123 lines
3.3 KiB
C
123 lines
3.3 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) 2012 Sebastian Pancratz
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******************************************************************************/
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#include "qadic.h"
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/*
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Computes the norm of an element $x$ of $\mathbf{Z}_q$ via the identity
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$\Norm(x) = \exp \Trace \log (x)$
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whenever $y = 1-x$ has valuation $v$ greater than $(p-1)^{-1}$.
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Assumes that $y$ is non-zero.
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*/
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void _qadic_norm_analytic(fmpz_t rop, const fmpz *y, slong v, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N)
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{
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const slong d = j[lena - 1];
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fmpz_t pN, tru;
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slong trv;
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fmpz *lg;
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fmpz_init(pN);
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fmpz_init(tru);
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lg = _fmpz_vec_init(d);
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fmpz_pow_ui(pN, p, N);
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_qadic_log(lg, y, v, len, a, j, lena, p, N, pN);
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_qadic_trace(tru, lg, d, a, j, lena, pN);
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if (!fmpz_is_zero(tru))
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{
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trv = fmpz_remove(tru, tru, p);
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_padic_exp(rop, tru, trv, p, N);
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fmpz_mod(rop, rop, pN);
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}
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else
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{
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fmpz_one(rop);
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}
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fmpz_clear(pN);
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fmpz_clear(tru);
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_fmpz_vec_clear(lg, d);
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}
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void qadic_norm_analytic(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
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{
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const slong N = padic_prec(rop);
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const slong d = qadic_ctx_degree(ctx);
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const fmpz *p = (&ctx->pctx)->p;
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/* N(p^v u) = p^{dv} N(u) */
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if (qadic_is_zero(op) || d * op->val >= N)
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{
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padic_zero(rop);
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}
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else if (op->length == 1)
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{
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fmpz_t pN;
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int alloc;
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alloc = _padic_ctx_pow_ui(pN, N - d * op->val, (&ctx->pctx));
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fmpz_powm_ui(padic_unit(rop), op->coeffs + 0, d, pN);
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padic_val(rop) = d * op->val;
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if (alloc)
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fmpz_clear(pN);
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}
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else /* len >= 2 */
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{
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fmpz *y;
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slong w;
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y = _fmpz_vec_init(op->length);
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_fmpz_vec_neg(y, op->coeffs, op->length);
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fmpz_add_ui(y + 0, y + 0, 1);
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w = _fmpz_vec_ord_p(y, op->length, p);
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if ((w < 2 && *p == WORD(2)) || w < 1)
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{
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flint_printf("ERROR (qadic_norm_analytic). w = %wd.\n", w);
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abort();
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}
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_qadic_norm_analytic(padic_unit(rop), y, w, op->length,
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ctx->a, ctx->j, ctx->len, p, N - d * op->val);
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padic_val(rop) = d * op->val;
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_fmpz_vec_clear(y, op->length);
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}
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}
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