Class SquarefreeFieldCharP<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.SquarefreeAbstract<C>

edu.jas.ufd.SquarefreeFieldCharP<C>

All Implemented Interfaces:

Squarefree<C>, Serializable

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.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final AlgebraicNumberRing<C>	aCoFac	Factory for a algebraic extension of a finite field of characteristic p coefficients.
protected final RingFactory<C>	coFac	Factory for finite field of characteristic p coefficients.
private static final org.apache.logging.log4j.Logger	logger
protected final QuotientRing<C>	qCoFac	Factory for a transcendental extension of a finite field of characteristic p coefficients.

Fields inherited from class SquarefreeAbstract

engine

Constructor Summary

Constructors

Constructor	Description
SquarefreeFieldCharP(RingFactory<C> fac)	Constructor.

Method Summary

Modifier and Type	Method	Description
abstract GenPolynomial<C>	baseRootCharacteristic(GenPolynomial<C> P)	GenPolynomial char-th root univariate polynomial.
SortedMap<GenPolynomial<C>, 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, SortedMap<GenPolynomial<C>, 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, SortedMap<GenPolynomial<GenPolynomial<C>>, 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.
SortedMap<GenPolynomial<GenPolynomial<C>>, 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.
SortedMap<C,Long>	squarefreeFactors(C coeff)	Coefficient squarefree factorization.
SortedMap<GenPolynomial<C>, Long>	squarefreeFactors(GenPolynomial<C> P)	GenPolynomial squarefree factorization.
GenPolynomial<C>	squarefreePart(GenPolynomial<C> P)	GenPolynomial greatest squarefree divisor.
String	toString()	Get the String representation.

Methods inherited from class SquarefreeAbstract

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

Methods inherited from class Object

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

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

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 Details

SquarefreeFieldCharP

public SquarefreeFieldCharP(RingFactory<C> fac)

Constructor.

Method Details

toString

public String toString()

Get the String representation.

Overrides:

toString in class 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 SortedMap<GenPolynomial<C>, 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 A = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree and gcd(p_i, p_j) = 1, for i != j.

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 SortedMap<GenPolynomial<GenPolynomial<C>>, 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 and gcd(p_i, p_j) = 1, for i != j.

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 SortedMap<GenPolynomial<C>, 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 and gcd(p_i, p_j) = 1, for i != j.

squarefreeFactors

public SortedMap<C,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 coeff = prod_{i=1,...,k} p_i^{e_i} and p_i squarefree and gcd(p_i, p_j) = 1, for i != j.

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,
 SortedMap<GenPolynomial<C>, 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,
 SortedMap<GenPolynomial<GenPolynomial<C>>, 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.