144 lines
3.6 KiB
C
144 lines
3.6 KiB
C
/*=============================================================================
|
|
|
|
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) 2010 Sebastian Pancratz
|
|
|
|
******************************************************************************/
|
|
|
|
#include <stdlib.h>
|
|
#include <gmp.h>
|
|
#include "flint.h"
|
|
#include "fmpz.h"
|
|
#include "fmpz_vec.h"
|
|
#include "fmpz_poly.h"
|
|
|
|
void _fmpz_poly_signature(slong * r1, slong * r2, const fmpz * poly, slong len)
|
|
{
|
|
fmpz *A, *B, *f, *g, *h, *w;
|
|
slong lenA, lenB;
|
|
int s, t;
|
|
|
|
if (len <= 2)
|
|
{
|
|
*r1 = (len == 2);
|
|
*r2 = 0;
|
|
return;
|
|
}
|
|
|
|
w = _fmpz_vec_init(2 * len + 2);
|
|
A = w;
|
|
B = w + len;
|
|
lenA = len;
|
|
lenB = lenA - 1;
|
|
f = w + 2 * len - 1;
|
|
g = w + 2 * len;
|
|
h = w + 2 * len + 1;
|
|
|
|
_fmpz_poly_primitive_part(A, poly, lenA);
|
|
_fmpz_poly_derivative(B, A, lenA);
|
|
_fmpz_poly_primitive_part(B, B, lenB);
|
|
|
|
fmpz_one(g);
|
|
fmpz_one(h);
|
|
|
|
s = 1;
|
|
t = (lenA & WORD(1)) ? -s : s;
|
|
*r1 = 1;
|
|
|
|
while (1)
|
|
{
|
|
slong delta = lenA - lenB;
|
|
int sgnA;
|
|
|
|
_fmpz_poly_pseudo_rem_cohen(A, A, lenA, B, lenB);
|
|
|
|
lenA = lenB;
|
|
FMPZ_VEC_NORM(A, lenA);
|
|
|
|
if (lenA == 0)
|
|
{
|
|
flint_printf("Exception (fmpz_poly_signature). Non-squarefree polynomial detected.\n");
|
|
_fmpz_vec_clear(w, 2 * len + 2);
|
|
abort();
|
|
}
|
|
|
|
if ((fmpz_sgn(B + (lenB - 1)) > 0) || (delta & WORD(1)))
|
|
_fmpz_vec_neg(A, A, lenA);
|
|
|
|
sgnA = fmpz_sgn(A + (lenA - 1));
|
|
if (sgnA != s)
|
|
{
|
|
s = -s;
|
|
(*r1)--;
|
|
}
|
|
if (sgnA != ((lenA & WORD(1)) ? t : -t))
|
|
{
|
|
t = -t;
|
|
(*r1)++;
|
|
}
|
|
|
|
if (lenA == 1)
|
|
{
|
|
*r2 = ((len - 1) - *r1) / 2;
|
|
|
|
_fmpz_vec_clear(w, 2 * len + 2);
|
|
return;
|
|
}
|
|
else
|
|
{
|
|
{
|
|
fmpz * temp = A;
|
|
A = B;
|
|
B = temp;
|
|
}
|
|
{
|
|
slong temp = lenA;
|
|
lenA = lenB;
|
|
lenB = temp;
|
|
}
|
|
|
|
if (delta == 1)
|
|
{
|
|
fmpz_mul(f, g, h);
|
|
_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, f);
|
|
fmpz_set(g, A + (lenA - 1));
|
|
fmpz_set(h, g);
|
|
}
|
|
else
|
|
{
|
|
fmpz_pow_ui(f, h, delta);
|
|
fmpz_mul(f, f, g);
|
|
_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, f);
|
|
fmpz_pow_ui(f, h, delta - 1);
|
|
fmpz_pow_ui(g, A + (lenA - 1), delta);
|
|
fmpz_divexact(h, g, f);
|
|
fmpz_set(g, A + (lenA - 1));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void fmpz_poly_signature(slong * r1, slong * r2, const fmpz_poly_t poly)
|
|
{
|
|
_fmpz_poly_signature(r1, r2, poly->coeffs, poly->length);
|
|
}
|
|
|