Package edu.jas.ufd

Class SquarefreeFieldCharP<C extends GcdRingElem<C>>

    • Field Detail

      • logger

        private static final org.apache.logging.log4j.Logger logger
      • coFac

        protected final RingFactory<C extends GcdRingElem<C>> coFac
        Factory for finite field of characteristic p coefficients.
      • aCoFac

        protected final AlgebraicNumberRing<C extends GcdRingElem<C>> aCoFac
        Factory for a algebraic extension of a finite field of characteristic p coefficients. If coFac is an algebraic extension, then aCoFac is equal to coFac, else aCoFac is null.
      • qCoFac

        protected final QuotientRing<C extends GcdRingElem<C>> qCoFac
        Factory for a transcendental extension of a finite field of characteristic p coefficients. If coFac is an transcendental extension, then qCoFac is equal to coFac, else qCoFac is null.
    • Constructor Detail

      • SquarefreeFieldCharP

        public SquarefreeFieldCharP​(RingFactory<C> fac)
        Constructor.
    • Method Detail

      • toString

        public java.lang.String toString()
        Get the String representation.
        Overrides:
        toString in class java.lang.Object
        See Also:
        Object.toString()
      • baseSquarefreeFactors

        public java.util.SortedMap<GenPolynomial<C>,​java.lang.Long> baseSquarefreeFactors​(GenPolynomial<C> A)
        GenPolynomial polynomial squarefree factorization.
        Specified by:
        baseSquarefreeFactors in class SquarefreeAbstract<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.
      • squarefreeFactors

        public java.util.SortedMap<C,​java.lang.Long> squarefreeFactors​(C coeff)
        Coefficient squarefree factorization.
        Specified by:
        squarefreeFactors in class SquarefreeAbstract<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.
      • 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.
      • 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.
      • 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.
      • 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.
      • 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.