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/*
Copyright (C) 2015 Vladimir Glazachev
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/>.
*/
#include "ulong_extras.h"
#include "fmpz.h"
#include "fmpz_mod_poly.h"
#include "aprcl.h"
/*
Computes f such that \sigma_x(f) = g.
*/
void
unity_zp_aut_inv(unity_zp f, const unity_zp g, ulong x)
{
ulong i, j, p_pow1, p_pow2, m, p_pow_preinv;
fmpz_t f_coeff, g_coeff;
fmpz_init(f_coeff);
fmpz_init(g_coeff);
p_pow1 = n_pow(f->p, f->exp - 1); /* p_pow1 = p^{k - 1} */
p_pow2 = p_pow1 * f->p; /* p_pow2 = p^k */
m = (f->p - 1) * p_pow1; /* m = (p - 1) * p^{k - 1} */
p_pow_preinv = n_preinvert_limb(p_pow2);
unity_zp_set_zero(f);
/* for i = 0, 1,..., m - 1 set f[i] = g[xi mod p^k] */
for (i = 0; i < m; i++)
{
/* set g_ind = x * i mod p^k */
ulong g_ind = n_mulmod2_preinv(x, i, p_pow2, p_pow_preinv);
/* set g_coeff to g[g_ind] */
fmpz_mod_poly_get_coeff_fmpz(g_coeff, g->poly, g_ind, g->ctx);
/* set f[i] = g[x * i mod p^k] */
unity_zp_coeff_set_fmpz(f, i, g_coeff);
}
/*
for i = m, m + 1,..., p^k - 1
for j = 1, 2,..., p - 1
set f[i - j * p^{k - 1}] =
(f[i - j * p^{k - 1}] - g[x * i mod p^k]) mod n
*/
for (i = m; i < p_pow2; i++)
{
/* set g_ind = x * i mod p^k */
ulong g_ind = n_mulmod2_preinv(x, i, p_pow2, p_pow_preinv);
for (j = 1; j < f->p; j++)
{
/* set f_ind = i - j * p^{k - 1} */
ulong f_ind = i - j * p_pow1;
/* set g_coeff = g[x * i mod p^k] */
fmpz_mod_poly_get_coeff_fmpz(g_coeff, g->poly, g_ind, g->ctx);
/* set f_coeff = f[i - j * p^{k - 1}] */
fmpz_mod_poly_get_coeff_fmpz(f_coeff, f->poly, f_ind, f->ctx);
/* set f_coeff = f[i - j * p^{k - 1}] - g[x * i mod p^k] */
fmpz_sub(f_coeff, f_coeff, g_coeff);
/* set f[i - j * p^{k - 1}] = f_coeff */
unity_zp_coeff_set_fmpz(f, f_ind, f_coeff);
}
}
fmpz_clear(f_coeff);
fmpz_clear(g_coeff);
}