RealRoots
edu.jas.root

Interface RealRoots<C extends RingElem<C> & Rational>

    • Method Detail

      • realRootBound

        C realRootBound(GenPolynomial<C> f)
        Real root bound. With f(M) * f(-M) != 0.
        Parameters:
        f - univariate polynomial.
        Returns:
        M such that -M < root(f) > M.
      • realRoots

        List<Interval<C>> realRoots(GenPolynomial<C> f)
        Isolating intervals for the real roots.
        Parameters:
        f - univariate polynomial.
        Returns:
        a list of isolating intervalls for the real roots of f.
      • realRoots

        List<Interval<C>> realRoots(GenPolynomial<C> f,                          C eps)
        Isolating intervals for the real roots.
        Parameters:
        f - univariate polynomial.
        eps - requested intervals length.
        Returns:
        a list of isolating intervals v such that |v| < eps.
      • realRoots

        List<Interval<C>> realRoots(GenPolynomial<C> f,                          BigRational eps)
        Isolating intervals for the real roots.
        Parameters:
        f - univariate polynomial.
        eps - requested intervals length.
        Returns:
        a list of isolating intervals v such that |v| < eps.
      • signChange

        boolean signChange(Interval<C> iv,                 GenPolynomial<C> f)
        Sign changes on interval bounds.
        Parameters:
        iv - root isolating interval with f(left) * f(right) != 0.
        f - univariate polynomial.
        Returns:
        true if f(left) * f(right) < 0, else false
      • realRootCount

        long realRootCount(Interval<C> iv,                 GenPolynomial<C> f)
        Number of real roots in interval.
        Parameters:
        iv - interval with f(left) * f(right) != 0.
        f - univariate polynomial.
        Returns:
        number of real roots of f in I.
      • refineInterval

        Interval<C> refineInterval(Interval<C> iv,                         GenPolynomial<C> f,                         C eps)
        Refine interval.
        Parameters:
        iv - root isolating interval with f(left) * f(right) < 0.
        f - univariate polynomial, non-zero.
        eps - requested interval length.
        Returns:
        a new interval v such that |v| < eps.
      • refineIntervals

        List<Interval<C>> refineIntervals(List<Interval<C>> V,                                GenPolynomial<C> f,                                C eps)
        Refine intervals.
        Parameters:
        V - list of isolating intervals with f(left) * f(right) < 0.
        f - univariate polynomial, non-zero.
        eps - requested intervals length.
        Returns:
        a list of new intervals v such that |v| < eps.
      • realSign

        int realSign(Interval<C> iv,           GenPolynomial<C> f,           GenPolynomial<C> g)
        Real algebraic number sign.
        Parameters:
        iv - root isolating interval for f, with f(left) * f(right) < 0.
        f - univariate polynomial, non-zero.
        g - univariate polynomial, gcd(f,g) == 1.
        Returns:
        sign(g(v)), with v a new interval contained in iv such that g(v) != 0.
      • realMagnitude

        C realMagnitude(Interval<C> iv,              GenPolynomial<C> f,              GenPolynomial<C> g,              C eps)
        Real algebraic number magnitude.
        Parameters:
        iv - root isolating interval for f, with f(left) * f(right) < 0.
        f - univariate polynomial, non-zero.
        g - univariate polynomial, gcd(f,g) == 1.
        eps - length limit for interval length.
        Returns:
        g(iv).

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