257 lines
7.6 KiB
C
257 lines
7.6 KiB
C
/*=============================================================================
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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) 2009 William Hart
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Copyright (C) 2010 Sebastian Pancratz
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******************************************************************************/
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#include <stdio.h>
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#include <stdlib.h>
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "fmpz_poly.h"
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#include "ulong_extras.h"
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/*
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Tests whether the polynomial is suitably normalised for the
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result of a GCD operation, that is, whether it's leading
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coefficient is non-negative.
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*/
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static
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int _t_gcd_is_canonical(const fmpz_poly_t poly)
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{
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return fmpz_poly_is_zero(poly) || (fmpz_sgn(fmpz_poly_lead(poly)) > 0);
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}
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int
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main(void)
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{
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int i, result;
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FLINT_TEST_INIT(state);
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flint_printf("gcd_modular....");
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fflush(stdout);
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/* Check aliasing of a and b */
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for (i = 0; i < 100 * flint_test_multiplier(); i++)
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{
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fmpz_poly_t a, b, c;
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fmpz_poly_init(a);
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fmpz_poly_init(b);
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fmpz_poly_init(c);
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fmpz_poly_randtest(b, state, n_randint(state, 40), 80);
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fmpz_poly_randtest(c, state, n_randint(state, 40), 80);
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fmpz_poly_gcd_modular(a, b, c);
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fmpz_poly_gcd_modular(b, b, c);
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result = (fmpz_poly_equal(a, b) && _t_gcd_is_canonical(a));
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if (!result)
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{
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flint_printf("FAIL (aliasing a and b):\n");
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flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
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flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
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abort();
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}
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fmpz_poly_clear(a);
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fmpz_poly_clear(b);
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fmpz_poly_clear(c);
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}
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/* Check aliasing of a and c */
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for (i = 0; i < 100 * flint_test_multiplier(); i++)
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{
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fmpz_poly_t a, b, c;
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fmpz_poly_init(a);
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fmpz_poly_init(b);
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fmpz_poly_init(c);
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fmpz_poly_randtest(b, state, n_randint(state, 40), 80);
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fmpz_poly_randtest(c, state, n_randint(state, 40), 80);
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fmpz_poly_gcd_modular(a, b, c);
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fmpz_poly_gcd_modular(c, b, c);
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result = (fmpz_poly_equal(a, c) && _t_gcd_is_canonical(a));
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if (!result)
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{
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flint_printf("FAIL (aliasing a and c):\n");
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flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
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flint_printf("c = "), fmpz_poly_print(c), flint_printf("\n\n");
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abort();
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}
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fmpz_poly_clear(a);
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fmpz_poly_clear(b);
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fmpz_poly_clear(c);
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}
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/* Check that a divides GCD(af, ag) */
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for (i = 0; i < 300 * flint_test_multiplier(); i++)
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{
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fmpz_poly_t a, d, f, g, q, r;
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fmpz_poly_init(a);
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fmpz_poly_init(d);
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fmpz_poly_init(f);
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fmpz_poly_init(g);
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fmpz_poly_init(q);
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fmpz_poly_init(r);
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fmpz_poly_randtest_not_zero(a, state, n_randint(state, 100) + 1, 40);
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fmpz_poly_randtest(f, state, n_randint(state, 100), 40);
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fmpz_poly_randtest(g, state, n_randint(state, 100), 40);
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fmpz_poly_mul(f, a, f);
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fmpz_poly_mul(g, a, g);
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fmpz_poly_gcd_modular(d, f, g);
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fmpz_poly_divrem_divconquer(q, r, d, a);
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result = fmpz_poly_is_zero(r) && _t_gcd_is_canonical(d);
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if (!result)
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{
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flint_printf("FAIL (check a | gcd(af, ag)):\n");
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flint_printf("f = "), fmpz_poly_print(f), flint_printf("\n");
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flint_printf("g = "), fmpz_poly_print(g), flint_printf("\n");
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flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n");
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flint_printf("d = "), fmpz_poly_print(d), flint_printf("\n");
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abort();
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}
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fmpz_poly_clear(a);
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fmpz_poly_clear(d);
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fmpz_poly_clear(f);
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fmpz_poly_clear(g);
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fmpz_poly_clear(q);
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fmpz_poly_clear(r);
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}
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/* Check that a == GCD(af, ag) when GCD(f, g) = 1 */
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for (i = 0; i < 300 * flint_test_multiplier(); i++)
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{
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fmpz_poly_t a, d, f, g, q, r;
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fmpz_poly_init(a);
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fmpz_poly_init(d);
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fmpz_poly_init(f);
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fmpz_poly_init(g);
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fmpz_poly_init(q);
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fmpz_poly_init(r);
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fmpz_poly_randtest_not_zero(a, state, n_randint(state, 100) + 1, 200);
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do {
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fmpz_poly_randtest(f, state, n_randint(state, 100), 200);
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fmpz_poly_randtest(g, state, n_randint(state, 100), 200);
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fmpz_poly_gcd_heuristic(d, f, g);
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} while (!(d->length == 1 && fmpz_is_one(d->coeffs)));
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fmpz_poly_mul(f, a, f);
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fmpz_poly_mul(g, a, g);
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fmpz_poly_gcd_modular(d, f, g);
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if (!_t_gcd_is_canonical(a)) fmpz_poly_neg(a, a);
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result = fmpz_poly_equal(d, a) && _t_gcd_is_canonical(d);
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if (!result)
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{
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flint_printf("FAIL (check a == gcd(af, ag) when gcd(f, g) = 1):\n");
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flint_printf("f = "), fmpz_poly_print(f), flint_printf("\n");
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flint_printf("g = "), fmpz_poly_print(g), flint_printf("\n");
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flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n");
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flint_printf("d = "), fmpz_poly_print(d), flint_printf("\n");
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abort();
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}
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fmpz_poly_clear(a);
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fmpz_poly_clear(d);
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fmpz_poly_clear(f);
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fmpz_poly_clear(g);
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fmpz_poly_clear(q);
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fmpz_poly_clear(r);
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}
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/* Sebastian's test case */
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{
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fmpz_poly_t a, b, d;
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fmpz_poly_init(a);
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fmpz_poly_init(b);
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fmpz_poly_init(d);
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fmpz_poly_set_coeff_ui(b, 2, 1);
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fmpz_poly_set_coeff_si(a, 0, -32);
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fmpz_poly_set_coeff_si(a, 1, 24);
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fmpz_poly_gcd_modular(d, a, b);
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result = (d->length == 1 && fmpz_is_one(d->coeffs));
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if (!result)
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{
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flint_printf("FAIL (check 1 == gcd(x^2, 24*x - 32):\n");
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fmpz_poly_print(d); flint_printf("\n");
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abort();
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}
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fmpz_poly_clear(a);
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fmpz_poly_clear(b);
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fmpz_poly_clear(d);
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}
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/* another test case */
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{
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fmpz_poly_t a, b, d, e;
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fmpz_poly_init(a);
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fmpz_poly_init(b);
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fmpz_poly_init(d);
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fmpz_poly_init(e);
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fmpz_poly_set_str(a, "12 0 0 0 0 0 0 0 0 0 8582594367 -9297159048333985579007 33822867456");
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fmpz_poly_set_str(b, "8 0 0 -258272396248218664896 0 -2762 -549690802047 -3771028 8796059467776");
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fmpz_poly_set_str(e, "3 0 0 1");
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fmpz_poly_gcd_modular(d, a, b);
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result = fmpz_poly_equal(d, e);
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if (!result)
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{
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flint_printf("FAIL (check special #2):\n");
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fmpz_poly_print(d); flint_printf("\n");
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abort();
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}
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fmpz_poly_clear(a);
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fmpz_poly_clear(b);
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fmpz_poly_clear(d);
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fmpz_poly_clear(e);
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}
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FLINT_TEST_CLEANUP(state);
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flint_printf("PASS\n");
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return 0;
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}
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