Package edu.jas.ufd
Class SquarefreeFieldChar0<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.ufd.SquarefreeAbstract<C>
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- edu.jas.ufd.SquarefreeFieldChar0<C>
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- All Implemented Interfaces:
Squarefree<C>
,java.io.Serializable
- Direct Known Subclasses:
SquarefreeFieldChar0Yun
public class SquarefreeFieldChar0<C extends GcdRingElem<C>> extends SquarefreeAbstract<C>
Squarefree decomposition for coefficient fields of characteristic 0.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected RingFactory<C>
coFac
Factory for field of characteristic 0 coefficients.-
Fields inherited from class edu.jas.ufd.SquarefreeAbstract
engine
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Constructor Summary
Constructors Constructor Description SquarefreeFieldChar0(RingFactory<C> fac)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.util.SortedMap<GenPolynomial<C>,java.lang.Long>
baseSquarefreeFactors(GenPolynomial<C> A)
GenPolynomial polynomial squarefree factorization.GenPolynomial<C>
baseSquarefreePart(GenPolynomial<C> P)
GenPolynomial polynomial greatest squarefree divisor.boolean
isBaseSquarefree(GenPolynomial<C> P)
GenPolynomial test if is squarefree.boolean
isRecursiveUnivariateSquarefree(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial test if is squarefree.boolean
isSquarefree(GenPolynomial<C> P)
GenPolynomial test if is squarefree.java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long>
recursiveUnivariateSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial recursive univariate polynomial squarefree factorization.GenPolynomial<GenPolynomial<C>>
recursiveUnivariateSquarefreePart(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial recursive univariate polynomial greatest squarefree divisor.java.util.SortedMap<C,java.lang.Long>
squarefreeFactors(C P)
Coefficients squarefree factorization.java.util.SortedMap<GenPolynomial<C>,java.lang.Long>
squarefreeFactors(GenPolynomial<C> P)
GenPolynomial squarefree factorization.GenPolynomial<C>
squarefreePart(GenPolynomial<C> P)
GenPolynomial greatest squarefree divisor.java.lang.String
toString()
Get the String representation.-
Methods inherited from class edu.jas.ufd.SquarefreeAbstract
basePartialFraction, coPrimeSquarefree, coPrimeSquarefree, factorCount, isBasePartialFraction, isCoPrimeSquarefree, isFactorization, isFactorization, isRecursiveFactorization, isRecursiveSquarefree, isSquarefree, normalizeFactorization, recursiveSquarefreeFactors, recursiveSquarefreePart, squarefreePart
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Field Detail
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coFac
protected final RingFactory<C extends GcdRingElem<C>> coFac
Factory for field of characteristic 0 coefficients.
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Constructor Detail
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SquarefreeFieldChar0
public SquarefreeFieldChar0(RingFactory<C> fac)
Constructor.
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Method Detail
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toString
public java.lang.String toString()
Get the String representation.- Overrides:
toString
in classjava.lang.Object
- See Also:
Object.toString()
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baseSquarefreePart
public GenPolynomial<C> baseSquarefreePart(GenPolynomial<C> P)
GenPolynomial polynomial greatest squarefree divisor.- Specified by:
baseSquarefreePart
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
P
- GenPolynomial.- Returns:
- squarefree(P).
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isBaseSquarefree
public boolean isBaseSquarefree(GenPolynomial<C> P)
GenPolynomial test if is squarefree.- Parameters:
P
- GenPolynomial.- Returns:
- true if P is squarefree, else false.
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baseSquarefreeFactors
public java.util.SortedMap<GenPolynomial<C>,java.lang.Long> baseSquarefreeFactors(GenPolynomial<C> A)
GenPolynomial polynomial squarefree factorization.- Specified by:
baseSquarefreeFactors
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
A
- GenPolynomial.- Returns:
- [p_1 -> e_1, ..., p_k -> e_k] with A = 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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recursiveUnivariateSquarefreePart
public GenPolynomial<GenPolynomial<C>> recursiveUnivariateSquarefreePart(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial recursive univariate polynomial greatest squarefree divisor.- Specified by:
recursiveUnivariateSquarefreePart
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
P
- recursive univariate GenPolynomial.- Returns:
- squarefree(P).
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isRecursiveUnivariateSquarefree
public boolean isRecursiveUnivariateSquarefree(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial test if is squarefree.- Parameters:
P
- GenPolynomial.- Returns:
- true if P is squarefree, else false.
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recursiveUnivariateSquarefreeFactors
public java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long> recursiveUnivariateSquarefreeFactors(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial recursive univariate polynomial squarefree factorization.- Specified by:
recursiveUnivariateSquarefreeFactors
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
P
- recursive univariate GenPolynomial.- 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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squarefreePart
public GenPolynomial<C> squarefreePart(GenPolynomial<C> P)
GenPolynomial greatest squarefree divisor.- Specified by:
squarefreePart
in interfaceSquarefree<C extends GcdRingElem<C>>
- Specified by:
squarefreePart
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
P
- GenPolynomial.- Returns:
- squarefree(pp(P)).
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isSquarefree
public boolean isSquarefree(GenPolynomial<C> P)
GenPolynomial test if is squarefree.- Specified by:
isSquarefree
in interfaceSquarefree<C extends GcdRingElem<C>>
- Overrides:
isSquarefree
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
P
- GenPolynomial.- Returns:
- true if P is squarefree, else false.
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squarefreeFactors
public java.util.SortedMap<GenPolynomial<C>,java.lang.Long> squarefreeFactors(GenPolynomial<C> P)
GenPolynomial squarefree factorization.- Specified by:
squarefreeFactors
in interfaceSquarefree<C extends GcdRingElem<C>>
- Specified by:
squarefreeFactors
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
P
- GenPolynomial.- 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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squarefreeFactors
public java.util.SortedMap<C,java.lang.Long> squarefreeFactors(C P)
Coefficients squarefree factorization.- Specified by:
squarefreeFactors
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
P
- coefficient.- 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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