Package edu.jas.ufd
Class SquarefreeFieldCharP<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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- All Implemented Interfaces:
Squarefree<C>
,java.io.Serializable
- Direct Known Subclasses:
SquarefreeFiniteFieldCharP
,SquarefreeInfiniteAlgebraicFieldCharP
,SquarefreeInfiniteFieldCharP
public abstract class SquarefreeFieldCharP<C extends GcdRingElem<C>> extends SquarefreeAbstract<C>
Squarefree decomposition for coefficient fields of characteristic p.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected AlgebraicNumberRing<C>
aCoFac
Factory for a algebraic extension of a finite field of characteristic p coefficients.protected RingFactory<C>
coFac
Factory for finite field of characteristic p coefficients.protected QuotientRing<C>
qCoFac
Factory for a transcendental extension of a finite field of characteristic p coefficients.-
Fields inherited from class edu.jas.ufd.SquarefreeAbstract
engine
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Constructor Summary
Constructors Constructor Description SquarefreeFieldCharP(RingFactory<C> fac)
Constructor.
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Method Summary
All Methods Instance Methods Abstract Methods Concrete Methods Modifier and Type Method Description abstract GenPolynomial<C>
baseRootCharacteristic(GenPolynomial<C> P)
GenPolynomial char-th root univariate polynomial.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
isCharRoot(GenPolynomial<C> P, java.util.SortedMap<GenPolynomial<C>,java.lang.Long> F)
Polynomial is char-th root.boolean
isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> r)
Recursive polynomial is char-th root.boolean
isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P, java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long> F)
Recursive polynomial is char-th root.abstract GenPolynomial<GenPolynomial<C>>
recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial char-th root univariate polynomial with polynomial coefficients.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 coeff)
Coefficient 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, 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 finite field of characteristic p coefficients.
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aCoFac
protected final AlgebraicNumberRing<C extends GcdRingElem<C>> aCoFac
Factory for a algebraic extension of a finite field of characteristic p coefficients. IfcoFac
is an algebraic extension, thenaCoFac
is equal tocoFac
, elseaCoFac
isnull
.
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qCoFac
protected final QuotientRing<C extends GcdRingElem<C>> qCoFac
Factory for a transcendental extension of a finite field of characteristic p coefficients. IfcoFac
is an transcendental extension, thenqCoFac
is equal tocoFac
, elseqCoFac
isnull
.
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Constructor Detail
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SquarefreeFieldCharP
public SquarefreeFieldCharP(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(pp(P)).
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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(pp(P)).
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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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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 coeff)
Coefficient squarefree factorization.- Specified by:
squarefreeFactors
in classSquarefreeAbstract<C extends GcdRingElem<C>>
- Parameters:
coeff
- coefficient.- Returns:
- [p_1 -> e_1, ..., p_k -> e_k] with coeff = 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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baseRootCharacteristic
public abstract GenPolynomial<C> baseRootCharacteristic(GenPolynomial<C> P)
GenPolynomial char-th root univariate polynomial.- Parameters:
P
- GenPolynomial.- Returns:
- char-th_rootOf(P), or null if no char-th root.
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recursiveUnivariateRootCharacteristic
public abstract GenPolynomial<GenPolynomial<C>> recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<C>> P)
GenPolynomial char-th root univariate polynomial with polynomial coefficients.- Parameters:
P
- recursive univariate GenPolynomial.- Returns:
- char-th_rootOf(P), or null if P is no char-th root.
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isCharRoot
public boolean isCharRoot(GenPolynomial<C> P, java.util.SortedMap<GenPolynomial<C>,java.lang.Long> F)
Polynomial is char-th root.- Parameters:
P
- polynomial.F
- = [p_1 -> e_1, ..., p_k -> e_k].- Returns:
- true if P = prod_{i=1,...,k} p_i**(e_i*p), else false.
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isRecursiveCharRoot
public boolean isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P, java.util.SortedMap<GenPolynomial<GenPolynomial<C>>,java.lang.Long> F)
Recursive polynomial is char-th root.- Parameters:
P
- recursive polynomial.F
- = [p_1 -> e_1, ..., p_k -> e_k].- Returns:
- true if P = prod_{i=1,...,k} p_i**(e_i*p), else false.
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isRecursiveCharRoot
public boolean isRecursiveCharRoot(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> r)
Recursive polynomial is char-th root.- Parameters:
P
- recursive polynomial.r
- = recursive polynomial.- Returns:
- true if P = r**p, else false.
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