poly_and_ratio.hpp

/**
* Ðåàë³çàö³ÿ êëàñ³â ïîë³íîì òà ðàö³îíàëüíà ôóíêö³ÿ, êîåô³ö³ºíòè ÿêèõ íàëåæàòü äåÿêîìó ê³ëüöþ ëèøê³â
*/
#include <unordered_map>
#include <string>
#include "modular_arithmetic.hpp"


#ifndef POLY_AND_RATIO_H
#define POLY_AND_RATIO_H


/**
* Êëàñ ïîë³íîì
* data - õåø-òàáëèöÿ êîåô³ö³ºíò³â Galois, â ÿê³é êëþ÷ ìຠìàòè âèãëÿä "m, k",
* ùî â³äïîâ³äຠìîíîìó x^m * y^k, äå k, m º íåâ³ä'ºìíèìè ö³ëèìè ÷èñëàìè
* ïàðàìåòð mod âèçíà÷ຠÿêîìó ê³ëüöþ ëèøê³â ìàþòü íàëåæàòè êîåô³ö³ºíòè
*/
class Poly
{
private:
	std::unordered_map<std::string, Galois> data;
	int_fast64_t mod;

public:
	Poly(std::unordered_map<std::string, Galois>& data, int_fast64_t mod);

	/**
	* Ñòâîðþº ïîë³íîì 0 * x^0 * y^0 ç êîåô³ö³ºíòàìè, ÿê³ íàëåæàòü ê³ëüöþ ëèøê³â ïî ìîäóëþ mod
	*/
	Poly(uint_fast32_t mod);

	Poly() {}

	Poly operator+ (const Poly& other);

	Poly operator* (const Poly& other);

	Poly operator* (const Galois& other);

	/**
	* Ïîâåðòຠçíà÷åííÿ ïîë³íîìà â òî÷ö³ (x, y)
	*/
	Galois value(Galois& x, Galois& y);

	/**
	* Ïîâåðòຠñòðîêîâå ïðåäñòàâëåííÿ ïîë³íîìà
	*/
	std::string get_str();

	int_fast16_t get_mod();

	/**
	* Ïîâåðòຠõåø-òàáëèöþ êîåô³ö³ºíò³â ïîë³íîìà
	*/
	std::unordered_map<std::string, Galois> get_data();
};


/**
* Êëàñ ðàö³îíàëüíà ôóíêö³ÿ
* numerator, denominator - ïîë³íîìè, ÿê³ ìàþòü êîåô³ö³ºíòè ç îäíîãî ê³ëüöÿ ëèøê³â
*/
class Ratio
{
private:
	Poly numerator, denominator;

public:
	Ratio(Poly& p1, Poly& p2);

	Ratio(uint_fast32_t mod);

	Ratio operator* (const Ratio& other);

	Ratio operator* (const Poly& other);

	Ratio operator* (const Galois& other);

	/**
	* Ïîâåðòຠñòðîêîâå ïðåäñòàâëåííÿ ðàö³îíàëüíî¿ ôóíêö³¿
	*/
	std::string get_str();

	/**
	* Ïîâåðòຠçíà÷åííÿ ðàö³îíàëüíî¿ ôóíêö³¿ â òî÷ö³ (x, y)
	*/
	Galois value(Galois& x, Galois& y);
};

#endif