePolynomial<C> P,
                                    GenSolvablePolynomial<C> S)
```
    GenSolvablePolynomial greatest common divisor.
    
    Specified by:
    
    gcd in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    S - GenSolvablePolynomial.
    
    Returns:
    
    gcd(P,S).
  - lcm
```
public GenSolvablePolynomial<C> lcm(GenSolvablePolynomial<C> P,
                                    GenSolvablePolynomial<C> S)
```
    GenSolvablePolynomial least common multiple.
    
    Specified by:
    
    lcm in interface GreatestCommonDivisor<C extends GcdRingElem<C>>
    
    Parameters:
    
    P - GenSolvablePolynomial.
    
    S - GenSolvablePolynomial.
    
    Returns:
    
    lcm(P,S).
  - gcd
```
public GenSolvablePolynomial<C> gcd(java.util.List<GenSolvablePolynomial<C>> A)
```
    List of GenSolvablePolynomials greatest common divisor.
    
    Parameters:
    
    A - non empty list of GenSolvablePolynomials.
    
    Returns:
    
    gcd(A_i).
  - coPrime
```
public java.util.List<GenSolvablePolynomial<C>> coPrime(java.util.List<GenSolvablePolynomial<C>> A)
```
    GenSolvablePolynomial co-prime list.
    
    Specified by:
    
    coPrime 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.
  - coPrimeRec
```
public java.util.List<GenSolvablePolynomial<C>> coPrimeRec(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.
  - coPrime
```
public java.util.List<GenSolvablePolynomial<C>> coPrime(GenSolvablePolynomial<C> a,
                                                        java.util.List<GenSolvablePolynomial<C>> P)
```
    GenSolvablePolynomial 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.
  - isCoPrime
```
public boolean isCoPrime(java.util.List<GenSolvablePolynomial<C>> A)
```
    GenSolvablePolynomial test for co-prime list.
    
    Specified by:
    
    isCoPrime 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.
  - isCoPrime
```
public boolean isCoPrime(java.util.List<GenSolvablePolynomial<C>> P,
                         java.util.List<GenSolvablePolynomial<C>> A)
```
    GenSolvablePolynomial test for 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

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Class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

GreatestCommonDivisorAbstract

Method Detail

toString

baseContent

basePrimitivePart

baseGcd

recursiveContent

recursivePrimitivePart

baseRecursiveContent

baseRecursivePrimitivePart

recursiveGcd

recursiveUnivariateGcd

content

primitivePart

divide

gcd

gcd

lcm

gcd

coPrime

coPrimeRec

coPrime

isCoPrime

isCoPrime

baseExtendedGcd

baseHalfExtendedGcd

baseGcdDiophant

leftOreCond

leftOreCond