edu.jas.ufd

Class SquarefreeInfiniteFieldCharP<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.SquarefreeAbstract<C>

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

edu.jas.ufd.SquarefreeInfiniteFieldCharP<C>

All Implemented Interfaces:

Squarefree<Quotient<C>>, java.io.Serializable

public class SquarefreeInfiniteFieldCharP<C extends GcdRingElem<C>>
extends SquarefreeFieldCharP<Quotient<C>>

Squarefree decomposition for infinite coefficient fields of characteristic p.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected SquarefreeAbstract<C>	qengine Squarefree engine for infinite ring of characteristic p base coefficients.

Fields inherited from class edu.jas.ufd.SquarefreeFieldCharP

aCoFac, coFac, qCoFac

Fields inherited from class edu.jas.ufd.SquarefreeAbstract

engine

Constructor Summary

Constructors

Constructor and Description
SquarefreeInfiniteFieldCharP(RingFactory<Quotient<C>> fac) Constructor.

Method Summary

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

Methods inherited from class edu.jas.ufd.SquarefreeFieldCharP

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

Methods inherited from class edu.jas.ufd.SquarefreeAbstract

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

Methods inherited from class java.lang.Object

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

Field Detail

qengine

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

Squarefree engine for infinite ring of characteristic p base coefficients.

Constructor Detail

SquarefreeInfiniteFieldCharP

public SquarefreeInfiniteFieldCharP(RingFactory<Quotient<C>> fac)

Constructor.

Method Detail

squarefreeFactors

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

Squarefree factors of a Quotient.

Overrides:

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

Parameters:

P - Quotient.

Returns:

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

rootCharacteristic

public java.util.SortedMap<Quotient<C>,java.lang.Long> rootCharacteristic(Quotient<C> P)

Characteristics root of a Quotient.

Parameters:

P - Quotient.

Returns:

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

rootCharacteristic

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

GenPolynomial char-th root main variable.

Parameters:

P - univariate GenPolynomial with Quotient coefficients.

Returns:

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

baseRootCharacteristic

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

GenPolynomial char-th root univariate polynomial.

Specified by:

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

Parameters:

P - GenPolynomial.

Returns:

char-th_rootOf(P).

recursiveUnivariateRootCharacteristic

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

GenPolynomial char-th root univariate polynomial with polynomial coefficients.

Specified by:

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

Parameters:

P - recursive univariate GenPolynomial.

Returns:

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