mirror of
https://github.com/vale981/arb
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70 lines
1.7 KiB
C
70 lines
1.7 KiB
C
/*
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Copyright (C) 2016 Pascal Molin
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_dirichlet.h"
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void
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acb_dirichlet_gauss_sum_factor(acb_t res, const dirichlet_group_t G, const 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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/* early check */
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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->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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dirichlet_group_t Gp;
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dirichlet_char_t chip;
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dirichlet_subgroup_init(Gp, G, pe);
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dirichlet_char_init(chip, Gp);
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chip->n = chi->n % pe;
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if (k == 1 && G->neven == 2)
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{
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chip->log[0] = chi->log[0];
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chip->log[1] = chi->log[1];
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}
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else
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chip->log[0] = chi->log[k];
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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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dirichlet_char_clear(chip);
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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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