RealRootsSturm
edu.jas.root

Class RealRootsSturm<C extends RingElem<C> & Rational>

    • Constructor Detail

      • RealRootsSturm

        public RealRootsSturm()
    • Method Detail

      • sturmSequence

        public List<GenPolynomial<C>> sturmSequence(GenPolynomial<C> f)
        Sturm sequence.
        Parameters:
        f - univariate polynomial.
        Returns:
        a Sturm sequence for f.
      • realRoots

        public List<Interval<C>> realRoots(Interval<C> iv,                          List<GenPolynomial<C>> S)
        Isolating intervals for the real roots.
        Parameters:
        iv - interval with f(left) * f(right) != 0.
        S - sturm sequence for f and I.
        Returns:
        a list of isolating intervals for the real roots of f in I.
      • realRootCount

        public long realRootCount(Interval<C> iv,                 List<GenPolynomial<C>> S)
        Number of real roots in interval.
        Parameters:
        iv - interval with f(left) * f(right) != 0.
        S - sturm sequence for f and I.
        Returns:
        number of real roots of f in I.
      • invariantSignInterval

        public Interval<C> invariantSignInterval(Interval<C> iv,                                GenPolynomial<C> f,                                List<GenPolynomial<C>> Sg)
        Invariant interval for algebraic number sign.
        Parameters:
        iv - root isolating interval for f, with f(left) * f(right) < 0.
        f - univariate polynomial, non-zero.
        Sg - Sturm sequence for g, a univariate polynomial with gcd(f,g) == 1.
        Returns:
        v with v a new interval contained in iv such that g(w) != 0 for w in v.

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