1 /*
2 Copyright (C) 2012 Sebastian Pancratz
3
4 This file is part of FLINT.
5
6 FLINT is free software: you can redistribute it and/or modify it under
7 the terms of the GNU Lesser General Public License (LGPL) as published
8 by the Free Software Foundation; either version 2.1 of the License, or
9 (at your option) any later version. See <http://www.gnu.org/licenses/>.
10 */
11
12 #include "qadic.h"
13
14 /*
15 Computes the norm of an element $x$ of $\mathbf{Z}_q$ via the identity
16
17 $\Norm(x) = \exp \Trace \log (x)$
18
19 whenever $y = 1-x$ has valuation $v$ greater than $(p-1)^{-1}$.
20
21 Assumes that $y$ is non-zero.
22 */
23
_qadic_norm_analytic(fmpz_t rop,const fmpz * y,slong v,slong len,const fmpz * a,const slong * j,slong lena,const fmpz_t p,slong N)24 void _qadic_norm_analytic(fmpz_t rop, const fmpz *y, slong v, slong len,
25 const fmpz *a, const slong *j, slong lena,
26 const fmpz_t p, slong N)
27 {
28 const slong d = j[lena - 1];
29 fmpz_t pN, tru;
30 slong trv;
31 fmpz *lg;
32
33 fmpz_init(pN);
34 fmpz_init(tru);
35 lg = _fmpz_vec_init(d);
36
37 fmpz_pow_ui(pN, p, N);
38
39 _qadic_log(lg, y, v, len, a, j, lena, p, N, pN);
40
41 _qadic_trace(tru, lg, d, a, j, lena, pN);
42
43 if (!fmpz_is_zero(tru))
44 {
45 trv = fmpz_remove(tru, tru, p);
46 _padic_exp(rop, tru, trv, p, N);
47 fmpz_mod(rop, rop, pN);
48 }
49 else
50 {
51 fmpz_one(rop);
52 }
53
54 fmpz_clear(pN);
55 fmpz_clear(tru);
56 _fmpz_vec_clear(lg, d);
57 }
58
qadic_norm_analytic(padic_t rop,const qadic_t op,const qadic_ctx_t ctx)59 void qadic_norm_analytic(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
60 {
61 const slong N = padic_prec(rop);
62 const slong d = qadic_ctx_degree(ctx);
63 const fmpz *p = (&ctx->pctx)->p;
64
65 /* N(p^v u) = p^{dv} N(u) */
66
67 if (qadic_is_zero(op) || d * op->val >= N)
68 {
69 padic_zero(rop);
70 }
71 else if (op->length == 1)
72 {
73 fmpz_t pN;
74 int alloc;
75
76 alloc = _padic_ctx_pow_ui(pN, N - d * op->val, (&ctx->pctx));
77
78 fmpz_powm_ui(padic_unit(rop), op->coeffs + 0, d, pN);
79 padic_val(rop) = d * op->val;
80
81 if (alloc)
82 fmpz_clear(pN);
83 }
84 else /* len >= 2 */
85 {
86 fmpz *y;
87 slong w;
88
89 y = _fmpz_vec_init(op->length);
90
91 _fmpz_vec_neg(y, op->coeffs, op->length);
92 fmpz_add_ui(y + 0, y + 0, 1);
93 w = _fmpz_vec_ord_p(y, op->length, p);
94
95 if ((w < 2 && *p == WORD(2)) || w < 1)
96 {
97 flint_printf("ERROR (qadic_norm_analytic). w = %wd.\n", w);
98 flint_abort();
99 }
100
101 _qadic_norm_analytic(padic_unit(rop), y, w, op->length,
102 ctx->a, ctx->j, ctx->len, p, N - d * op->val);
103 padic_val(rop) = d * op->val;
104
105 _fmpz_vec_clear(y, op->length);
106 }
107 }
108
109