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/*
Copyright (C) 2013 William Hart
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#ifndef NF_H
#define NF_H
#include "fmpz_poly.h"
#include "fmpq_poly.h"
#ifdef __cplusplus
extern "C" {
#endif
typedef struct {
fmpq_poly_t pol; /* defining polynomial */
union {
/* insert any precomputed inverse for zz case here */
fmpz_preinvn_t qq; /* precomputed inverse for leading coeff of num(pol), QQ case */
} pinv;
union { /* powers of the generator mod pol */
fmpq_poly_powers_precomp_t qq;
fmpz_poly_powers_precomp_t zz;
} powers;
fmpq_poly_t traces; /* S_k = sum_i \theta_i^k for k = 0, 1, 2, ..., (n-1) */
ulong flag; /* 1 = pol monic over ZZ, 2, = linear, 4 = quadratic field */
} nf_struct;
typedef nf_struct nf_t[1];
#define NF_POWERS_CUTOFF 30 /* maximum length of pol where we precompute powers */
#define NF_GENERIC 0
#define NF_MONIC 1
#define NF_LINEAR 2
#define NF_QUADRATIC 4
#define NF_GAUSSIAN 8
/******************************************************************************
Initialisation
******************************************************************************/
void nf_init(nf_t nf, const fmpq_poly_t pol);
void nf_init_randtest(nf_t nf, flint_rand_t state, slong len, flint_bitcnt_t bits_in);
void nf_clear(nf_t nf);
void nf_print(const nf_t nf);
#ifdef __cplusplus
}
#endif
#endif