complex_root_isolation.hpp

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#include "computation_context.hpp"
#pragma once
 
#include "internal/exact_root.hpp"
#include "internal/exact_sturm.hpp"
 
namespace LMCAS::detail::complex_root {
 
using Poly = Polynomial<Rational>;
 
struct RationalRectangle {
    Rational real_lower;
    Rational real_upper;
    Rational imaginary_lower;
    Rational imaginary_upper;
};
 
struct RectangleCount {
    bool boundary_clear = false;
    std::size_t count = 0;
};
 
struct CoordinateProjections {
    Poly real;
    Poly imaginary;
};
 
int rational_sign(const Rational& value);
Poly scale_poly(Poly polynomial, const Rational& scalar);
Poly clear_denominators(Poly polynomial);
Result<CoordinateProjections> coordinate_projections(
    const Poly& polynomial, ComputationContext& context,
    const std::string& operation);
Result<void> refine_interval(
    const Poly& polynomial, RationalInterval& interval,
    ComputationContext& context, const std::string& operation);
Result<RectangleCount> count_rectangle_roots(
    const Poly& polynomial, const RationalRectangle& rectangle,
    ComputationContext& context, const std::string& operation);
Result<std::vector<ComplexIsolation>> isolate_nonreal_roots(
    const Poly& polynomial, std::size_t complex_count,
    ComputationContext& context, const std::string& operation);
 
}