exact_root.hpp

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#pragma once
 
#include "internal/exact_root_id.hpp"
#include "internal/exact_algebraic.hpp"
#include "numeric_value.hpp"
#include "result.hpp"
 
#include <variant>
#include <vector>
 
namespace LMCAS::detail {
 
struct RealIsolation {
    ExactRealAlgebraic value;
};
 
struct ComplexIsolation {
    Rational real_lower;
    Rational real_upper;
    Rational imaginary_lower;
    Rational imaginary_upper;
    ExactRealAlgebraic real_projection;
    ExactRealAlgebraic imaginary_projection;
};
 
using RootIsolation = std::variant<RealIsolation, ComplexIsolation>;
 
struct NumericEvaluationOptions {
    double absolute_tolerance = 1e-12;
    double relative_tolerance = 1e-12;
};
 
Result<ExactRootId> make_exact_root_id(
    Polynomial<Rational> polynomial,
    std::size_t index,
    ComputationContext& context,
    const std::string& operation = "rootof.construct");
 
Result<std::vector<RootIsolation>> isolate_exact_roots(
    const Polynomial<Rational>& polynomial,
    ComputationContext& context,
    const std::string& operation = "rootof.isolate");
 
Result<RootIsolation> isolate_exact_root(
    const ExactRootId& root,
    ComputationContext& context,
    const std::string& operation = "rootof.isolate");
 
Result<void> refine_complex_isolation(
    const Polynomial<Rational>& polynomial,
    ComplexIsolation& isolation,
    const NumericEvaluationOptions& options,
    ComputationContext& context,
    const std::string& operation = "rootof.refine_complex");
 
Result<ApproxReal> evaluate_root_real(
    const ExactRootId& root,
    const NumericEvaluationOptions& options,
    ComputationContext& context);
 
Result<ApproxComplex> evaluate_root_complex(
    const ExactRootId& root,
    const NumericEvaluationOptions& options,
    ComputationContext& context);
 
}