int
main(void)
{
flint_rand_t state;
int iter;
printf("one/is_one....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
nmod_poly_mat_t A;
long m, n;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
m = n_randint(state, 10);
n = n_randint(state, 10);
nmod_poly_mat_init(A, m, n, mod);
nmod_poly_mat_randtest(A, state, n_randint(state, 5));
nmod_poly_mat_one(A);
if (!nmod_poly_mat_is_one(A))
{
printf("FAIL: expected matrix to be one\n");
abort();
}
if (m > 0 && n > 0)
{
m = n_randint(state, m);
n = n_randint(state, n);
if (m != n)
nmod_poly_randtest_not_zero(nmod_poly_mat_entry(A, m, n),
state, 5);
else
do { nmod_poly_randtest_not_zero(nmod_poly_mat_entry(A, m, n),
state, 5); }
while (nmod_poly_is_one(nmod_poly_mat_entry(A, m, n)));
if (nmod_poly_mat_is_one(A))
{
printf("FAIL: expected matrix not to be one\n");
abort();
}
}
nmod_poly_mat_clear(A);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int main (void)
{
double t;
nmod_poly_t f, g, h;
for (int i= 15001;i < 16000; i++)
{
nmod_poly_init2 (f, 17, i/2+1);
nmod_poly_init2 (g, 17, i+1);
nmod_poly_set_coeff_ui (f, i/2, 1);
nmod_poly_set_coeff_ui (f, 1, 1);
nmod_poly_set_coeff_ui (f, 0, ((i%17)*(i%17)+3) % 17);
nmod_poly_set_coeff_ui (g, i, 1);
nmod_poly_set_coeff_ui (g, i/2+1, 1);
nmod_poly_set_coeff_ui (g, 1, ((i % 17)+1)%17);
nmod_poly_set_coeff_ui (g, 0, 15);
nmod_poly_init (h, 17);
nmod_poly_gcd (h, f, g);
if (!nmod_poly_is_one (h))
{
flint_printf ("i= %d\n", i);
nmod_poly_factor_t factors;
nmod_poly_factor_init (factors);
t= clock();
nmod_poly_factor (factors, h);
t = (clock() - t) / CLOCKS_PER_SEC;
flint_printf("factorization %.2lf\n", t);
nmod_poly_factor_clear (factors);
}
nmod_poly_clear (f);
nmod_poly_clear (g);
nmod_poly_clear (h);
}
return EXIT_SUCCESS;
}
void
nmod_poly_factor_squarefree(nmod_poly_factor_t res, const nmod_poly_t f)
{
nmod_poly_t f_d, g, g_1;
mp_limb_t p;
slong deg, i;
if (f->length <= 1)
{
res->num = 0;
return;
}
if (f->length == 2)
{
nmod_poly_factor_insert(res, f, 1);
return;
}
p = nmod_poly_modulus(f);
deg = nmod_poly_degree(f);
/* Step 1, look at f', if it is zero then we are done since f = h(x)^p
for some particular h(x), clearly f(x) = sum a_k x^kp, k <= deg(f) */
nmod_poly_init(g_1, p);
nmod_poly_init(f_d, p);
nmod_poly_init(g, p);
nmod_poly_derivative(f_d, f);
/* Case 1 */
if (nmod_poly_is_zero(f_d))
{
nmod_poly_factor_t new_res;
nmod_poly_t h;
nmod_poly_init(h, p);
for (i = 0; i <= deg / p; i++) /* this will be an integer since f'=0 */
{
nmod_poly_set_coeff_ui(h, i, nmod_poly_get_coeff_ui(f, i * p));
}
/* Now run square-free on h, and return it to the pth power */
nmod_poly_factor_init(new_res);
nmod_poly_factor_squarefree(new_res, h);
nmod_poly_factor_pow(new_res, p);
nmod_poly_factor_concat(res, new_res);
nmod_poly_clear(h);
nmod_poly_factor_clear(new_res);
}
else
{
nmod_poly_t h, z;
nmod_poly_gcd(g, f, f_d);
nmod_poly_div(g_1, f, g);
i = 1;
nmod_poly_init(h, p);
nmod_poly_init(z, p);
/* Case 2 */
while (!nmod_poly_is_one(g_1))
{
nmod_poly_gcd(h, g_1, g);
nmod_poly_div(z, g_1, h);
/* out <- out.z */
if (z->length > 1)
{
nmod_poly_factor_insert(res, z, 1);
nmod_poly_make_monic(res->p + (res->num - 1),
res->p + (res->num - 1));
if (res->num)
res->exp[res->num - 1] *= i;
}
i++;
nmod_poly_set(g_1, h);
nmod_poly_div(g, g, h);
}
nmod_poly_clear(h);
nmod_poly_clear(z);
nmod_poly_make_monic(g, g);
if (!nmod_poly_is_one(g))
{
/* so now we multiply res with square-free(g^1/p) ^ p */
nmod_poly_t g_p; /* g^(1/p) */
nmod_poly_factor_t new_res_2;
nmod_poly_init(g_p, p);
for (i = 0; i <= nmod_poly_degree(g) / p; i++)
nmod_poly_set_coeff_ui(g_p, i, nmod_poly_get_coeff_ui(g, i*p));
nmod_poly_factor_init(new_res_2);
/* square-free(g^(1/p)) */
nmod_poly_factor_squarefree(new_res_2, g_p);
nmod_poly_factor_pow(new_res_2, p);
nmod_poly_factor_concat(res, new_res_2);
nmod_poly_clear(g_p);
nmod_poly_factor_clear(new_res_2);
}
}
nmod_poly_clear(g_1);
nmod_poly_clear(f_d);
nmod_poly_clear(g);
}
