#ifndef QEXT_H
#define QEXT_H

#include <gmp.h>

struct qext_type {
	int rank;
	const int *integer_coeffs;  // actually the rank+1 coefficients of the polynomial
	mpq_t *coeffs;  // components of a^rank
};

struct qext_number_internal {
	struct qext_type *type;
	mpq_t *a;
};

typedef struct qext_number_internal qext_number[1];

extern struct qext_type *QT_TRIVIAL;
extern struct qext_type *QT_SQRT5;
extern struct qext_type *QT_GAUSS_SQRT5;

struct qext_type *qext_newtype(int rank, const int *coeffs);
void qext_init(qext_number x, struct qext_type *type);
void qext_clear(qext_number x);
void qext_set(qext_number x, qext_number y);
void qext_set_int(qext_number x, int y);
void qext_set_q(qext_number x, mpq_t y);
void qext_add(qext_number result, qext_number x, qext_number y);
void qext_sub(qext_number result, qext_number x, qext_number y);
void qext_neg(qext_number result, qext_number x);
void qext_mul(qext_number out, qext_number x, qext_number y);
void qext_inv(qext_number out, qext_number in);
void qext_div(qext_number out, qext_number x, qext_number y);
int qext_cmp(qext_number x, qext_number y);
void qext_print(qext_number x);
void qext_snprint(char *str, size_t len, qext_number x);

#endif