Package edu.jas.ufd
Class SquarefreeFiniteFieldCharP<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.ufd.SquarefreeAbstract<C>
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- edu.jas.ufd.SquarefreeFieldCharP<C>
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- edu.jas.ufd.SquarefreeFiniteFieldCharP<C>
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- All Implemented Interfaces:
Squarefree<C>
,java.io.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
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Field Summary
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Fields inherited from class edu.jas.ufd.SquarefreeFieldCharP
aCoFac, coFac, qCoFac
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Fields inherited from class edu.jas.ufd.SquarefreeAbstract
engine
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Constructor Summary
Constructors Constructor Description SquarefreeFiniteFieldCharP(RingFactory<C> fac)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods 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.java.util.SortedMap<C,java.lang.Long>
rootCharacteristic(C p)
Characteristics root of a coefficient.java.util.SortedMap<GenPolynomial<C>,java.lang.Long>
rootCharacteristic(GenPolynomial<C> P)
Characteristics root of a polynomial.-
Methods inherited from class edu.jas.ufd.SquarefreeFieldCharP
baseSquarefreeFactors, baseSquarefreePart, isCharRoot, isRecursiveCharRoot, isRecursiveCharRoot, recursiveUnivariateSquarefreeFactors, recursiveUnivariateSquarefreePart, squarefreeFactors, squarefreeFactors, squarefreePart, toString
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Methods inherited from class edu.jas.ufd.SquarefreeAbstract
basePartialFraction, coPrimeSquarefree, coPrimeSquarefree, factorCount, isBasePartialFraction, isCoPrimeSquarefree, isFactorization, isFactorization, isRecursiveFactorization, isRecursiveSquarefree, isSquarefree, isSquarefree, normalizeFactorization, recursiveSquarefreeFactors, recursiveSquarefreePart, squarefreePart
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Constructor Detail
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SquarefreeFiniteFieldCharP
public SquarefreeFiniteFieldCharP(RingFactory<C> fac)
Constructor.
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Method Detail
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rootCharacteristic
public java.util.SortedMap<C,java.lang.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.
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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.
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rootCharacteristic
public java.util.SortedMap<GenPolynomial<C>,java.lang.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.
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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 classSquarefreeFieldCharP<C extends GcdRingElem<C>>
- Parameters:
P
- GenPolynomial.- Returns:
- char-th_rootOf(P), or null if no char-th root.
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recursiveUnivariateRootCharacteristic
public GenPolynomial<GenPolynomial<C>> recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial char-th root univariate polynomial with polynomial coefficients.- Specified by:
recursiveUnivariateRootCharacteristic
in classSquarefreeFieldCharP<C extends GcdRingElem<C>>
- Parameters:
P
- recursive univariate GenPolynomial.- Returns:
- char-th_rootOf(P), or null if P is no char-th root.
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