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Merge remote-tracking branch 'pascal/dirichlet' into dirichlet

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This commit is contained in:
Fredrik Johansson 2016-09-14 13:48:06 +02:00
commit 37e0ad9610
5 changed files with 83 additions and 39 deletions
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4
acb_dirichlet.h
View file

@ -255,11 +255,15 @@ void _acb_dirichlet_theta_argument_at_arb(arb_t xt, ulong q, const arb_t t, slon
void acb_dirichlet_theta_arb(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, const arb_t t, slong prec);
void acb_dirichlet_ui_theta_arb(acb_t res, const acb_dirichlet_group_t G, ulong a, const arb_t t, slong prec);
void acb_dirichlet_gauss_sum_order2(acb_t res, const acb_dirichlet_char_t chi, slong prec);
void acb_dirichlet_gauss_sum_naive(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec);
void acb_dirichlet_gauss_sum_theta(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec);
void acb_dirichlet_gauss_sum_factor(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec);
void acb_dirichlet_gauss_sum(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec);
void _acb_dirichlet_root_number(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec);
void acb_dirichlet_root_number(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec);
void acb_dirichlet_si_poly_evaluate(acb_t res, slong * v, slong len, const acb_t z, slong prec);
void acb_dirichlet_jacobi_sum_naive(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi1, const acb_dirichlet_char_t chi2, slong prec);

4
acb_dirichlet/dft_fast.c
View file

@ -161,7 +161,7 @@ _acb_dft_cyc(acb_ptr w, acb_srcptr v, dft_cyc_step * cyc, slong num, slong prec)
/* reorder */
for (i = 0; i < m; i++)
for (j = 0; j < M; j++)
w[j + M * i] = t[i + m * j];
acb_set(w + j + M * i, t + i + m * j);
_acb_vec_clear(t, m * M);
}
}
@ -216,7 +216,7 @@ _acb_dft_prod(acb_ptr w, acb_srcptr v, dft_prod_step * cyc, slong num, slong pre
/* reorder */
for (i = 0; i < m; i++)
for (j = 0; j < M; j++)
w[j + M * i] = t[i + m * j];
acb_set(w + j + M * i, t + i + m * j);
_acb_vec_clear(t, m * M);
}
}

25
acb_dirichlet/gauss_sum.c
View file

@ -74,6 +74,20 @@ gauss_sum_non_primitive(acb_t res, const acb_dirichlet_group_t G, const acb_diri
}
}
void
acb_dirichlet_gauss_sum_order2(acb_t res, const acb_dirichlet_char_t chi, slong prec)
{
if (chi->parity)
{
arb_zero(acb_realref(res));
arb_sqrt_ui(acb_imagref(res), chi->q, prec);
}
else
{
arb_zero(acb_imagref(res));
arb_sqrt_ui(acb_realref(res), chi->q, prec);
}
}
void
acb_dirichlet_gauss_sum(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec)
{
@ -84,16 +98,7 @@ acb_dirichlet_gauss_sum(acb_t res, const acb_dirichlet_group_t G, const acb_diri
}
else if (chi->order.n <= 2)
{
if (chi->parity)
{
arb_sqrt_ui(acb_imagref(res), G->q, prec);
arb_zero(acb_realref(res));
}
else
{
arb_sqrt_ui(acb_realref(res), G->q, prec);
arb_zero(acb_imagref(res));
}
acb_dirichlet_gauss_sum_order2(res, chi, prec);
}
else if (G->num > 1 && G->num > G->neven)
{

37
acb_dirichlet/gauss_sum_theta.c
View file

@ -14,38 +14,21 @@
void
acb_dirichlet_gauss_sum_theta(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec)
{
arb_t x;
acb_t eps;
arb_init(x);
if (chi->conductor < G->q || (G->q == 300 && (chi->x->n == 71 || chi->x->n == 131))
|| (G->q == 600 && (chi->x->n == 11 || chi->x->n == 491)))
{
/* or could use l'Hopital rule */
acb_dirichlet_gauss_sum_naive(res, G, chi, prec);
return;
}
arb_one(x);
acb_dirichlet_theta_arb(res, G, chi, x, prec);
acb_init(eps);
acb_conj(eps, res);
acb_div(eps, res, eps, prec);
if (chi->parity)
{
arb_zero(acb_realref(res));
arb_sqrt_ui(acb_imagref(res), G->q, prec);
flint_printf("gauss_sum_theta: non available for non primitive character"
"or exceptional characters chi_300(71,.), chi_300(131,.), "
"chi_600(11,.) and chi_600(491,.)\n");
abort();
}
else
{
arb_zero(acb_imagref(res));
arb_sqrt_ui(acb_realref(res), G->q, prec);
acb_t iq;
acb_init(iq);
acb_dirichlet_gauss_sum_order2(iq, chi, prec);
_acb_dirichlet_root_number(res, G, chi, prec);
acb_mul(res, res, iq, prec);
acb_clear(iq);
}
acb_mul(res, res, eps, prec);
arb_clear(x);
acb_clear(eps);
}

52
acb_dirichlet/root_number.c Normal file
View file

@ -0,0 +1,52 @@
/*
Copyright (C) 2016 Pascal Molin
This file is part of Arb.
Arb 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/>.
*/
#include "acb_dirichlet.h"
void
_acb_dirichlet_root_number(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec)
{
arb_t x;
acb_t eps;
arb_init(x);
arb_one(x);
acb_dirichlet_theta_arb(res, G, chi, x, prec);
acb_init(eps);
acb_conj(eps, res);
acb_div(res, res, eps, prec);
arb_clear(x);
acb_clear(eps);
}
void
acb_dirichlet_root_number(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong prec)
{
if (chi->conductor < G->q)
{
flint_printf("root number: need primitive character\n");
abort();
}
else if (G->num > 1)
{
acb_t iq;
acb_init(iq);
acb_dirichlet_gauss_sum_order2(iq, chi, prec);
acb_dirichlet_gauss_sum(res, G, chi, prec);
acb_div(res, res, iq, prec);
acb_clear(iq);
}
else
{
_acb_dirichlet_root_number(res, G, chi, prec);
}
}