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

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

All Implemented Interfaces:

Squarefree<AlgebraicNumber<C>>

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

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

Author:

Heinz Kredel

Field Summary

protected SquarefreeAbstract<C>

rengine GCD 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

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

Method Summary

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.
java.util.SortedMap<AlgebraicNumber<C>,java.lang.Long>	rootCharacteristic(AlgebraicNumber<C> P) Characteristics root of a AlgebraicNumber.
GenPolynomial<AlgebraicNumber<C>>	rootCharacteristic(GenPolynomial<AlgebraicNumber<C>> P) GenPolynomial char-th root main variable.
java.util.SortedMap<AlgebraicNumber<C>,java.lang.Long>	squarefreeFactors(AlgebraicNumber<C> P) Squarefree factors of a AlgebraicNumber.

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, 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 infinite ring of characteristic p base coefficients.

Constructor Detail

SquarefreeInfiniteAlgebraicFieldCharP

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

Constructor.

Method Detail

squarefreeFactors

public java.util.SortedMap<AlgebraicNumber<C>,java.lang.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_k.

rootCharacteristic

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

Characteristics root of a AlgebraicNumber.

Parameters:

P - AlgebraicNumber.

Returns:

[p -> k] if exists k with e=charactristic(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.