mirror of
https://github.com/vale981/arb
synced 2025-03-05 17:31:38 -05:00
126 lines
3.3 KiB
C
126 lines
3.3 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2016 Pascal Molin
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******************************************************************************/
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#include "acb_dirichlet.h"
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/*
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void
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acb_dirichlet_gauss_sum_naive_prime(acb_t res, acb_dirichlet_prime_group_struct P, ulong expo, slong prec)
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{
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acb_t z;
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acb_ptr v;
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v = _acb_vec_init(G->q);
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acb_dirichlet_chi_vec(v, G, chi, G->q, prec);
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acb_init(z);
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acb_dirichlet_nth_root(z, G->q, prec);
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_acb_poly_evaluate(res, v, G->q, z, prec);
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acb_clear(z);
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_acb_vec_clear(v, G->q);
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}
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static void
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acb_dirichlet_gauss_sum_prime(acb_t res, acb_dirichlet_prime_group_struct P, ulong expo, slong prec)
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{
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if (expo % P.p == 0)
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{
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if (P.e == 1)
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acb_set_si(res, -1);
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else
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acb_zero(res);
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}
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else
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{
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if (acb_dirichlet_theta_length_d(P.pe.n, 1, prec) > P.pe.n)
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acb_dirichlet_gauss_sum_naive_prime(res, P, expo, prec);
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else
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acb_dirichlet_gauss_sum_naive_prime(res, P, expo, prec);
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}
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}
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*/
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void
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acb_dirichlet_gauss_sum_factor(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec)
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{
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slong k;
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acb_t tmp;
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for (k = (G->neven == 2); k < G->num; k++)
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{
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/* if e > 1 and not primitive, 0 */
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if (chi->x->log[k] % G->P[k].p == 0 && G->P[k].e > 1)
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{
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acb_zero(res);
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return;
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}
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}
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/* factor */
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acb_one(res);
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acb_init(tmp);
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for (k = (G->neven == 2); k < G->num; k++)
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{
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ulong pe = G->P[k].pe.n;
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acb_dirichlet_group_t Gp;
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acb_dirichlet_char_t chip;
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acb_dirichlet_subgroup_init(Gp, G, pe);
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acb_dirichlet_char_init(chip, Gp);
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chip->x->n = chi->x->n % pe;
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if (k == 1 && G->neven == 2)
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{
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chip->x->log[0] = chi->x->log[0];
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chip->x->log[1] = chi->x->log[1];
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}
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else
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chip->x->log[0] = chi->x->log[k];
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acb_dirichlet_char_conrey(chip, Gp, NULL);
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/* chi_pe(a, q/pe) * G_pe(a) */
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acb_dirichlet_gauss_sum(tmp, Gp, chip, prec);
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acb_mul(res, res, tmp, prec);
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acb_dirichlet_chi(tmp, Gp, chip, (G->q / pe) % pe, prec);
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acb_mul(res, res, tmp, prec);
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acb_dirichlet_char_clear(chip);
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acb_dirichlet_group_clear(Gp);
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}
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if (G->q_even == 2)
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acb_neg(res, res);
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acb_clear(tmp);
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}
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