Class SquarefreeFiniteFieldCharP<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.SquarefreeAbstract<C>

edu.jas.ufd.SquarefreeFieldCharP<C>

edu.jas.ufd.SquarefreeFiniteFieldCharP<C>

All Implemented Interfaces:

Squarefree<C>, Serializable

public class SquarefreeFiniteFieldCharP<C extends GcdRingElem<C>>
extends SquarefreeFieldCharP<C>

Squarefree decomposition for finite coefficient fields of characteristic p.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields inherited from class SquarefreeFieldCharP

aCoFac, coFac, qCoFac

Fields inherited from class SquarefreeAbstract

engine

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
GenPolynomial<C>	baseRootCharacteristic(GenPolynomial<C> P)	GenPolynomial char-th root univariate polynomial.
C	coeffRootCharacteristic(C c)	Characteristics root of a coefficient.
GenPolynomial<GenPolynomial<C>>	recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<C>> P)	GenPolynomial char-th root univariate polynomial with polynomial coefficients.
SortedMap<C,Long>	rootCharacteristic(C p)	Characteristics root of a coefficient.
SortedMap<GenPolynomial<C>, Long>	rootCharacteristic(GenPolynomial<C> P)	Characteristics root of a polynomial.

Methods inherited from class SquarefreeFieldCharP

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

Methods inherited from class SquarefreeAbstract

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

Methods inherited from class Object

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

Constructor Details

SquarefreeFiniteFieldCharP

public SquarefreeFiniteFieldCharP(RingFactory<C> fac)

Constructor.

Method Details

rootCharacteristic

public SortedMap<C,Long> rootCharacteristic(C p)

Characteristics root of a coefficient. Note: not needed at the moment.

Parameters:

p - coefficient.

Returns:

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

coeffRootCharacteristic

public C coeffRootCharacteristic(C c)

Characteristics root of a coefficient.

Parameters:

c - coefficient.

Returns:

r with r**p == c, if such an r exists, else null.

rootCharacteristic

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

Characteristics root of a polynomial. Note: call only in recursion.

Parameters:

P - polynomial.

Returns:

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

baseRootCharacteristic

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

GenPolynomial char-th root univariate polynomial. Base coefficient type must be finite field, that is ModInteger or AlgebraicNumber<ModInteger> etc.

Specified by:

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

Parameters:

P - GenPolynomial.

Returns:

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

recursiveUnivariateRootCharacteristic

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

GenPolynomial char-th root univariate polynomial with polynomial coefficients.

Specified by:

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

Parameters:

P - recursive univariate GenPolynomial.

Returns:

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