mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
114 lines
3.8 KiB
C
114 lines
3.8 KiB
C
/*
|
|
Copyright (C) 2015 Jonathan Bober
|
|
Copyright (C) 2016 Fredrik Johansson
|
|
|
|
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/>.
|
|
*/
|
|
|
|
#ifndef ACB_DIRICHLET_H
|
|
#define ACB_DIRICHLET_H
|
|
|
|
#include "acb.h"
|
|
|
|
#ifdef __cplusplus
|
|
extern "C" {
|
|
#endif
|
|
|
|
typedef struct
|
|
{
|
|
ulong q; /* modulus */
|
|
ulong q_even; /* even part of modulus */
|
|
ulong q_odd; /* odd part of modulus */
|
|
ulong phi_q; /* phi(q) = group size */
|
|
ulong expo; /* group exponent = lcm(phi(q_even), phi(p[k]^e[k]) ) */
|
|
slong neven; /* number of even components (in 0,1,2)*/
|
|
slong num; /* number of prime components (even + odd) */
|
|
ulong * primes; /* primes p[k] */
|
|
ulong * exponents; /* exponents e[k] */
|
|
ulong * primepowers; /* powers p[k]^[k] */
|
|
ulong * generators; /* generator for each prime p[k] lifted mod q */
|
|
ulong * phi; /* phi(k) = phi(p[k]^e[k]) */
|
|
ulong * PHI; /* PHI(k) = expo / phi(k) */
|
|
}
|
|
acb_dirichlet_group_struct;
|
|
|
|
typedef acb_dirichlet_group_struct acb_dirichlet_group_t[1];
|
|
|
|
/* elements of the group, keep both number and log */
|
|
typedef struct
|
|
{
|
|
ulong n; /* number */
|
|
ulong * log; /* s.t. prod generators[k]^log[k] = number */
|
|
}
|
|
acb_conrey_struct;
|
|
|
|
typedef acb_conrey_struct acb_conrey_t[1];
|
|
|
|
void _acb_dirichlet_euler_product_real_ui(arb_t res, ulong s,
|
|
const signed char * chi, int mod, int reciprocal, slong prec);
|
|
|
|
void acb_dirichlet_eta(acb_t res, const acb_t s, slong prec);
|
|
|
|
void acb_dirichlet_group_init(acb_dirichlet_group_t G, ulong q);
|
|
|
|
void acb_dirichlet_group_clear(acb_dirichlet_group_t G);
|
|
|
|
void acb_conrey_init(acb_conrey_t x, const acb_dirichlet_group_t G);
|
|
|
|
void acb_conrey_clear(acb_conrey_t x);
|
|
|
|
void acb_conrey_one(acb_conrey_t x, const acb_dirichlet_group_t G);
|
|
|
|
void acb_conrey_first_primitive(acb_conrey_t x, const acb_dirichlet_group_t G);
|
|
|
|
void acb_conrey_log(acb_conrey_t x, const acb_dirichlet_group_t G, ulong m);
|
|
|
|
int acb_conrey_next(acb_conrey_t x, const acb_dirichlet_group_t G);
|
|
|
|
long n_dirichlet_chi_conrey(const acb_dirichlet_group_t G, const acb_conrey_t a, const acb_conrey_t b);
|
|
|
|
long n_dirichlet_chi(const acb_dirichlet_group_t G, ulong m, ulong n);
|
|
|
|
void acb_dirichlet_chi_conrey(acb_t res, const acb_dirichlet_group_t G, const acb_conrey_t a, const acb_conrey_t b, slong prec);
|
|
|
|
void acb_dirichlet_chi(acb_t res, const acb_dirichlet_group_t G, ulong m, ulong n, slong prec);
|
|
|
|
/* introducing character type */
|
|
|
|
/* character = reduced exponents, keep order and number */
|
|
typedef struct
|
|
{
|
|
ulong q; /* modulus */
|
|
ulong n; /* number */
|
|
ulong order; /* order */
|
|
ulong * expo; /* reduced exponents ( order * log[k] / gcd( ) ) */
|
|
}
|
|
acb_dirichlet_char_struct;
|
|
|
|
typedef acb_dirichlet_char_struct acb_dirichlet_char_t[1];
|
|
|
|
void acb_dirichlet_char_init(acb_dirichlet_char_t chi, const acb_dirichlet_group_t G);
|
|
|
|
void acb_dirichlet_char_clear(acb_dirichlet_char_t chi);
|
|
|
|
void acb_dirichlet_char(acb_dirichlet_char_t chi, const acb_dirichlet_group_t G, ulong n);
|
|
|
|
long n_dirichlet_char_eval(const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, ulong n);
|
|
|
|
void acb_dirichlet_char_eval(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, ulong n, slong prec);
|
|
|
|
void n_dirichlet_char_vec(long *v, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, ulong nv);
|
|
|
|
void acb_dirichlet_char_vec(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, ulong n, slong prec);
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|
|
|
|
#endif
|
|
|