pqc/external/flint-2.4.3/qadic/norm_resultant.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2012 Sebastian Pancratz
******************************************************************************/
#include "qadic.h"
/*
Computes the characteristic polynomial of the $n \times n$ matrix $M$
modulo \code{pN} using a division-free algorithm in $O(n^4)$ ring
operations.
Only returns the determinant.
Assumes that $n$ is at least $2$.
*/
static
void _fmpz_mod_mat_det(fmpz_t rop, const fmpz *M, slong n, const fmpz_t pN)
{
fmpz *F;
fmpz *a;
fmpz *A;
fmpz_t s;
slong t, i, j, p, k;
F = _fmpz_vec_init(n);
a = _fmpz_vec_init((n-1) * n);
A = _fmpz_vec_init(n);
fmpz_init(s);
fmpz_neg(F + 0, M + 0*n + 0);
for (t = 1; t < n; t++)
{
for (i = 0; i <= t; i++)
fmpz_set(a + 0*n + i, M + i*n + t);
fmpz_set(A + 0, M + t*n + t);
for (p = 1; p < t; p++)
{
for (i = 0; i <= t; i++)
{
fmpz_zero(s);
for (j = 0; j <= t; j++)
fmpz_addmul(s, M + i*n + j, a + (p-1)*n + j);
fmpz_mod(a + p*n + i, s, pN);
}
fmpz_set(A + p, a + p*n + t);
}
fmpz_zero(s);
for (j = 0; j <= t; j++)
fmpz_addmul(s, M + t*n + j, a + (t-1)*n + j);
fmpz_mod(A + t, s, pN);
for (p = 0; p <= t; p++)
{
fmpz_sub(F + p, F + p, A + p);
for (k = 0; k < p; k++)
fmpz_submul(F + p, A + k, F + (p-k-1));
fmpz_mod(F + p, F + p, pN);
}
}
/*
Now [F{n-1}, F{n-2}, ..., F{0}, 1] is the
characteristic polynomial of the matrix M.
*/
if (n % WORD(2) == 0)
{
fmpz_set(rop, F + (n-1));
}
else
{
fmpz_neg(rop, F + (n-1));
fmpz_mod(rop, rop, pN);
}
_fmpz_vec_clear(F, n);
_fmpz_vec_clear(a, (n-1)*n);
_fmpz_vec_clear(A, n);
fmpz_clear(s);
}
void _qadic_norm_resultant(fmpz_t rop, const fmpz *op, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
fmpz_t pN;
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
if (len == 1)
{
fmpz_powm_ui(rop, op + 0, d, pN);
}
else /* len >= 2 */
{
{
const slong n = d + len - 1;
slong i, k;
fmpz *M;
M = flint_calloc(n * n, sizeof(fmpz));
for (k = 0; k < len-1; k++)
{
for (i = 0; i < lena; i++)
{
M[k * n + k + (d - j[i])] = a[i];
}
}
for (k = 0; k < d; k++)
{
for (i = 0; i < len; i++)
{
M[(len-1 + k) * n + k + (len-1 - i)] = op[i];
}
}
_fmpz_mod_mat_det(rop, M, n, pN);
flint_free(M);
}
/*
XXX: This part of the code is currently untested as the Conway
polynomials used for the extension Qq/Qp are monic.
*/
if (!fmpz_is_one(a + (lena - 1)))
{
fmpz_t f;
fmpz_init(f);
fmpz_powm_ui(f, a + (lena - 1), len - 1, pN);
_padic_inv(f, f, p, N);
fmpz_mul(rop, f, rop);
fmpz_mod(rop, rop, pN);
fmpz_clear(f);
}
}
fmpz_clear(pN);
}
void qadic_norm_resultant(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
const slong N = padic_prec(rop);
const slong d = qadic_ctx_degree(ctx);
/* N(p^v u) = p^{dv} N(u) */
if (qadic_is_zero(op) || d * op->val >= N)
{
padic_zero(rop);
}
else
{
_qadic_norm_resultant(padic_unit(rop), op->coeffs, op->length,
ctx->a, ctx->j, ctx->len, (&ctx->pctx)->p,
N - d * op->val);
padic_val(rop) = d * op->val;
}
}