exact_sturm.hpp

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#pragma once
 
#include "computation_context.hpp"
#include "polynomial.hpp"
#include "result.hpp"
 
#include <string>
#include <utility>
#include <vector>
 
namespace LMCAS::detail {
 
using RationalInterval = std::pair<Rational, Rational>;
inline Rational strict_cauchy_root_bound(
    const Polynomial<Rational>& polynomial) {
    Rational maximum(0);
    const Rational leading = polynomial.lead_coeff().abs();
    for (int degree = 0; degree < polynomial.degree(); ++degree) {
        const Rational ratio =
            polynomial.coeffs[static_cast<std::size_t>(degree)].abs() / leading;
        if (maximum < ratio) maximum = ratio;
    }
    return Rational(2) + maximum;
}
 
 
Result<std::vector<RationalInterval>> isolate_real_roots_exact(
    const Polynomial<Rational>& polynomial,
    ComputationContext& context,
    const std::string& operation);
 
Result<std::size_t> count_real_roots_exact(
    const Polynomial<Rational>& polynomial,
    const Rational& lower,
    const Rational& upper,
    ComputationContext& context,
    const std::string& operation);
 
}