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>>, java.io.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

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and 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.
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, normalizeFactorization, recursiveSquarefreeFactors, recursiveSquarefreePart, squarefreePart

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

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.