edu.jas.ufd
Class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>

java.lang.Object
  edu.jas.ufd.GreatestCommonDivisorAbstract<C>

All Implemented Interfaces:

GreatestCommonDivisor<C>

Direct Known Subclasses:

GCDProxy, GreatestCommonDivisorModEval, GreatestCommonDivisorModular, GreatestCommonDivisorPrimitive, GreatestCommonDivisorSimple, GreatestCommonDivisorSubres

public abstract class GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>
extends java.lang.Object
implements GreatestCommonDivisor<C>

Greatest common divisor algorithms.

Author:

Heinz Kredel

Constructor Summary

GreatestCommonDivisorAbstract()

Method Summary

C	baseContent(GenPolynomial<C> P) GenPolynomial base coefficient content.
abstract GenPolynomial<C>	baseGcd(GenPolynomial<C> P, GenPolynomial<C> S) Univariate GenPolynomial greatest common divisor.
GenPolynomial<C>	basePrimitivePart(GenPolynomial<C> P) GenPolynomial base coefficient primitive part.
java.util.SortedMap<java.lang.Integer,GenPolynomial<C>>	baseSquarefreeFactors(GenPolynomial<C> P) GenPolynomial polynomial squarefee factorization.
GenPolynomial<C>	baseSquarefreePart(GenPolynomial<C> P) GenPolynomial polynomial greatest squarefee divisor.
GenPolynomial<C>	content(GenPolynomial<C> P) GenPolynomial content.
GenPolynomial<C>	divide(GenPolynomial<C> a, C b) GenPolynomial division.
C	gcd(C a, C b) Coefficient greatest common divisor.
GenPolynomial<C>	gcd(GenPolynomial<C> P, GenPolynomial<C> S) GenPolynomial greatest common divisor.
GenPolynomial<C>	lcm(GenPolynomial<C> P, GenPolynomial<C> S) GenPolynomial least common multiple.
GenPolynomial<C>	primitivePart(GenPolynomial<C> P) GenPolynomial primitive part.
GenPolynomial<C>	recursiveContent(GenPolynomial<GenPolynomial<C>> P) GenPolynomial recursive content.
abstract GenPolynomial<GenPolynomial<C>>	recursiveGcd(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S) Univariate GenPolynomial recursive greatest common divisor.
GenPolynomial<GenPolynomial<C>>	recursivePrimitivePart(GenPolynomial<GenPolynomial<C>> P) GenPolynomial recursive primitive part.
java.util.SortedMap<java.lang.Integer,GenPolynomial<GenPolynomial<C>>>	recursiveSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P) GenPolynomial recursive polynomial squarefee factorization.
GenPolynomial<GenPolynomial<C>>	recursiveSquarefreePart(GenPolynomial<GenPolynomial<C>> P) GenPolynomial recursive polynomial greatest squarefee divisor.
GenPolynomial<C>	resultant(GenPolynomial<C> P, GenPolynomial<C> S) GenPolynomial resultant.
java.util.SortedMap<java.lang.Integer,GenPolynomial<C>>	squarefreeFactors(GenPolynomial<C> P) GenPolynomial squarefree factorization.
GenPolynomial<C>	squarefreePart(GenPolynomial<C> P) GenPolynomial greatest squarefree divisor.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GreatestCommonDivisorAbstract

public GreatestCommonDivisorAbstract()

Method Detail

baseContent

public C baseContent(GenPolynomial<C> P)

GenPolynomial base coefficient content.

Parameters:

P - GenPolynomial.

Returns:

cont(P).

basePrimitivePart

public GenPolynomial<C> basePrimitivePart(GenPolynomial<C> P)

GenPolynomial base coefficient primitive part.

Parameters:

P - GenPolynomial.

Returns:

pp(P).

baseGcd

public abstract GenPolynomial<C> baseGcd(GenPolynomial<C> P,
                                         GenPolynomial<C> S)

Univariate GenPolynomial greatest common divisor. Uses sparse pseudoRemainder for remainder.

Parameters:

P - univariate GenPolynomial.

S - univariate GenPolynomial.

Returns:

gcd(P,S).

baseSquarefreePart

public GenPolynomial<C> baseSquarefreePart(GenPolynomial<C> P)

GenPolynomial polynomial greatest squarefee divisor.

Parameters:

P - GenPolynomial.

Returns:

squarefree(pp(P)).

baseSquarefreeFactors

public java.util.SortedMap<java.lang.Integer,GenPolynomial<C>> baseSquarefreeFactors(GenPolynomial<C> P)

GenPolynomial polynomial squarefee factorization.

Parameters:

P - primitive! GenPolynomial.

Returns:

squarefreeFactors(P).

recursiveContent

public GenPolynomial<C> recursiveContent(GenPolynomial<GenPolynomial<C>> P)

GenPolynomial recursive content.

Parameters:

P - recursive GenPolynomial.

Returns:

cont(P).

recursivePrimitivePart

public GenPolynomial<GenPolynomial<C>> recursivePrimitivePart(GenPolynomial<GenPolynomial<C>> P)

GenPolynomial recursive primitive part.

Parameters:

P - recursive GenPolynomial.

Returns:

pp(P).

recursiveGcd

public abstract GenPolynomial<GenPolynomial<C>> recursiveGcd(GenPolynomial<GenPolynomial<C>> P,
                                                             GenPolynomial<GenPolynomial<C>> S)

Univariate GenPolynomial recursive greatest common divisor. Uses pseudoRemainder for remainder.

Parameters:

P - univariate recursive GenPolynomial.

S - univariate recursive GenPolynomial.

Returns:

gcd(P,S).

recursiveSquarefreePart

public GenPolynomial<GenPolynomial<C>> recursiveSquarefreePart(GenPolynomial<GenPolynomial<C>> P)

GenPolynomial recursive polynomial greatest squarefee divisor.

Parameters:

P - recursive GenPolynomial.

Returns:

squarefree(pp(P)).

recursiveSquarefreeFactors

public java.util.SortedMap<java.lang.Integer,GenPolynomial<GenPolynomial<C>>> recursiveSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P)

GenPolynomial recursive polynomial squarefee factorization.

Parameters:

P - primitive recursive GenPolynomial.

Returns:

squarefreeFactors(P).

content

public GenPolynomial<C> content(GenPolynomial<C> P)

GenPolynomial content.

Specified by:

content in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

Returns:

cont(P).

primitivePart

public GenPolynomial<C> primitivePart(GenPolynomial<C> P)

GenPolynomial primitive part.

Specified by:

primitivePart in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

Returns:

pp(P).

divide

public GenPolynomial<C> divide(GenPolynomial<C> a,
                               C b)

GenPolynomial division. Indirection to GenPolynomial method.

Parameters:

a - GenPolynomial.

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 GenPolynomial<C> gcd(GenPolynomial<C> P,
                            GenPolynomial<C> S)

GenPolynomial greatest common divisor.

Specified by:

gcd in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

gcd(P,S).

lcm

public GenPolynomial<C> lcm(GenPolynomial<C> P,
                            GenPolynomial<C> S)

GenPolynomial least common multiple.

Specified by:

lcm in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

lcm(P,S).

squarefreePart

public GenPolynomial<C> squarefreePart(GenPolynomial<C> P)

GenPolynomial greatest squarefree divisor.

Specified by:

squarefreePart in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

Returns:

squarefree(pp(P)).

squarefreeFactors

public java.util.SortedMap<java.lang.Integer,GenPolynomial<C>> squarefreeFactors(GenPolynomial<C> P)

GenPolynomial squarefree factorization.

Specified by:

squarefreeFactors in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Parameters:

P - primitive GenPolynomial.

Returns:

squarefreeFactors(P).

resultant

public GenPolynomial<C> resultant(GenPolynomial<C> P,
                                  GenPolynomial<C> S)

GenPolynomial resultant.

Specified by:

resultant in interface GreatestCommonDivisor<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

S - GenPolynomial.

Returns:

res(P,S).