124 lines
3.2 KiB
C
124 lines
3.2 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT 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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FLINT 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 FLINT; 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) 2011, 2012 Sebastian Pancratz
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******************************************************************************/
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#include "padic.h"
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void _padic_teichmuller(fmpz_t rop, const fmpz_t op, const fmpz_t p, slong N)
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{
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if (fmpz_equal_ui(p, 2))
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{
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fmpz_one(rop);
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}
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else if (N == 1)
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{
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fmpz_mod(rop, op, p);
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}
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else
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{
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slong *a, i, n;
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fmpz *pow, *u;
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fmpz_t s, t;
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fmpz_t inv;
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fmpz_t pm1;
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a = _padic_lifts_exps(&n, N);
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pow = _fmpz_vec_init(2 * n);
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u = pow + n;
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_padic_lifts_pows(pow, a, n, p);
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fmpz_init(s);
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fmpz_init(t);
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fmpz_init(inv);
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fmpz_init(pm1);
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fmpz_sub_ui(pm1, p, 1);
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/* Compute reduced units for (p-1) */
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{
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fmpz_mod(u + 0, pm1, pow + 0);
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}
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for (i = 1; i < n; i++)
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{
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fmpz_mod(u + i, u + (i - 1), pow + i);
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}
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/* Run Newton iteration */
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i = n - 1;
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{
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fmpz_mod(rop, op, pow + i);
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fmpz_set(inv, pm1);
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}
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for (i--; i >= 0; i--)
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{
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/* Lift rop */
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fmpz_powm(s, rop, p, pow + i);
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fmpz_sub(s, s, rop);
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fmpz_mul(t, s, inv);
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fmpz_sub(rop, rop, t);
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fmpz_mod(rop, rop, pow + i);
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/* Lift inv */
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if (i > 0)
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{
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fmpz_mul(s, inv, inv);
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fmpz_mul(t, u + i, s);
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fmpz_mul_2exp(inv, inv, 1);
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fmpz_sub(inv, inv, t);
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fmpz_mod(inv, inv, pow + i);
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}
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}
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fmpz_clear(s);
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fmpz_clear(t);
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fmpz_clear(inv);
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fmpz_clear(pm1);
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_fmpz_vec_clear(pow, 2 * n);
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flint_free(a);
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}
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}
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void padic_teichmuller(padic_t rop, const padic_t op, const padic_ctx_t ctx)
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{
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if (padic_val(op) < 0)
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{
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flint_printf("Exception (padic_teichmuller). op is not a p-adic integer.\n");
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abort();
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}
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if (padic_is_zero(op) || padic_val(op) > 0 || padic_prec(rop) <= 0)
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{
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padic_zero(rop);
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}
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else
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{
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_padic_teichmuller(padic_unit(rop), padic_unit(op), ctx->p, padic_prec(rop));
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padic_val(rop) = 0;
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}
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}
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