mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
106 lines
4.8 KiB
C
106 lines
4.8 KiB
C
/*
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Copyright (C) 2015 Jonathan Bober
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Copyright (C) 2016 Fredrik Johansson
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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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#ifndef ACB_DIRICHLET_H
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#define ACB_DIRICHLET_H
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#ifdef ACB_DIRICHLET_INLINES_C
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#define ACB_DIRICHLET_INLINE
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#else
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#define ACB_DIRICHLET_INLINE static __inline__
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#endif
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#include "acb.h"
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#include "dirichlet.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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void _acb_dirichlet_euler_product_real_ui(arb_t res, ulong s,
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const signed char * chi, int mod, int reciprocal, slong prec);
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void acb_dirichlet_eta(acb_t res, const acb_t s, slong prec);
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void acb_dirichlet_pairing(acb_t res, const dirichlet_group_t G, ulong m, ulong n, slong prec);
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void acb_dirichlet_chi_char(acb_t res, const dirichlet_group_t G, const dirichlet_char_t a, const dirichlet_char_t b, slong prec);
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/* precompute powers of a root of unity */
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typedef struct
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{
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ulong order;
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acb_t z;
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slong size;
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slong depth;
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acb_ptr * Z;
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}
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acb_dirichlet_powers_struct;
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typedef acb_dirichlet_powers_struct acb_dirichlet_powers_t[1];
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void _acb_dirichlet_powers_init(acb_dirichlet_powers_t t, ulong order, slong size, slong depth, slong prec);
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void acb_dirichlet_powers_init(acb_dirichlet_powers_t t, ulong order, slong num, slong prec);
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void acb_dirichlet_powers_clear(acb_dirichlet_powers_t t);
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void acb_dirichlet_power(acb_t z, const acb_dirichlet_powers_t t, ulong n, slong prec);
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void acb_dirichlet_chi(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, ulong n, slong prec);
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void acb_dirichlet_chi_vec(acb_ptr v, const dirichlet_group_t G, const dirichlet_char_t chi, slong nv, slong prec);
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void acb_dirichlet_arb_quadratic_powers(arb_ptr v, slong nv, const arb_t x, slong prec);
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void acb_dirichlet_qseries_arb(acb_t res, acb_srcptr a, const arb_t x, slong len, slong prec);
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void acb_dirichlet_qseries_arb_powers_naive(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_powers_t z, slong len, slong prec);
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void acb_dirichlet_qseries_arb_powers_smallorder(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_powers_t z, slong len, slong prec);
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ulong acb_dirichlet_theta_length_d(ulong q, double x, slong prec);
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ulong acb_dirichlet_theta_length(ulong q, const arb_t x, slong prec);
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void mag_tail_kexpk2_arb(mag_t res, const arb_t a, ulong n);
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void _acb_dirichlet_theta_argument_at_arb(arb_t xt, ulong q, const arb_t t, slong prec);
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void acb_dirichlet_theta_arb(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const arb_t t, slong prec);
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void acb_dirichlet_ui_theta_arb(acb_t res, const dirichlet_group_t G, ulong a, const arb_t t, slong prec);
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void acb_dirichlet_gauss_sum_naive(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum_factor(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum_order2(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum_theta(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_root_number_theta(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_root_number(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_si_poly_evaluate(acb_t res, slong * v, slong len, const acb_t z, slong prec);
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void acb_dirichlet_jacobi_sum_naive(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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ulong jacobi_one_prime(ulong p, ulong e, ulong pe, ulong cond);
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void acb_dirichlet_jacobi_sum_factor(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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void acb_dirichlet_jacobi_sum_gauss(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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void acb_dirichlet_jacobi_sum(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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void acb_dirichlet_jacobi_sum_ui(acb_t res, const dirichlet_group_t G, ulong a, ulong b, slong prec);
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void acb_dirichlet_l_hurwitz(acb_t res, const acb_t s, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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/* utils */
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ACB_DIRICHLET_INLINE void
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acb_vec_printd(acb_srcptr vec, slong len, slong digits)
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{
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slong i;
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for (i = 0; i < len; i++)
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acb_printd(vec + i, digits), flint_printf("\n");
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}
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#ifdef __cplusplus
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}
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#endif
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#endif
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