#pragma once

#include <optional>
#include <string>
#include <variant>
#include <vector>


struct Product {
	double cnst;
	std::vector<std::string> vars;

	const Product times(double x) const;
	void times_inplace(double x);
	const Product times(const Product &p) const;
	bool contains(const std::string &var) const;
	const Product without(const std::string &var) const;

	bool operator==(const Product &other) const;
};

struct Sum {
	std::vector<Product> terms;

	const Sum times(double x) const;
	const Sum substitute(const std::string &var, Sum sum) const;
	void simplify();
	// Returns std::nullopt if there are variables in the terms
	std::optional<double> evaluate() const;
};

// An equation is not allowed to contain a variable name more than once.
struct Equation {
	Sum lhs, rhs;

	std::optional<std::string> validate() const;
	const Equation substitute(const std::string &var, Sum sum) const;
	void substitute_inplace(const std::string &var, Sum sum);
	int num_vars() const;
	std::vector<std::string> all_vars() const;
	bool isolatable(const std::string &target) const;
	void isolate_left(const std::string &target);
	void simplify();
};

struct System {
	std::vector<Equation> eqs;

	std::variant<
		std::string,  // description of the error
		std::vector<std::pair<std::string, double>>  // result assignment
	> solve_inplace(bool debug);

	void substitute_inplace(const std::string &var, Sum sum);
};

std::ostream& operator<<(std::ostream &os, const Product &p);
std::ostream& operator<<(std::ostream &os, const Sum &s);
std::ostream& operator<<(std::ostream &os, const Equation &eq);
std::ostream& operator<<(std::ostream &os, const System &sys);

// vim: set sw=4 ts=4 noet: