Class SquarefreeInfiniteAlgebraicFieldCharP<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.SquarefreeAbstract<AlgebraicNumber<C>>

edu.jas.ufd.SquarefreeFieldCharP<AlgebraicNumber<C>>

edu.jas.ufd.SquarefreeInfiniteAlgebraicFieldCharP<C>

All Implemented Interfaces:

Squarefree<AlgebraicNumber<C>>, Serializable

public class SquarefreeInfiniteAlgebraicFieldCharP<C extends GcdRingElem<C>>
extends SquarefreeFieldCharP<AlgebraicNumber<C>>

Squarefree decomposition for algebraic extensions of infinite coefficient fields of characteristic p > 0.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final SquarefreeAbstract<C>	aengine	Squarefree engine for infinite ring of characteristic p base coefficients.
private static final org.apache.logging.log4j.Logger	logger

Fields inherited from class SquarefreeFieldCharP

aCoFac, coFac, qCoFac

Fields inherited from class SquarefreeAbstract

engine

Constructor Summary

Constructors

Constructor	Description
SquarefreeInfiniteAlgebraicFieldCharP(RingFactory<AlgebraicNumber<C>> fac)	Constructor.

Method Summary

Modifier and Type	Method	Description
GenPolynomial<AlgebraicNumber<C>>	baseRootCharacteristic(GenPolynomial<AlgebraicNumber<C>> P)	GenPolynomial char-th root univariate polynomial.
GenPolynomial<GenPolynomial<AlgebraicNumber<C>>>	recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<AlgebraicNumber<C>>> P)	GenPolynomial char-th root univariate polynomial with polynomial coefficients.
SortedMap<AlgebraicNumber<C>, Long>	rootCharacteristic(AlgebraicNumber<C> P)	Characteristics root of a AlgebraicNumber.
GenPolynomial<AlgebraicNumber<C>>	rootCharacteristic(GenPolynomial<AlgebraicNumber<C>> P)	GenPolynomial char-th root main variable.
SortedMap<AlgebraicNumber<C>, Long>	squarefreeFactors(AlgebraicNumber<C> P)	Squarefree factors of a AlgebraicNumber.

Methods inherited from class SquarefreeFieldCharP

baseSquarefreeFactors, baseSquarefreePart, isCharRoot, isRecursiveCharRoot, isRecursiveCharRoot, recursiveUnivariateSquarefreeFactors, recursiveUnivariateSquarefreePart, squarefreeFactors, squarefreePart, toString

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

aengine

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

Squarefree engine for infinite ring of characteristic p base coefficients.

Constructor Details

SquarefreeInfiniteAlgebraicFieldCharP

public SquarefreeInfiniteAlgebraicFieldCharP(RingFactory<AlgebraicNumber<C>> fac)

Constructor.

Method Details

squarefreeFactors

public SortedMap<AlgebraicNumber<C>, Long> squarefreeFactors(AlgebraicNumber<C> P)

Squarefree factors of a AlgebraicNumber.

Overrides:

squarefreeFactors in class SquarefreeFieldCharP<AlgebraicNumber<C extends GcdRingElem<C>>>

Parameters:

P - AlgebraicNumber.

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.

rootCharacteristic

public SortedMap<AlgebraicNumber<C>, Long> rootCharacteristic(AlgebraicNumber<C> P)

Characteristics root of a AlgebraicNumber.

Parameters:

P - AlgebraicNumber.

Returns:

[p -> k] if exists k with e=characteristic(P)*k and P = p**e, else null.

rootCharacteristic

public GenPolynomial<AlgebraicNumber<C>> rootCharacteristic(GenPolynomial<AlgebraicNumber<C>> P)

GenPolynomial char-th root main variable.

Parameters:

P - univariate GenPolynomial with AlgebraicNumber coefficients.

Returns:

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

baseRootCharacteristic

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

GenPolynomial char-th root univariate polynomial.

Specified by:

baseRootCharacteristic in class SquarefreeFieldCharP<AlgebraicNumber<C extends GcdRingElem<C>>>

Parameters:

P - GenPolynomial.

Returns:

char-th_rootOf(P).

recursiveUnivariateRootCharacteristic

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

GenPolynomial char-th root univariate polynomial with polynomial coefficients.

Specified by:

recursiveUnivariateRootCharacteristic in class SquarefreeFieldCharP<AlgebraicNumber<C extends GcdRingElem<C>>>

Parameters:

P - recursive univariate GenPolynomial.

Returns:

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