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

java.lang.Object
  edu.jas.ufd.SquarefreeAbstract<C>
      edu.jas.ufd.SquarefreeFieldCharP<C>

All Implemented Interfaces:

Squarefree<C>

Direct Known Subclasses:

SquarefreeFiniteFieldCharP, SquarefreeInfiniteAlgebraicFieldCharP, SquarefreeInfiniteFieldCharP

public abstract class SquarefreeFieldCharP<C extends GcdRingElem<C>>
extends SquarefreeAbstract<C>

Squarefree decomposition for coefficient fields of characteristic p.

Author:

Heinz Kredel

Field Summary

protected AlgebraicNumberRing<C>	aCoFac Factory for a algebraic extension of a finite field of characteristic p coefficients.
protected RingFactory<C>	coFac Factory for finite field of characteristic p coefficients.
protected QuotientRing<C>	qCoFac Factory for a transcendental extension of a finite field of characteristic p coefficients.
protected SquarefreeAbstract<C>	rengine GCD engine for characteristic p base coefficients.

Fields inherited from class edu.jas.ufd.SquarefreeAbstract

engine

Constructor Summary

SquarefreeFieldCharP(RingFactory<C> fac)
Constructor.

Method Summary

abstract GenPolynomial<C>	baseRootCharacteristic(GenPolynomial<C> P) GenPolynomial char-th root univariate polynomial.
java.util.SortedMap<GenPolynomial<C>,java.lang.Long>	baseSquarefreeFactors(GenPolynomial<C> A) GenPolynomial polynomial squarefree factorization.
GenPolynomial<C>	baseSquarefreePart(GenPolynomial<C> P) GenPolynomial polynomial greatest squarefree divisor.
boolean	isCharRoot(GenPolynomial<C> P, java.util.SortedMap<GenPolynomial<C>,java.lang.Long> F) Polynomial is char-th root.
boolean	isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> r) Recursive polynomial is char-th root.
boolean	isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P, java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long> F) Recursive polynomial is char-th root.
abstract GenPolynomial<GenPolynomial<C>>	recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<C>> P) GenPolynomial char-th root univariate polynomial with polynomial coefficients.
java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long>	recursiveUnivariateSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P) GenPolynomial recursive univariate polynomial squarefree factorization.
GenPolynomial<GenPolynomial<C>>	recursiveUnivariateSquarefreePart(GenPolynomial<GenPolynomial<C>> P) GenPolynomial recursive univariate polynomial greatest squarefree divisor.
java.util.SortedMap<C,java.lang.Long>	squarefreeFactors(C coeff) Coefficient squarefree factorization.
java.util.SortedMap<GenPolynomial<C>,java.lang.Long>	squarefreeFactors(GenPolynomial<C> P) GenPolynomial squarefree factorization.
GenPolynomial<C>	squarefreePart(GenPolynomial<C> P) GenPolynomial greatest squarefree divisor.
java.lang.String	toString() Get the String representation.

Methods inherited from class edu.jas.ufd.SquarefreeAbstract

basePartialFraction, coPrimeSquarefree, coPrimeSquarefree, factorCount, isBasePartialFraction, isCoPrimeSquarefree, isFactorization, isFactorization, isRecursiveFactorization, isRecursiveSquarefree, isSquarefree, isSquarefree, recursiveSquarefreeFactors, recursiveSquarefreePart, squarefreePart

Methods inherited from class java.lang.Object

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

Field Detail

rengine

protected final SquarefreeAbstract<C extends GcdRingElem<C>> rengine

GCD engine for characteristic p base coefficients.

coFac

protected final RingFactory<C extends GcdRingElem<C>> coFac

Factory for finite field of characteristic p coefficients.

aCoFac

protected final AlgebraicNumberRing<C extends GcdRingElem<C>> aCoFac

Factory for a algebraic extension of a finite field of characteristic p coefficients. If coFac is an algebraic extension, then aCoFac is equal to coFac, else aCoFac is null.

qCoFac

protected final QuotientRing<C extends GcdRingElem<C>> qCoFac

Factory for a transcendental extension of a finite field of characteristic p coefficients. If coFac is an transcendental extension, then qCoFac is equal to coFac, else qCoFac is null.

Constructor Detail

SquarefreeFieldCharP

public SquarefreeFieldCharP(RingFactory<C> fac)

Constructor.

Method Detail

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

baseSquarefreePart

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

GenPolynomial polynomial greatest squarefree divisor.

Specified by:

baseSquarefreePart in class SquarefreeAbstract<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

Returns:

squarefree(pp(P)).

baseSquarefreeFactors

public java.util.SortedMap<GenPolynomial<C>,java.lang.Long> baseSquarefreeFactors(GenPolynomial<C> A)

GenPolynomial polynomial squarefree factorization.

Specified by:

baseSquarefreeFactors in class SquarefreeAbstract<C extends GcdRingElem<C>>

Parameters:

A - GenPolynomial.

Returns:

[p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.

recursiveUnivariateSquarefreePart

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

GenPolynomial recursive univariate polynomial greatest squarefree divisor.

Specified by:

recursiveUnivariateSquarefreePart in class SquarefreeAbstract<C extends GcdRingElem<C>>

Parameters:

P - recursive univariate GenPolynomial.

Returns:

squarefree(pp(P)).

recursiveUnivariateSquarefreeFactors

public java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long> recursiveUnivariateSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P)

GenPolynomial recursive univariate polynomial squarefree factorization.

Specified by:

recursiveUnivariateSquarefreeFactors in class SquarefreeAbstract<C extends GcdRingElem<C>>

Parameters:

P - recursive univariate GenPolynomial.

Returns:

[p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.

squarefreePart

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

GenPolynomial greatest squarefree divisor.

Specified by:

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

Specified by:

squarefreePart in class SquarefreeAbstract<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

Returns:

squarefree(pp(P)).

squarefreeFactors

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

GenPolynomial squarefree factorization.

Specified by:

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

Specified by:

squarefreeFactors in class SquarefreeAbstract<C extends GcdRingElem<C>>

Parameters:

P - GenPolynomial.

Returns:

[p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.

squarefreeFactors

public java.util.SortedMap<C,java.lang.Long> squarefreeFactors(C coeff)

Coefficient squarefree factorization.

Specified by:

squarefreeFactors in class SquarefreeAbstract<C extends GcdRingElem<C>>

Parameters:

coeff - coefficient.

Returns:

[p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree.

baseRootCharacteristic

public abstract GenPolynomial<C> baseRootCharacteristic(GenPolynomial<C> P)

GenPolynomial char-th root univariate polynomial.

Parameters:

P - GenPolynomial.

Returns:

char-th_rootOf(P), or null if no char-th root.

recursiveUnivariateRootCharacteristic

public abstract GenPolynomial<GenPolynomial<C>> recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<C>> P)

GenPolynomial char-th root univariate polynomial with polynomial coefficients.

Parameters:

P - recursive univariate GenPolynomial.

Returns:

char-th_rootOf(P), or null if P is no char-th root.

isCharRoot

public boolean isCharRoot(GenPolynomial<C> P,
                          java.util.SortedMap<GenPolynomial<C>,java.lang.Long> F)

Polynomial is char-th root.

Parameters:

P - polynomial.

F - = [p_1 -> e_1, ..., p_k -> e_k].

Returns:

true if P = prod_{i=1,...,k} p_i**(e_i*p), else false.

isRecursiveCharRoot

public boolean isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P,
                                   java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long> F)

Recursive polynomial is char-th root.

Parameters:

P - recursive polynomial.

F - = [p_1 -> e_1, ..., p_k -> e_k].

Returns:

true if P = prod_{i=1,...,k} p_i**(e_i*p), else false.

isRecursiveCharRoot

public boolean isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P,
                                   GenPolynomial<GenPolynomial<C>> r)

Recursive polynomial is char-th root.

Parameters:

P - recursive polynomial.

r - = recursive polynomial.

Returns:

true if P = r**p, else false.