Package edu.jas.ufd
Class SquarefreeInfiniteAlgebraicFieldCharP<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.ufd.SquarefreeAbstract<C>
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- edu.jas.ufd.SquarefreeFieldCharP<AlgebraicNumber<C>>
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- edu.jas.ufd.SquarefreeInfiniteAlgebraicFieldCharP<C>
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- 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.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected SquarefreeAbstract<C>
aengine
Squarefree engine for infinite ring of characteristic p base coefficients.-
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 SquarefreeInfiniteAlgebraicFieldCharP(RingFactory<AlgebraicNumber<C>> fac)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method 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
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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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Field Detail
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aengine
protected final SquarefreeAbstract<C extends GcdRingElem<C>> aengine
Squarefree engine for infinite ring of characteristic p base coefficients.
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Constructor Detail
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SquarefreeInfiniteAlgebraicFieldCharP
public SquarefreeInfiniteAlgebraicFieldCharP(RingFactory<AlgebraicNumber<C>> fac)
Constructor.
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Method Detail
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squarefreeFactors
public java.util.SortedMap<AlgebraicNumber<C>,java.lang.Long> squarefreeFactors(AlgebraicNumber<C> P)
Squarefree factors of a AlgebraicNumber.- Overrides:
squarefreeFactors
in classSquarefreeFieldCharP<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_i} and p_i squarefree and gcd(p_i, p_j) = 1, for i != j.
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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=characteristic(P)*k and P = p**e, else null.
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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.
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baseRootCharacteristic
public GenPolynomial<AlgebraicNumber<C>> baseRootCharacteristic(GenPolynomial<AlgebraicNumber<C>> P)
GenPolynomial char-th root univariate polynomial.- Specified by:
baseRootCharacteristic
in classSquarefreeFieldCharP<AlgebraicNumber<C extends GcdRingElem<C>>>
- Parameters:
P
- GenPolynomial.- Returns:
- char-th_rootOf(P).
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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 classSquarefreeFieldCharP<AlgebraicNumber<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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