int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("swap....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, c;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest(b, state, n_randint(state, 100));
fmpz_mod_poly_set(c, b);
fmpz_mod_poly_swap(a, b);
result = (fmpz_mod_poly_equal(a, c));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_mod_poly_print(a), flint_printf("\n\n");
fmpz_mod_poly_print(b), flint_printf("\n\n");
fmpz_mod_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("neg....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, c;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_neg(b, a);
fmpz_mod_poly_neg(c, b);
result = (fmpz_mod_poly_equal(a, c));
if (!result)
{
printf("FAIL:\n");
fmpz_mod_poly_print(a), printf("\n\n");
fmpz_mod_poly_print(b), printf("\n\n");
fmpz_mod_poly_print(c), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
fmpz_clear(p);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("zero....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_zero(a);
result = (fmpz_mod_poly_is_zero(a));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), fmpz_mod_poly_print(a), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("divrem_f....");
fflush(stdout);
/* Check q*b + r = a when gcd(lead(B),p) = 1, no aliasing */
for (i = 0; i < 5000; i++)
{
fmpz_t f, p;
fmpz_mod_poly_t a, b, q, r, t;
fmpz_init(f);
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_init(r, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_divrem_f(f, q, r, a, b);
fmpz_mod_poly_mul(t, q, b);
fmpz_mod_poly_add(t, t, r);
result = (fmpz_is_one(f) && fmpz_mod_poly_equal(a, t));
if (!result)
{
flint_printf("FAIL (divrem):\n");
flint_printf("p = "), fmpz_print(p), flint_printf("\n\n");
flint_printf("f = "), fmpz_print(f), flint_printf("\n\n");
flint_printf("a = "), fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("q = "), fmpz_mod_poly_print(q), flint_printf("\n\n");
flint_printf("r = "), fmpz_mod_poly_print(r), flint_printf("\n\n");
flint_printf("t = "), fmpz_mod_poly_print(t), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_mod_poly_clear(r);
fmpz_mod_poly_clear(t);
fmpz_clear(f);
fmpz_clear(p);
}
/* Check f | p when gcd(lead(B),p) > 1 */
for (i = 0; i < 5000; i++)
{
fmpz_t f, p, q1, q2;
fmpz_mod_poly_t a, b, q, r, t;
fmpz_init(f);
fmpz_init(p);
fmpz_init(q1);
fmpz_init(q2);
fmpz_randtest_unsigned(q1, state, 2 * FLINT_BITS);
fmpz_randtest_unsigned(q2, state, 2 * FLINT_BITS);
fmpz_add_ui(q1, q1, 2);
fmpz_add_ui(q2, q2, 2);
fmpz_mul(p, q1, q2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_init(r, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
if (fmpz_is_one(d))
fmpz_set(leadB, q1);
fmpz_clear(d);
}
fmpz_mod_poly_divrem_f(f, q, r, a, b);
fmpz_mod_poly_mul(t, q, b);
fmpz_mod_poly_add(t, t, r);
result = (fmpz_cmp_ui(f, 1) > 0 && fmpz_cmp(f, p) < 0 && fmpz_divisible(p, f));
if (!result)
{
flint_printf("FAIL (factor):\n");
flint_printf("p = "), fmpz_print(p), flint_printf("\n\n");
flint_printf("f = "), fmpz_print(f), flint_printf("\n\n");
flint_printf("q1 = "), fmpz_print(q1), flint_printf("\n\n");
flint_printf("q2 = "), fmpz_print(q2), flint_printf("\n\n");
flint_printf("a = "), fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("q = "), fmpz_mod_poly_print(q), flint_printf("\n\n");
flint_printf("r = "), fmpz_mod_poly_print(r), flint_printf("\n\n");
flint_printf("t = "), fmpz_mod_poly_print(t), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_mod_poly_clear(r);
fmpz_mod_poly_clear(t);
fmpz_clear(f);
fmpz_clear(p);
fmpz_clear(q1);
fmpz_clear(q2);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main() {
slong n = 7;
fmpz_t mod;
fmpz* xs = _fmpz_vec_init(n);
fmpz* ys = _fmpz_vec_init(n);
fmpz_mod_poly_t res;
fmpz_poly_t res2;
fmpz_init(mod);
fmpz_set_ui(mod, 11);
fmpz_set_ui(xs, 0);
fmpz_set_ui(xs+1, 1);
fmpz_set_ui(xs+2, 2);
fmpz_set_ui(xs+3, 3);
fmpz_set_ui(xs+4, 4);
fmpz_set_ui(xs+5, 5);
fmpz_set_ui(xs+6, 6);
fmpz_set_si(ys, 5);
fmpz_set_si(ys+1, 1);
fmpz_set_si(ys+2, 4);
fmpz_set_si(ys+3, 8);
fmpz_set_si(ys+4, 4);
fmpz_set_si(ys+5, 1);
fmpz_set_si(ys+6, 5);
printf("xs :\n");
_fmpz_vec_print(xs,n);
printf("\n");
printf("ys :\n");
_fmpz_vec_print(ys,n);
printf("\n");
fmpz_mod_poly_init(res,mod);
fmpz_mod_poly_interpolate_fmpz_vec_fast(res, xs, ys, n, mod);
fmpz_poly_init(res2);
fmpz_poly_interpolate_fmpz_vec(res2, xs, ys, n);
printf("Nouvelle interpolation (f(xs) = ys) :\n");
fmpz_mod_poly_print(res);
printf("\n");
fmpz* zs = _fmpz_vec_init(n);
fmpz_poly_evaluate_fmpz_vec(zs, res2, xs, n);
fmpz* as = _fmpz_vec_init(n);
fmpz_mod_poly_evaluate_fmpz_vec(as, res, xs, n);
printf("f(xs) :\n");
_fmpz_vec_print(as,n);
printf("\n");
printf("FLINT :\n");
fmpz_poly_print(res2);
printf("\n");
printf("f(xs) :\n");
_fmpz_vec_print(zs,n);
printf("\n");
fmpz_clear(mod);
_fmpz_vec_clear(xs,n);
_fmpz_vec_clear(ys,n);
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("pow_trunc....");
fflush(stdout);
/* Check aliasing */
for (i = 0; i < 10000; i++)
{
fmpz_mod_poly_t a, b, c;
fmpz_t p;
slong e, trunc;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 30));
e = n_randint(state, 20);
trunc = n_randint(state, 30);
fmpz_mod_poly_set(c, a);
fmpz_mod_poly_pow_trunc(b, a, e, trunc);
fmpz_mod_poly_pow_trunc(c, c, e, trunc);
result = (fmpz_mod_poly_equal(b, c));
if (!result)
{
flint_printf("FAIL aliasing:\n");
flint_printf("a->length = %wd, p = %wu, exp = %wd, trunc = %wd\n",
a->length, a->p, e, trunc);
flint_printf("a:\n"); fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b:\n"); fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("c:\n"); fmpz_mod_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_clear(p);
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
}
/* Check powering against naive method */
for (i = 0; i < 10000; i++)
{
fmpz_mod_poly_t a, b, c;
fmpz_t p;
slong e, trunc;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 30));
e = n_randint(state, 20);
trunc = n_randint(state, 30);
fmpz_mod_poly_pow_trunc(b, a, e, trunc);
fmpz_mod_poly_pow(c, a, e);
fmpz_mod_poly_truncate(c, trunc);
result = (fmpz_mod_poly_equal(b, c)
|| (a->length == 0 && e == 0 && c->length == 1 && c->coeffs[0] == 1));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a->length = %wd, p = %wu, exp = %wd, trunc = %wd\n",
a->length, a->p, e, trunc);
flint_printf("a:\n"); fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b:\n"); fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("c:\n"); fmpz_mod_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_clear(p);
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("derivative....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, c;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_set(b, a);
fmpz_mod_poly_derivative(c, b);
fmpz_mod_poly_derivative(b, b);
result = (fmpz_mod_poly_equal(b, c));
if (!result)
{
printf("FAIL (alias):\n");
fmpz_mod_poly_print(a), printf("\n\n");
fmpz_mod_poly_print(b), printf("\n\n");
fmpz_mod_poly_print(c), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
fmpz_clear(p);
}
/* Check constants have derivative zero */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 2));
fmpz_mod_poly_derivative(b, a);
result = (b->length == 0);
if (!result)
{
printf("FAIL (da == 0):\n");
fmpz_mod_poly_print(a), printf("\n\n");
fmpz_mod_poly_print(b), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_clear(p);
}
/* Check (f g)' = f' g + f g' */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, c, d, lhs, rhs;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_init(d, p);
fmpz_mod_poly_init(lhs, p);
fmpz_mod_poly_init(rhs, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest(b, state, n_randint(state, 100));
fmpz_mod_poly_mul(lhs, a, b);
fmpz_mod_poly_derivative(lhs, lhs);
fmpz_mod_poly_derivative(c, a);
fmpz_mod_poly_derivative(d, b);
fmpz_mod_poly_mul(c, c, b);
fmpz_mod_poly_mul(d, a, d);
fmpz_mod_poly_add(rhs, c, d);
result = fmpz_mod_poly_equal(lhs, rhs);
if (!result)
{
printf("FAIL (Leibniz):\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("(ab)' = "), fmpz_mod_poly_print(lhs), printf("\n\n");
printf("a'b + ab' = "), fmpz_mod_poly_print(rhs), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
fmpz_mod_poly_clear(d);
fmpz_mod_poly_clear(lhs);
fmpz_mod_poly_clear(rhs);
fmpz_clear(p);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("div_basecase....");
fflush(stdout);
flint_randinit(state);
/* Compare to divrem_basecase */
for (i = 0; i < 5000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q, q2, r2;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_init(q2, p);
fmpz_mod_poly_init(r2, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_divrem_basecase(q2, r2, a, b);
result = (fmpz_mod_poly_equal(q, q2));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
printf("q2 = "), fmpz_mod_poly_print(q2), printf("\n\n");
printf("r2 = "), fmpz_mod_poly_print(r2), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_mod_poly_clear(q2);
fmpz_mod_poly_clear(r2);
fmpz_clear(p);
}
/* Alias a and q */
for (i = 0; i < 500; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_div_basecase(a, a, b);
result = (fmpz_mod_poly_equal(q, a));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_clear(p);
}
/* Alias b and q */
for (i = 0; i < 500; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_div_basecase(b, a, b);
result = (fmpz_mod_poly_equal(q, b));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_clear(p);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
FlintZZ_pX()
{
FlintZZ f_p(ZZ_p::modulus());
fmpz_mod_poly_init(value, f_p.value);
}
void frob(const mpoly_t P, const ctx_t ctxFracQt,
const qadic_t t1, const qadic_ctx_t Qq,
prec_t *prec, const prec_t *prec_in,
int verbose)
{
const padic_ctx_struct *Qp = &Qq->pctx;
const fmpz *p = Qp->p;
const long a = qadic_ctx_degree(Qq);
const long n = P->n - 1;
const long d = mpoly_degree(P, -1, ctxFracQt);
const long b = gmc_basis_size(n, d);
long i, j, k;
/* Diagonal fibre */
padic_mat_t F0;
/* Gauss--Manin Connection */
mat_t M;
mon_t *bR, *bC;
fmpz_poly_t r;
/* Local solution */
fmpz_poly_mat_t C, Cinv;
long vC, vCinv;
/* Frobenius */
fmpz_poly_mat_t F;
long vF;
fmpz_poly_mat_t F1;
long vF1;
fmpz_poly_t cp;
clock_t c0, c1;
double c;
if (verbose)
{
printf("Input:\n");
printf(" P = "), mpoly_print(P, ctxFracQt), printf("\n");
printf(" p = "), fmpz_print(p), printf("\n");
printf(" t1 = "), qadic_print_pretty(t1, Qq), printf("\n");
printf("\n");
fflush(stdout);
}
/* Step 1 {M, r} *********************************************************/
c0 = clock();
mat_init(M, b, b, ctxFracQt);
fmpz_poly_init(r);
gmc_compute(M, &bR, &bC, P, ctxFracQt);
{
fmpz_poly_t t;
fmpz_poly_init(t);
fmpz_poly_set_ui(r, 1);
for (i = 0; i < M->m; i++)
for (j = 0; j < M->n; j++)
{
fmpz_poly_lcm(t, r, fmpz_poly_q_denref(
(fmpz_poly_q_struct *) mat_entry(M, i, j, ctxFracQt)));
fmpz_poly_swap(r, t);
}
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Gauss-Manin connection:\n");
printf(" r(t) = "), fmpz_poly_print_pretty(r, "t"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
{
qadic_t t;
qadic_init2(t, 1);
fmpz_poly_evaluate_qadic(t, r, t1, Qq);
if (qadic_is_zero(t))
{
printf("Exception (deformation_frob).\n");
printf("The resultant r evaluates to zero (mod p) at t1.\n");
abort();
}
qadic_clear(t);
}
/* Precisions ************************************************************/
if (prec_in != NULL)
{
*prec = *prec_in;
}
else
{
deformation_precisions(prec, p, a, n, d, fmpz_poly_degree(r));
}
if (verbose)
{
printf("Precisions:\n");
printf(" N0 = %ld\n", prec->N0);
printf(" N1 = %ld\n", prec->N1);
printf(" N2 = %ld\n", prec->N2);
printf(" N3 = %ld\n", prec->N3);
printf(" N3i = %ld\n", prec->N3i);
printf(" N3w = %ld\n", prec->N3w);
printf(" N3iw = %ld\n", prec->N3iw);
printf(" N4 = %ld\n", prec->N4);
printf(" m = %ld\n", prec->m);
printf(" K = %ld\n", prec->K);
printf(" r = %ld\n", prec->r);
printf(" s = %ld\n", prec->s);
printf("\n");
fflush(stdout);
}
/* Initialisation ********************************************************/
padic_mat_init2(F0, b, b, prec->N4);
fmpz_poly_mat_init(C, b, b);
fmpz_poly_mat_init(Cinv, b, b);
fmpz_poly_mat_init(F, b, b);
vF = 0;
fmpz_poly_mat_init(F1, b, b);
vF1 = 0;
fmpz_poly_init(cp);
/* Step 2 {F0} ***********************************************************/
{
padic_ctx_t pctx_F0;
fmpz *t;
padic_ctx_init(pctx_F0, p, FLINT_MIN(prec->N4 - 10, 0), prec->N4, PADIC_VAL_UNIT);
t = _fmpz_vec_init(n + 1);
c0 = clock();
mpoly_diagonal_fibre(t, P, ctxFracQt);
diagfrob(F0, t, n, d, prec->N4, pctx_F0, 0);
padic_mat_transpose(F0, F0);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Diagonal fibre:\n");
printf(" P(0) = {"), _fmpz_vec_print(t, n + 1), printf("}\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
_fmpz_vec_clear(t, n + 1);
padic_ctx_clear(pctx_F0);
}
/* Step 3 {C, Cinv} ******************************************************/
/*
Compute C as a matrix over Z_p[[t]]. A is the same but as a series
of matrices over Z_p. Mt is the matrix -M^t, and Cinv is C^{-1}^t,
the local solution of the differential equation replacing M by Mt.
*/
c0 = clock();
{
const long K = prec->K;
padic_mat_struct *A;
gmde_solve(&A, K, p, prec->N3, prec->N3w, M, ctxFracQt);
gmde_convert_soln(C, &vC, A, K, p);
for(i = 0; i < K; i++)
padic_mat_clear(A + i);
free(A);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Local solution:\n");
printf(" Time for C = %f\n", c);
fflush(stdout);
}
c0 = clock();
{
const long K = (prec->K + (*p) - 1) / (*p);
mat_t Mt;
padic_mat_struct *Ainv;
mat_init(Mt, b, b, ctxFracQt);
mat_transpose(Mt, M, ctxFracQt);
mat_neg(Mt, Mt, ctxFracQt);
gmde_solve(&Ainv, K, p, prec->N3i, prec->N3iw, Mt, ctxFracQt);
gmde_convert_soln(Cinv, &vCinv, Ainv, K, p);
fmpz_poly_mat_transpose(Cinv, Cinv);
fmpz_poly_mat_compose_pow(Cinv, Cinv, *p);
for(i = 0; i < K; i++)
padic_mat_clear(Ainv + i);
free(Ainv);
mat_clear(Mt, ctxFracQt);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf(" Time for C^{-1} = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 4 {F(t) := C(t) F(0) C(t^p)^{-1}} ********************************/
/*
Computes the product C(t) F(0) C(t^p)^{-1} modulo (p^{N_2}, t^K).
This is done by first computing the unit part of the product
exactly over the integers modulo t^K.
*/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
for (i = 0; i < b; i++)
{
/* Find the unique k s.t. F0(i,k) is non-zero */
for (k = 0; k < b; k++)
if (!fmpz_is_zero(padic_mat_entry(F0, i, k)))
break;
if (k == b)
{
printf("Exception (frob). F0 is singular.\n\n");
abort();
}
for (j = 0; j < b; j++)
{
fmpz_poly_scalar_mul_fmpz(fmpz_poly_mat_entry(T, i, j),
fmpz_poly_mat_entry(Cinv, k, j),
padic_mat_entry(F0, i, k));
}
}
fmpz_poly_mat_mul(F, C, T);
fmpz_poly_mat_truncate(F, prec->K);
vF = vC + padic_mat_val(F0) + vCinv;
/* Canonicalise (F, vF) */
{
long v = fmpz_poly_mat_ord_p(F, p);
if (v == LONG_MAX)
{
printf("ERROR (deformation_frob). F(t) == 0.\n");
abort();
}
else if (v > 0)
{
fmpz_pow_ui(pN, p, v);
fmpz_poly_mat_scalar_divexact_fmpz(F, F, pN);
vF = vF + v;
}
}
/* Reduce (F, vF) modulo p^{N2} */
fmpz_pow_ui(pN, p, prec->N2 - vF);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Matrix for F(t):\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 5 {G = r(t)^m F(t)} **********************************************/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_t t;
fmpz_init(pN);
fmpz_poly_init(t);
fmpz_pow_ui(pN, p, prec->N2 - vF);
/* Compute r(t)^m mod p^{N2-vF} */
if (prec->denR == NULL)
{
fmpz_mod_poly_t _t;
fmpz_mod_poly_init(_t, pN);
fmpz_mod_poly_set_fmpz_poly(_t, r);
fmpz_mod_poly_pow(_t, _t, prec->m);
fmpz_mod_poly_get_fmpz_poly(t, _t);
fmpz_mod_poly_clear(_t);
}
else
{
/* TODO: We don't really need a copy */
fmpz_poly_set(t, prec->denR);
}
fmpz_poly_mat_scalar_mul_fmpz_poly(F, F, t);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
/* TODO: This should not be necessary? */
fmpz_poly_mat_truncate(F, prec->K);
fmpz_clear(pN);
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Analytic continuation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Steps 6 and 7 *********************************************************/
if (a == 1)
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t f, g, t, pN;
fmpz_init(f);
fmpz_init(g);
fmpz_init(t);
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_padic_teichmuller(f, t1->coeffs + 0, p, N);
if (prec->denR == NULL)
{
_fmpz_mod_poly_evaluate_fmpz(g, r->coeffs, r->length, f, pN);
fmpz_powm_ui(t, g, prec->m, pN);
}
else
{
_fmpz_mod_poly_evaluate_fmpz(t, prec->denR->coeffs, prec->denR->length, f, pN);
}
_padic_inv(g, t, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
if (len == 0)
{
fmpz_poly_zero(fmpz_poly_mat_entry(F1, i, j));
}
else
{
fmpz_poly_fit_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_mod_poly_evaluate_fmpz(t, poly->coeffs, len, f, pN);
fmpz_mul(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, g, t);
fmpz_mod(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0,
fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, pN);
_fmpz_poly_set_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_poly_normalise(fmpz_poly_mat_entry(F1, i, j));
}
}
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(t);
fmpz_clear(pN);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
else
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t pN;
fmpz *f, *g, *t;
fmpz_init(pN);
f = _fmpz_vec_init(a);
g = _fmpz_vec_init(2 * a - 1);
t = _fmpz_vec_init(2 * a - 1);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_qadic_teichmuller(f, t1->coeffs, t1->length, Qq->a, Qq->j, Qq->len, p, N);
if (prec->denR == NULL)
{
fmpz_t e;
fmpz_init_set_ui(e, prec->m);
_fmpz_mod_poly_compose_smod(g, r->coeffs, r->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
_qadic_pow(t, g, a, e, Qq->a, Qq->j, Qq->len, pN);
fmpz_clear(e);
}
else
{
_fmpz_mod_poly_reduce(prec->denR->coeffs, prec->denR->length, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_normalise(prec->denR);
_fmpz_mod_poly_compose_smod(t, prec->denR->coeffs, prec->denR->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
}
_qadic_inv(g, t, a, Qq->a, Qq->j, Qq->len, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
fmpz_poly_struct *poly2 = fmpz_poly_mat_entry(F1, i, j);
if (len == 0)
{
fmpz_poly_zero(poly2);
}
else
{
_fmpz_mod_poly_compose_smod(t, poly->coeffs, len, f, a,
Qq->a, Qq->j, Qq->len, pN);
fmpz_poly_fit_length(poly2, 2 * a - 1);
_fmpz_poly_mul(poly2->coeffs, g, a, t, a);
_fmpz_mod_poly_reduce(poly2->coeffs, 2 * a - 1, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_set_length(poly2, a);
_fmpz_poly_normalise(poly2);
}
}
/* Now the matrix for p^{-1} F_p at t=t_1 is (F1, vF1). */
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
_fmpz_vec_clear(f, a);
_fmpz_vec_clear(g, 2 * a - 1);
_fmpz_vec_clear(t, 2 * a - 1);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 7 {Norm} *****************************************************/
/*
Computes the matrix for $q^{-1} F_q$ at $t = t_1$ as the
product $F \sigma(F) \dotsm \sigma^{a-1}(F)$ up appropriate
transpositions because our convention of columns vs rows is
the opposite of that used by Gerkmann.
Note that, in any case, transpositions do not affect
the characteristic polynomial.
*/
c0 = clock();
{
const long N = prec->N1 - a * vF1;
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
fmpz_pow_ui(pN, p, N);
fmpz_poly_mat_frobenius(T, F1, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
for (i = 2; i < a; i++)
{
fmpz_poly_mat_frobenius(T, T, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
}
vF1 = a * vF1;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Norm:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
/* Step 8 {Reverse characteristic polynomial} ****************************/
c0 = clock();
deformation_revcharpoly(cp, F1, vF1, n, d, prec->N0, prec->r, prec->s, Qq);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Reverse characteristic polynomial:\n");
printf(" p(T) = "), fmpz_poly_print_pretty(cp, "T"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Clean up **************************************************************/
padic_mat_clear(F0);
mat_clear(M, ctxFracQt);
free(bR);
free(bC);
fmpz_poly_clear(r);
fmpz_poly_mat_clear(C);
fmpz_poly_mat_clear(Cinv);
fmpz_poly_mat_clear(F);
fmpz_poly_mat_clear(F1);
fmpz_poly_clear(cp);
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("xgcd....");
fflush(stdout);
/* Generic case, most likely co-prime arguments ******************************/
/* Compare with result from GCD and check correctness */
for (i = 0; i < 1000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, d, g, s, t, v, w;
fmpz_init(p);
fmpz_set_ui(p, n_randtest_prime(state, 0));
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(d, p);
fmpz_mod_poly_init(g, p);
fmpz_mod_poly_init(s, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_init(v, p);
fmpz_mod_poly_init(w, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest(b, state, n_randint(state, 100));
fmpz_mod_poly_gcd(d, a, b);
fmpz_mod_poly_xgcd(g, s, t, a, b);
fmpz_mod_poly_mul(v, s, a);
fmpz_mod_poly_mul(w, t, b);
fmpz_mod_poly_add(w, v, w);
result = (fmpz_mod_poly_equal(d, g) && fmpz_mod_poly_equal(g, w));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_mod_poly_print(a), flint_printf("\n\n");
fmpz_mod_poly_print(b), flint_printf("\n\n");
fmpz_mod_poly_print(d), flint_printf("\n\n");
fmpz_mod_poly_print(g), flint_printf("\n\n");
fmpz_mod_poly_print(s), flint_printf("\n\n");
fmpz_mod_poly_print(t), flint_printf("\n\n");
fmpz_mod_poly_print(v), flint_printf("\n\n");
fmpz_mod_poly_print(w), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(d);
fmpz_mod_poly_clear(g);
fmpz_mod_poly_clear(s);
fmpz_mod_poly_clear(t);
fmpz_mod_poly_clear(v);
fmpz_mod_poly_clear(w);
fmpz_clear(p);
}
/* Special case, arguments share a factor ********************************/
/* Compare with result from GCD and check correctness */
for (i = 0; i < 1000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, d, f, g, s, t, v, w;
fmpz_init(p);
fmpz_set_ui(p, n_randtest_prime(state, 0));
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(d, p);
fmpz_mod_poly_init(f, p);
fmpz_mod_poly_init(g, p);
fmpz_mod_poly_init(s, p);
fmpz_mod_poly_init(t, p);
fmpz_mod_poly_init(v, p);
fmpz_mod_poly_init(w, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest(b, state, n_randint(state, 100));
fmpz_mod_poly_randtest(f, state, n_randint(state, 20));
fmpz_mod_poly_mul(a, a, f);
fmpz_mod_poly_mul(b, b, f);
fmpz_mod_poly_gcd(d, a, b);
fmpz_mod_poly_xgcd(g, s, t, a, b);
fmpz_mod_poly_mul(v, s, a);
fmpz_mod_poly_mul(w, t, b);
fmpz_mod_poly_add(w, v, w);
result = (fmpz_mod_poly_equal(d, g) && fmpz_mod_poly_equal(g, w));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_mod_poly_print(a), flint_printf("\n\n");
fmpz_mod_poly_print(b), flint_printf("\n\n");
fmpz_mod_poly_print(d), flint_printf("\n\n");
fmpz_mod_poly_print(f), flint_printf("\n\n");
fmpz_mod_poly_print(g), flint_printf("\n\n");
fmpz_mod_poly_print(s), flint_printf("\n\n");
fmpz_mod_poly_print(t), flint_printf("\n\n");
fmpz_mod_poly_print(v), flint_printf("\n\n");
fmpz_mod_poly_print(w), flint_printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(d);
fmpz_mod_poly_clear(f);
fmpz_mod_poly_clear(g);
fmpz_mod_poly_clear(s);
fmpz_mod_poly_clear(t);
fmpz_mod_poly_clear(v);
fmpz_mod_poly_clear(w);
fmpz_clear(p);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int fmpz_mod_poly_is_irreducible_ddf(const fmpz_mod_poly_t poly)
{
fmpz_mod_poly_t f, v, vinv, reducedH0, tmp;
fmpz_mod_poly_t *h, *H, *I;
slong i, j, l, m, n, d;
fmpz_t p;
double beta;
int result = 1;
n = fmpz_mod_poly_degree(poly);
if (n < 2)
return 1;
if (!fmpz_mod_poly_is_squarefree(poly))
return 0;
beta = 0.5 * (1. - (log(2) / log(n)));
l = ceil(pow(n, beta));
m = ceil(0.5 * n / l);
/* initialization */
fmpz_init(p);
fmpz_set(p, &poly->p);
fmpz_mod_poly_init(f, p);
fmpz_mod_poly_init(v, p);
fmpz_mod_poly_init(vinv, p);
fmpz_mod_poly_init(reducedH0, p);
fmpz_mod_poly_init(tmp, p);
if (!(h = flint_malloc((2 * m + l + 1) * sizeof(fmpz_mod_poly_struct))))
{
flint_printf("Exception (fmpz_mod_poly_is_irreducible_ddf): \n");
flint_printf("Not enough memory.\n");
abort();
}
H = h + (l + 1);
I = H + m;
for (i = 0; i < l + 1; i++)
fmpz_mod_poly_init(h[i], p);
for (i = 0; i < m; i++)
{
fmpz_mod_poly_init(H[i], p);
fmpz_mod_poly_init(I[i], p);
}
fmpz_mod_poly_make_monic(v, poly);
fmpz_mod_poly_reverse (vinv, v, v->length);
fmpz_mod_poly_inv_series_newton (vinv, vinv, v->length);
/* compute baby steps: h[i]=x^{p^i}mod v */
fmpz_mod_poly_set_coeff_ui(h[0], 1, 1);
for (i = 1; i < l + 1; i++)
fmpz_mod_poly_powmod_fmpz_binexp_preinv(h[i], h[i - 1], p, v, vinv);
/* compute coarse distinct-degree factorisation */
fmpz_mod_poly_set(H[0], h[l]);
fmpz_mod_poly_set(reducedH0, H[0]);
d = 1;
for (j = 0; j < m; j++)
{
/* compute giant steps: H[i]=x^{p^(li)}mod v */
if (j > 0)
{
fmpz_mod_poly_rem (reducedH0, reducedH0, v);
fmpz_mod_poly_rem (tmp, H[j-1], v);
fmpz_mod_poly_compose_mod_brent_kung_preinv(H[j], tmp, reducedH0,
v, vinv);
}
/* compute interval polynomials */
fmpz_mod_poly_set_coeff_ui(I[j], 0, 1);
for (i = l - 1; (i >= 0) && (2*d <= v->length - 1); i--, d++)
{
fmpz_mod_poly_rem(tmp, h[i], v);
fmpz_mod_poly_sub(tmp, H[j], tmp);
fmpz_mod_poly_mulmod_preinv (I[j], tmp, I[j], v, vinv);
}
/* compute F_j=f^{[j*l+1]} * ... * f^{[j*l+l]} */
/* F_j is stored on the place of I_j */
fmpz_mod_poly_gcd(I[j], v, I[j]);
if (I[j]->length > 1)
{
result = 0;
break;
}
}
fmpz_clear(p);
fmpz_mod_poly_clear(f);
fmpz_mod_poly_clear(reducedH0);
fmpz_mod_poly_clear(v);
fmpz_mod_poly_clear(vinv);
fmpz_mod_poly_clear(tmp);
for (i = 0; i < l + 1; i++)
fmpz_mod_poly_clear(h[i]);
for (i = 0; i < m; i++)
{
fmpz_mod_poly_clear(H[i]);
fmpz_mod_poly_clear(I[i]);
}
flint_free(h);
return result;
}
int
main(void)
{
int iter;
FLINT_TEST_INIT(state);
flint_printf("factor_squarefree....");
fflush(stdout);
for (iter = 0; iter < 300; iter++)
{
int result = 1;
fmpz_mod_poly_t pol1, poly, quot, rem;
fmpz_mod_poly_factor_t res;
fmpz_t modulus;
slong exp[5], prod1;
slong length, i, j, num;
fmpz_init_set_ui(modulus, n_randtest_prime(state, 0));
fmpz_mod_poly_init(pol1, modulus);
fmpz_mod_poly_init(poly, modulus);
fmpz_mod_poly_init(quot, modulus);
fmpz_mod_poly_init(rem, modulus);
fmpz_mod_poly_zero(pol1);
fmpz_mod_poly_set_coeff_ui(pol1, 0, 1);
length = n_randint(state, 7) + 2;
do
{
fmpz_mod_poly_randtest(poly, state, length);
fmpz_mod_poly_make_monic(poly, poly);
}
while ((!fmpz_mod_poly_is_irreducible(poly)) || (poly->length < 2));
exp[0] = n_randprime(state, 5, 0);
prod1 = exp[0];
for (i = 0; i < exp[0]; i++)
fmpz_mod_poly_mul(pol1, pol1, poly);
num = n_randint(state, 5) + 1;
for (i = 1; i < num; i++)
{
do
{
length = n_randint(state, 7) + 2;
fmpz_mod_poly_randtest(poly, state, length);
if (poly->length)
{
fmpz_mod_poly_make_monic(poly, poly);
fmpz_mod_poly_divrem(quot, rem, pol1, poly);
}
}
while ((!fmpz_mod_poly_is_irreducible(poly)) ||
(poly->length < 2) || (rem->length == 0));
do
exp[i] = n_randprime(state, 5, 0);
while (prod1 % exp[i] == 0);
prod1 *= exp[i];
for (j = 0; j < exp[i]; j++)
fmpz_mod_poly_mul(pol1, pol1, poly);
}
fmpz_mod_poly_factor_init(res);
fmpz_mod_poly_factor_squarefree(res, pol1);
result &= (res->num == num);
if (result)
{
ulong prod2 = 1;
for (i = 0; i < num; i++)
prod2 *= res->exp[i];
result &= (prod1 == prod2);
}
if (!result)
{
flint_printf("Error: exp don't match. Modulus = ");
fmpz_print(modulus);
flint_printf("\n");
for (i = 0; i < res->num; i++)
flint_printf("%wd ", res->exp[i]);
flint_printf("\n");
for (i = 0; i < num; i++)
flint_printf("%wd ", exp[i]);
flint_printf("\n");
abort();
}
fmpz_clear(modulus);
fmpz_mod_poly_clear(quot);
fmpz_mod_poly_clear(rem);
fmpz_mod_poly_clear(pol1);
fmpz_mod_poly_clear(poly);
fmpz_mod_poly_factor_clear(res);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("evaluate_fmpz....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing */
for (i = 0; i < 10000; i++)
{
fmpz_t a, b, p;
fmpz_mod_poly_t f;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_init(a);
fmpz_init(b);
fmpz_randm(a, state, p);
fmpz_mod_poly_init(f, p);
fmpz_mod_poly_randtest(f, state, n_randint(state, 100));
fmpz_mod_poly_evaluate_fmpz(b, f, a);
fmpz_mod_poly_evaluate_fmpz(a, f, a);
result = (fmpz_equal(a, b));
if (!result)
{
printf("FAIL:\n");
fmpz_mod_poly_print(f), printf("\n\n");
fmpz_print(a), printf("\n\n");
fmpz_print(b), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(f);
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(p);
}
/* Check that the result agrees with Z[X] */
for (i = 0; i < 10000; i++)
{
fmpz_t a, b, c, p;
fmpz_mod_poly_t f;
fmpz_poly_t g;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
fmpz_mod_poly_init(f, p);
fmpz_poly_init(g);
fmpz_randm(a, state, p);
fmpz_mod_poly_randtest(f, state, n_randint(state, 100));
fmpz_mod_poly_get_fmpz_poly(g, f);
fmpz_mod_poly_evaluate_fmpz(b, f, a);
fmpz_poly_evaluate_fmpz(c, g, a);
fmpz_mod(c, c, p);
result = (fmpz_equal(b, c));
if (!result)
{
printf("FAIL (cmp with fmpz_poly):\n");
fmpz_mod_poly_print(f), printf("\n\n");
fmpz_poly_print(g), printf("\n\n");
fmpz_print(a), printf("\n\n");
fmpz_print(b), printf("\n\n");
fmpz_print(c), printf("\n\n");
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
fmpz_clear(p);
fmpz_mod_poly_clear(f);
fmpz_poly_clear(g);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i;
flint_rand_t state;
printf("init/init2/realloc/clear....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init2(a, p, n_randint(state, 100));
fmpz_mod_poly_clear(a);
fmpz_clear(p);
}
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init2(a, p, n_randint(state, 100));
fmpz_mod_poly_realloc(a, n_randint(state, 100));
fmpz_mod_poly_clear(a);
fmpz_clear(p);
}
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_clear(a);
fmpz_clear(p);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
