int
main(void)
{
int i, result;
flint_rand_t state;
flint_randinit(state);
printf("rem....");
fflush(stdout);
/* Check result of rem */
for (i = 0; i < 1000; i++)
{
nmod_poly_t a, b, q, r, prod;
mp_limb_t n;
do n = n_randtest_not_zero(state);
while (!n_is_probabprime(n));
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(q, n);
nmod_poly_init(r, n);
nmod_poly_init(prod, n);
nmod_poly_randtest(a, state, n_randint(state, 2000));
do nmod_poly_randtest(b, state, n_randint(state, 2000));
while (b->length == 0);
nmod_poly_div(q, a, b);
nmod_poly_rem(r, a, b);
nmod_poly_mul(prod, q, b);
nmod_poly_add(prod, prod, r);
result = (nmod_poly_equal(a, prod));
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(a), printf("\n\n");
nmod_poly_print(prod), printf("\n\n");
nmod_poly_print(q), printf("\n\n");
nmod_poly_print(r), printf("\n\n");
printf("n = %ld\n", n);
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(q);
nmod_poly_clear(r);
nmod_poly_clear(prod);
}
/* Check aliasing of a and r */
for (i = 0; i < 1000; i++)
{
nmod_poly_t a, b, r;
mp_limb_t n;
do n = n_randtest(state);
while (!n_is_probabprime(n));
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(r, n);
nmod_poly_randtest(a, state, n_randint(state, 2000));
do nmod_poly_randtest(b, state, n_randint(state, 2000));
while (b->length == 0);
nmod_poly_rem(r, a, b);
nmod_poly_rem(a, a, b);
result = (nmod_poly_equal(a, r));
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(a), printf("\n\n");
nmod_poly_print(b), printf("\n\n");
nmod_poly_print(r), printf("\n\n");
printf("n = %ld\n", n);
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(r);
}
/* Check aliasing of b and r */
for (i = 0; i < 1000; i++)
{
nmod_poly_t a, b, r;
mp_limb_t n;
do n = n_randtest(state);
while (!n_is_probabprime(n));
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(r, n);
nmod_poly_randtest(a, state, n_randint(state, 2000));
do nmod_poly_randtest(b, state, n_randint(state, 2000));
while (b->length == 0);
nmod_poly_rem(r, a, b);
nmod_poly_rem(b, a, b);
result = (nmod_poly_equal(b, r));
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(a), printf("\n\n");
nmod_poly_print(b), printf("\n\n");
nmod_poly_print(r), printf("\n\n");
printf("n = %ld\n", n);
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(r);
}
/* Check result of rem_q1 */
for (i = 0; i < 5000; i++)
{
nmod_poly_t a, b, q0, r0, r;
mp_limb_t n = n_randprime(state, n_randint(state,FLINT_BITS-1)+2, 0);
nmod_poly_init(a, n);
nmod_poly_init(b, n);
nmod_poly_init(q0, n);
nmod_poly_init(r0, n);
nmod_poly_init(r, n);
do nmod_poly_randtest(a, state, n_randint(state, 1000));
while (a->length < 2);
nmod_poly_fit_length(b, a->length - 1);
mpn_zero(b->coeffs, a->length - 1);
nmod_poly_randtest_not_zero(b, state, n_randint(state, 1000) + 1);
do b->coeffs[a->length - 2] = n_randint(state, n);
while (b->coeffs[a->length - 2] == 0);
b->length = a->length - 1;
nmod_poly_divrem(q0, r0, a, b);
nmod_poly_rem(r, a, b);
result = (nmod_poly_equal(r0, r));
if (!result)
{
printf("FAIL:\n");
nmod_poly_print(a), printf("\n\n");
nmod_poly_print(b), printf("\n\n");
nmod_poly_print(q0), printf("\n\n");
nmod_poly_print(r0), printf("\n\n");
nmod_poly_print(r), printf("\n\n");
printf("n = %ld\n", n);
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(q0);
nmod_poly_clear(r0);
nmod_poly_clear(r);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
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);
}
slong
nmod_poly_mat_rref(nmod_poly_mat_t R, nmod_poly_t den, const nmod_poly_mat_t A)
{
slong i, j, k, m, n, rank;
slong *pivots, *nonpivots;
rank = nmod_poly_mat_fflu(R, den, NULL, A, 0);
m = nmod_poly_mat_nrows(R);
n = nmod_poly_mat_ncols(R);
/* clear bottom */
for (i = rank; i < m; i++)
for (j = 0; j < n; j++)
nmod_poly_zero(nmod_poly_mat_entry(R, i, j));
/* Convert row echelon form to reduced row echelon form */
if (rank > 1)
{
nmod_poly_t tmp, tmp2;
nmod_poly_init(tmp, nmod_poly_mat_modulus(R));
nmod_poly_init(tmp2, nmod_poly_mat_modulus(R));
pivots = flint_malloc(sizeof(slong) * n);
nonpivots = pivots + rank;
/* find pivot positions */
for (i = j = k = 0; i < rank; i++)
{
while (nmod_poly_is_zero(nmod_poly_mat_entry(R, i, j)))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < n - rank)
{
nonpivots[k] = j;
k++;
j++;
}
for (k = 0; k < n - rank; k++)
{
for (i = rank - 2; i >= 0; i--)
{
nmod_poly_mul(tmp, den, nmod_poly_mat_entry(R, i, nonpivots[k]));
for (j = i + 1; j < rank; j++)
{
nmod_poly_mul(tmp2, nmod_poly_mat_entry(R, i, pivots[j]),
nmod_poly_mat_entry(R, j, nonpivots[k]));
nmod_poly_sub(tmp, tmp, tmp2);
}
nmod_poly_div(nmod_poly_mat_entry(R, i, nonpivots[k]),
tmp, nmod_poly_mat_entry(R, i, pivots[i]));
}
}
/* clear pivot columns */
for (i = 0; i < rank; i++)
{
for (j = 0; j < rank; j++)
{
if (i == j)
nmod_poly_set(nmod_poly_mat_entry(R, j, pivots[i]), den);
else
nmod_poly_zero(nmod_poly_mat_entry(R, j, pivots[i]));
}
}
flint_free(pivots);
nmod_poly_clear(tmp);
nmod_poly_clear(tmp2);
}
return rank;
}
