Package edu.jas.ufd
Class SquarefreeFieldCharP<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.ufd.SquarefreeAbstract<C>
edu.jas.ufd.SquarefreeFieldCharP<C>
- All Implemented Interfaces:
Squarefree<C>
,Serializable
- Direct Known Subclasses:
SquarefreeFiniteFieldCharP
,SquarefreeInfiniteAlgebraicFieldCharP
,SquarefreeInfiniteFieldCharP
Squarefree decomposition for coefficient fields of characteristic p.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprotected final AlgebraicNumberRing
<C> Factory for a algebraic extension of a finite field of characteristic p coefficients.protected final RingFactory
<C> Factory for finite field of characteristic p coefficients.private static final org.apache.logging.log4j.Logger
protected final QuotientRing
<C> 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 -
Method Summary
Modifier and TypeMethodDescriptionabstract GenPolynomial
<C> GenPolynomial char-th root univariate polynomial.GenPolynomial polynomial squarefree factorization.GenPolynomial polynomial greatest squarefree divisor.boolean
isCharRoot
(GenPolynomial<C> P, SortedMap<GenPolynomial<C>, Long> F) Polynomial is char-th root.boolean
Recursive polynomial is char-th root.boolean
isRecursiveCharRoot
(GenPolynomial<GenPolynomial<C>> P, SortedMap<GenPolynomial<GenPolynomial<C>>, Long> F) Recursive polynomial is char-th root.abstract GenPolynomial
<GenPolynomial<C>> GenPolynomial char-th root univariate polynomial with polynomial coefficients.GenPolynomial recursive univariate polynomial squarefree factorization.GenPolynomial recursive univariate polynomial greatest squarefree divisor.squarefreeFactors
(C coeff) Coefficient squarefree factorization.GenPolynomial squarefree factorization.GenPolynomial greatest squarefree divisor.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, isSquarefreeAlternative, normalizeFactorization, recursiveSquarefreeFactors, recursiveSquarefreePart, squarefreePart
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
coFac
Factory for finite field of characteristic p coefficients. -
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
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 Details
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SquarefreeFieldCharP
Constructor.
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Method Details
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toString
Get the String representation. -
baseSquarefreePart
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
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 SortedMap<GenPolynomial<GenPolynomial<C>>,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
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
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
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
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
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, SortedMap<GenPolynomial<GenPolynomial<C>>, 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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