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/*=============================================================================
This file is part of Antic.
Antic 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
Copyright (C) 2013 William Hart
******************************************************************************/
#include "nf.h"
void nf_init(nf_t nf, const fmpq_poly_t pol)
{
slong i, j;
slong len = pol->length, deg = len - 1;
fmpz * pow, * lead = fmpq_poly_numref(pol) + len - 1;
fmpq_poly_init(nf->pol);
fmpq_poly_set(nf->pol, pol);
/**** Set up precomputed inverse of leading coeff of f(x) ****/
if (fmpz_is_one(fmpq_poly_denref(pol)) /* denominator is one and numerator is monic */
&& fmpz_is_one(lead))
nf->flag = NF_MONIC;
else
{
fmpz_preinvn_init(nf->pinv.qq, lead);
nf->flag = NF_GENERIC;
}
/**** Set up precomputed powers x^i mod f(x) ****/
if (len < 2)
{
flint_printf("Exception (nf_init). Degree must be at least 1.\n");
abort();
} else if (len == 2) /* linear case */
nf->flag |= NF_LINEAR;
else if (len == 3) /* quadratic case */
{
nf->flag |= NF_QUADRATIC;
if (fmpz_is_one(pol->coeffs + 0) && fmpz_is_zero(pol->coeffs + 1) &&
fmpz_is_one(pol->coeffs + 2) && fmpz_is_one(pol->den))
nf->flag |= NF_GAUSSIAN;
}
else if (len <= NF_POWERS_CUTOFF) /* compute powers of generator mod pol */
{
if (nf->flag & NF_MONIC)
{
nf->powers.zz->powers = _fmpz_poly_powers_precompute(fmpq_poly_numref(pol),
len);
nf->powers.zz->len = len;
}
else
{
nf->powers.qq->powers = _fmpq_poly_powers_precompute(fmpq_poly_numref(pol),
fmpq_poly_denref(pol), len);
nf->powers.qq->len = len;
}
}
/**** Set up precomputed traces S_k = \sum _i theta_i^k for roots theta_i of f(x) ****/
/*
Uses the recursive formula from pp. 163 of "A Course in Computational Algebraic
Number Theory" by Henri Cohen
*/
fmpq_poly_init2(nf->traces, deg);
pow = fmpq_poly_denref(nf->traces);
for (i = 1; i < deg; i++)
{
fmpz_mul_si(fmpq_poly_numref(nf->traces) + i,
fmpq_poly_numref(pol) + deg - i, i);
for (j = i - 1; j >= 1; j--)
{
fmpz_mul(fmpq_poly_numref(nf->traces) + i,
fmpq_poly_numref(nf->traces) + i, lead);
fmpz_addmul(fmpq_poly_numref(nf->traces) + i,
fmpq_poly_numref(pol) + deg - j,
fmpq_poly_numref(nf->traces) + i - j);
}
fmpz_neg(fmpq_poly_numref(nf->traces) + i,
fmpq_poly_numref(nf->traces) + i);
}
for (i = 1; i < deg; i++)
{
fmpz_mul(fmpq_poly_numref(nf->traces) + deg - i,
fmpq_poly_numref(nf->traces) + deg - i, pow);
fmpz_mul(pow, pow, lead);
}
fmpz_mul_si(fmpq_poly_numref(nf->traces), pow, deg);
}
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