Package edu.jas.ufd

Class FactorAbsolute<C extends GcdRingElem<C>>

  • Type Parameters:
    C - coefficient type
    All Implemented Interfaces:
    Factorization<C>, java.io.Serializable
    Direct Known Subclasses:
    FactorAlgebraic, FactorAlgebraicPrim, FactorComplex, FactorModular, FactorModularBerlekamp, FactorRational
    public abstract class FactorAbsolute<C extends GcdRingElem<C>>
extends FactorAbstract<C>
    Absolute factorization algorithms class. This class contains implementations of methods for factorization over algebraically closed fields. The required field extension is computed along with the factors. The methods have been tested for prime fields of characteristic zero, that is for BigRational. It might eventually also be used for prime fields of non-zero characteristic, that is with ModInteger. The field extension may yet not be minimal.
    Author:
    Heinz Kredel
    See Also:
    Serialized Form

    • Constructor Detail

      • FactorAbsolute

        protected FactorAbsolute()
        No argument constructor. Note: can't use this constructor.

    • Method Detail

      • isAbsoluteIrreducible

        public boolean isAbsoluteIrreducible​(GenPolynomial<C> P)
        GenPolynomial test if is absolute irreducible.
        Parameters:
        P - GenPolynomial.
        Returns:
        true if P is absolute irreducible, else false.

      • baseFactorsAbsolute

        public FactorsMap<C> baseFactorsAbsolute​(GenPolynomial<C> P)
        GenPolynomial absolute base factorization of a polynomial.
        Parameters:
        P - univariate GenPolynomial.
        Returns:
        factors map container: [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i**e_i. Note: K(alpha) not yet minimal.

      • baseFactorsAbsoluteSquarefree

        public FactorsList<C> baseFactorsAbsoluteSquarefree​(GenPolynomial<C> P)
        GenPolynomial absolute base factorization of a squarefree polynomial.
        Parameters:
        P - squarefree and primitive univariate GenPolynomial.
        Returns:
        factors list container: [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i. Note: K(alpha) not yet minimal.

      • baseFactorsAbsoluteIrreducible

        public Factors<C> baseFactorsAbsoluteIrreducible​(GenPolynomial<C> P)
        GenPolynomial base absolute factorization of a irreducible polynomial.
        Parameters:
        P - irreducible! univariate GenPolynomial.
        Returns:
        factors container: [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i in K(alpha)[x] for suitable alpha and p_i irreducible over L[x], where K \subset K(alpha) \subset L is an algebraically closed field over K. Note: K(alpha) not yet minimal.

      • baseAlgebraicPartialFraction

        public PartialFraction<C> baseAlgebraicPartialFraction​(GenPolynomial<C> A,
                                                       GenPolynomial<C> P)
        Univariate GenPolynomial algebraic partial fraction decomposition, Absolute factorization for elementary integration algorithm to linear factors.
        Parameters:
        A - univariate GenPolynomial, deg(A) ≤ deg(P).
        P - univariate squarefree GenPolynomial, gcd(A,P) == 1.
        Returns:
        partial fraction container.

      • factorsAbsolute

        public FactorsMap<C> factorsAbsolute​(GenPolynomial<C> P)
        GenPolynomial absolute factorization of a polynomial.
        Parameters:
        P - GenPolynomial.
        Returns:
        factors map container: [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i**e_i. Note: K(alpha) not yet minimal.

      • factorsAbsoluteSquarefree

        public FactorsList<C> factorsAbsoluteSquarefree​(GenPolynomial<C> P)
        GenPolynomial absolute factorization of a squarefree polynomial.
        Parameters:
        P - squarefree and primitive GenPolynomial.
        Returns:
        factors list container: [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i. Note: K(alpha) not yet minimal.

      • factorsAbsoluteIrreducible

        public Factors<C> factorsAbsoluteIrreducible​(GenPolynomial<C> P)
        GenPolynomial absolute factorization of a irreducible polynomial.
        Parameters:
        P - irreducible! GenPolynomial.
        Returns:
        factors container: [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i in K(alpha)[x] for suitable alpha and p_i irreducible over L[x], where K \subset K(alpha) \subset L is an algebraically closed field over K. Note: K(alpha) not yet minimal.

      • isAbsoluteFactorization

        public boolean isAbsoluteFactorization​(Factors<C> facs)
        GenPolynomial is absolute factorization.
        Parameters:
        facs - factors container.
        Returns:
        true if P = prod_{i=1,...,r} p_i, else false.

      • isAbsoluteFactorization

        public boolean isAbsoluteFactorization​(FactorsList<C> facs)
        GenPolynomial is absolute factorization.
        Parameters:
        facs - factors list container.
        Returns:
        true if P = prod_{i=1,...,r} p_i, else false.

      • isAbsoluteFactorization

        public boolean isAbsoluteFactorization​(FactorsMap<C> facs)
        GenPolynomial is absolute factorization.
        Parameters:
        facs - factors map container.
        Returns:
        true if P = prod_{i=1,...,k} p_i**e_i , else false.