ulong arb_fmpz_poly_deflation(const fmpz_poly_t input)
{
slong i, coeff, deflation;
if (input->length <= 1)
return input->length;
coeff = 1;
while (fmpz_is_zero(input->coeffs + coeff))
coeff++;
deflation = n_gcd(input->length - 1, coeff);
while ((deflation > 1) && (coeff + deflation < input->length))
{
for (i = 0; i < deflation - 1; i++)
{
coeff++;
if (!fmpz_is_zero(input->coeffs + coeff))
deflation = n_gcd(coeff, deflation);
}
if (i == deflation - 1)
coeff++;
}
return deflation;
}
ulong
z_gcd(long a, long b)
{
ulong ua = FLINT_ABS(a);
ulong ub = FLINT_ABS(b);
return (ua >= ub) ? n_gcd(ua, ub) : n_gcd(ub, ua);
}
static ulong
do_gcd(ulong q1, ulong q2)
{
ulong n, q, k;
for (n = 0, q = q1; q <= q2; q++)
for (k = 1; k < q; k++)
n += (n_gcd(k, q) == 1);
return n;
}
void
dlog_vec_trivial(ulong *v, ulong nv, ulong a, ulong va, const nmod_t mod, ulong na, const nmod_t order)
{
ulong k;
dlog_precomp_t pre;
dlog_precomp_n_init(pre, a, mod.n, na, 50);
for (k = 1; k < nv; k++)
if (n_gcd(k, mod.n) > 1)
v[k] = DLOG_NOT_FOUND;
else
v[k] = dlog_precomp(pre, k % mod.n);
dlog_precomp_clear(pre);
}
void
sec_init(sec_t * c, slong m, acb_srcptr x, slong d)
{
slong k;
c->m = m;
c->d = d;
c->delta = n_gcd(m,d);
c->g = ((m-1)*(d-1) - c->delta + 1)/ 2;
c->roots = _acb_vec_init(d);
for (k = 0; k < d; k++)
acb_set(c->roots + k, x + k);
}
void
acb_dirichlet_jacobi_sum_naive(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec)
{
ulong k1, k2, m1, m2, g, e, m;
ulong * v1, * v2;
slong *v;
nmod_t expo;
acb_t z;
v1 = flint_malloc(G->q * sizeof(ulong));
v2 = flint_malloc(G->q * sizeof(ulong));
dirichlet_vec_set_null(v1, G, G->q);
dirichlet_chi_vec_loop(v1, G, chi1, G->q);
dirichlet_vec_set_null(v2, G, G->q);
dirichlet_chi_vec_loop(v2, G, chi2, G->q);
nmod_init(&expo, G->expo);
m1 = dirichlet_order_char(G, chi1);
m2 = dirichlet_order_char(G, chi2);
g = m1 * m2 / n_gcd(m1, m2);
m = G->expo / g;
v = flint_malloc(g * sizeof(slong));
for (e = 0; e < g; e++)
v[e] = 0;
for (k1 = 2, k2 = G->q - 1; k2 > 1; k1++, k2--)
{
if (v1[k1] == DIRICHLET_CHI_NULL ||
v2[k2] == DIRICHLET_CHI_NULL)
continue;
e = nmod_add(v1[k1], v2[k2], expo) / m;
v[e]++;
}
acb_init(z);
acb_unit_root(z, g, prec);
acb_dirichlet_si_poly_evaluate(res, v, g, z, prec);
acb_clear(z);
flint_free(v);
flint_free(v2);
flint_free(v1);
}
int main(void)
{
int i, result;
flint_rand_t state;
printf("xgcd....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 100000; i++)
{
mp_limb_t a, b, c, g, bits1, bits2, bits3, ph, pl, qh, ql;
mp_limb_t s, t;
bits1 = n_randint(state, FLINT_BITS-1) + 1;
bits2 = n_randint(state, bits1) + 1;
bits3 = n_randint(state, FLINT_BITS - bits1) + 1;
do
{
a = n_randbits(state, bits1);
b = n_randbits(state, bits2);
} while ((n_gcd(a, b) != 1UL) || (b > a));
c = n_randbits(state, bits3);
g = n_xgcd(&s, &t, a*c, b*c);
umul_ppmm(ph, pl, a*c, s);
umul_ppmm(qh, ql, b*c, t);
sub_ddmmss(ph, pl, ph, pl, qh, ql);
result = ((g == c) && (ph == 0UL) && (pl == c));
if (!result)
{
printf("FAIL:\n");
printf("a = %lu, b = %lu, c = %lu, g = %lu, s = %lu, t = %lu\n", a, b, c, g, s, t);
abort();
}
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
static void
dirichlet_group_lift_generators(dirichlet_group_t G)
{
slong k;
dirichlet_prime_group_struct * P = G->P;
G->expo = G->phi_q = 1;
if (G->neven)
{
G->phi_q = G->q_even / 2;
G->expo = P[G->neven - 1].phi.n;
}
for (k = G->neven; k < G->num; k++)
{
G->phi_q *= P[k].phi.n;
G->expo *= P[k].phi.n / n_gcd(G->expo, P[k].p - 1);
}
for (k = 0; k < G->num; k++)
{
nmod_t pe;
ulong qpe, v;
G->PHI[k] = G->expo / G->P[k].phi.n;
/* lift generators mod q */
/* u * p^e + v * q/p^e = 1 -> g mod q = 1 + (g-1) * v*(q/p^e) */
pe = G->P[k].pe;
qpe = G->q / pe.n;
if (G->q < G->P[k].pe.n)
{
flint_printf("lift generator %wu from %wu to %wu e=%wu\n",
G->P[k].g, G->P[k].pe.n, G->q, G->P[k].e);
}
v = nmod_inv(qpe % pe.n, pe);
/* no overflow since v * qpe < q */
G->generators[k] = (1 + (G->P[k].g-1) * v * qpe) % G->q;
}
}
void
_arith_cos_minpoly(fmpz * coeffs, slong d, ulong n)
{
slong i, j;
fmpz * alpha;
fmpz_t half;
mpfr_t t, u;
mp_bitcnt_t prec;
slong exp;
if (n <= MAX_32BIT)
{
for (i = 0; i <= d; i++)
fmpz_set_si(coeffs + i, lookup_table[n - 1][i]);
return;
}
/* Direct formula for odd primes > 3 */
if (n_is_prime(n))
{
slong s = (n - 1) / 2;
switch (s % 4)
{
case 0:
fmpz_set_si(coeffs, WORD(1));
fmpz_set_si(coeffs + 1, -s);
break;
case 1:
fmpz_set_si(coeffs, WORD(1));
fmpz_set_si(coeffs + 1, s + 1);
break;
case 2:
fmpz_set_si(coeffs, WORD(-1));
fmpz_set_si(coeffs + 1, s);
break;
case 3:
fmpz_set_si(coeffs, WORD(-1));
fmpz_set_si(coeffs + 1, -s - 1);
break;
}
for (i = 2; i <= s; i++)
{
slong b = (s - i) % 2;
fmpz_mul2_uiui(coeffs + i, coeffs + i - 2, s+i-b, s+2-b-i);
fmpz_divexact2_uiui(coeffs + i, coeffs + i, i, i-1);
fmpz_neg(coeffs + i, coeffs + i);
}
return;
}
prec = magnitude_bound(d) + 5 + FLINT_BIT_COUNT(d);
alpha = _fmpz_vec_init(d);
fmpz_init(half);
mpfr_init2(t, prec);
mpfr_init2(u, prec);
fmpz_one(half);
fmpz_mul_2exp(half, half, prec - 1);
mpfr_const_pi(t, prec);
mpfr_div_ui(t, t, n, MPFR_RNDN);
for (i = j = 0; j < d; i++)
{
if (n_gcd(n, i) == 1)
{
mpfr_mul_ui(u, t, 2 * i, MPFR_RNDN);
mpfr_cos(u, u, MPFR_RNDN);
mpfr_neg(u, u, MPFR_RNDN);
exp = mpfr_get_z_2exp(_fmpz_promote(alpha + j), u);
_fmpz_demote_val(alpha + j);
fmpz_mul_or_div_2exp(alpha + j, alpha + j, exp + prec);
j++;
}
}
balanced_product(coeffs, alpha, d, prec);
/* Scale and round */
for (i = 0; i < d + 1; i++)
{
slong r = d;
if ((n & (n - 1)) == 0)
r--;
fmpz_mul_2exp(coeffs + i, coeffs + i, r);
fmpz_add(coeffs + i, coeffs + i, half);
fmpz_fdiv_q_2exp(coeffs + i, coeffs + i, prec);
}
fmpz_clear(half);
mpfr_clear(t);
mpfr_clear(u);
_fmpz_vec_clear(alpha, d);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("cos_pi_fmpq_algebraic....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t c1, c2;
ulong p, q, g;
slong prec;
prec = 2 + n_randint(state, 5000);
q = 1 + n_randint(state, 500);
p = n_randint(state, q / 2 + 1);
g = n_gcd(q, p);
q /= g;
p /= g;
arb_init(c1);
arb_init(c2);
_arb_cos_pi_fmpq_algebraic(c1, p, q, prec);
arb_const_pi(c2, prec);
arb_mul_ui(c2, c2, p, prec);
arb_div_ui(c2, c2, q, prec);
arb_cos(c2, c2, prec);
if (!arb_overlaps(c1, c2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n");
flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n");
flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n");
abort();
}
if (arb_rel_accuracy_bits(c1) < prec - 2)
{
flint_printf("FAIL: accuracy\n\n");
flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n");
flint_printf("prec=%wd eff=%wd\n", prec, arb_rel_accuracy_bits(c1));
flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n");
flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n");
abort();
}
arb_clear(c1);
arb_clear(c2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
acb_modular_hilbert_class_poly(fmpz_poly_t res, slong D)
{
slong i, a, b, c, ac, h, qbf_alloc, qbf_len, prec;
slong * qbf;
double lgh;
if (D >= 0 || ((D & 3) > 1))
{
fmpz_poly_zero(res);
return;
}
qbf_alloc = qbf_len = 0;
qbf = NULL;
b = D & 1;
h = 0;
/* Cohen algorithm 5.3.5 */
do
{
ac = (b*b - D) / 4;
a = FLINT_MAX(b, 1);
do
{
if (ac % a == 0 && n_gcd_full(n_gcd(a, b), ac/a) == 1)
{
c = ac / a;
if (qbf_len >= qbf_alloc)
{
qbf_alloc = FLINT_MAX(4, FLINT_MAX(qbf_len + 1, qbf_alloc * 2));
qbf = flint_realloc(qbf, qbf_alloc * 3 * sizeof(slong));
}
if (a == b || a*a == ac || b == 0)
{
qbf[3 * qbf_len + 0] = a;
qbf[3 * qbf_len + 1] = b;
qbf[3 * qbf_len + 2] = c;
h += 1;
}
else
{
/* -b indicates that we have both b and -b */
qbf[3 * qbf_len + 0] = a;
qbf[3 * qbf_len + 1] = -b;
qbf[3 * qbf_len + 2] = c;
h += 2;
}
qbf_len++;
}
a++;
}
while (a*a <= ac);
b += 2;
}
while (3*b*b <= -D);
/* Estimate precision - see p.7 in http://hal.inria.fr/inria-00001040 */
lgh = 0.0;
for (i = 0; i < qbf_len; i++)
{
if (qbf[3 * i + 1] < 0)
lgh += 2.0 / qbf[3 * i];
else
lgh += 1.0 / qbf[3 * i];
}
lgh = 3.141593 * sqrt(-D) * lgh;
#if 0
lgh += 3.012 * h;
prec = lgh * 1.442696;
prec = prec + 10;
#else
prec = lgh * 1.442696; /* heuristic, but more accurate */
prec = prec * 1.005 + 20;
#endif
while (!_acb_modular_hilbert_class_poly(res, D, qbf, qbf_len, prec))
{
flint_printf("hilbert_class_poly failed at %wd bits of precision\n", prec);
prec = prec * 1.2 + 10;
}
flint_free(qbf);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("chi....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t zn1, zn2, zn1n2, zn1zn2;
dirichlet_group_t G;
dirichlet_char_t chi;
ulong q, m, n1, n2, iter2;
int res;
q = 1 + n_randint(state, 1000);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
acb_init(zn1);
acb_init(zn2);
acb_init(zn1n2);
acb_init(zn1zn2);
/* check chi(n1) chi(n2) = chi(n1 n2) */
for (iter2 = 0; iter2 < 10; iter2++)
{
do {
m = 1 + n_randint(state, q);
} while (n_gcd(q, m) != 1);
dirichlet_char_log(chi, G, m);
n1 = n_randint(state, 1000);
n2 = n_randint(state, 1000);
acb_dirichlet_chi(zn1, G, chi, n1, 53);
acb_dirichlet_pairing(zn2, G, m, n1, 53);
if (!acb_overlaps(zn1, zn2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n = %wu\n\n", n1);
flint_printf("char = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_printf("pairing = "); acb_printd(zn2, 15); flint_printf("\n\n");
dirichlet_char_print(G, chi);
dirichlet_char_log(chi, G, m);
flint_printf("log(m) = "); dirichlet_char_print(G, chi);
dirichlet_char_log(chi, G, n1);
flint_printf("log(n1) = "); dirichlet_char_print(G, chi);
flint_abort();
}
acb_dirichlet_pairing(zn2, G, m, n2, 53);
acb_dirichlet_pairing(zn1n2, G, m, n1 * n2, 53);
acb_mul(zn1zn2, zn1, zn2, 53);
if (!acb_overlaps(zn1n2, zn1zn2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n1 = %wu\n\n", n1);
flint_printf("n2 = %wu\n\n", n2);
flint_printf("zn1 = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_printf("zn2 = "); acb_printd(zn2, 15); flint_printf("\n\n");
flint_printf("zn1n2 = "); acb_printd(zn1n2, 15); flint_printf("\n\n");
flint_printf("zn1zn2 = "); acb_printd(zn1zn2, 15); flint_printf("\n\n");
flint_abort();
}
}
if (iter % 10 == 0)
{
/* check orthogonality */
acb_zero(zn1);
n1 = n_randint(state, 1000);
for (m = 1; m <= q; m++)
{
if (n_gcd(q, m) == 1)
{
acb_dirichlet_pairing(zn2, G, m, n1, 53);
acb_add(zn1, zn1, zn2, 53);
}
}
if (n1 % q == 1 % q)
res = arb_contains_si(acb_realref(zn1), n_euler_phi(q)) &&
arb_contains_zero(acb_imagref(zn1));
else
res = acb_contains_zero(zn1);
if (!res)
{
flint_printf("FAIL: orthogonality\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("phi = %wu\n\n", n_euler_phi(q));
flint_printf("n1 = %wu\n\n", n1);
flint_printf("zn1 = "); acb_printd(zn1, 15); flint_printf("\n\n");
flint_abort();
}
}
dirichlet_group_clear(G);
dirichlet_char_clear(chi);
acb_clear(zn1);
acb_clear(zn2);
acb_clear(zn1n2);
acb_clear(zn1zn2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter, bits;
flint_rand_t state;
flint_printf("properties....");
fflush(stdout);
flint_randinit(state);
for (bits = 5; bits <= 30; bits += 5)
{
for (iter = 0; iter < 50; iter++)
{
dirichlet_group_t G;
dirichlet_char_t chi, psi;
ulong q, iter2;
q = 2 + n_randint(state, 1 << bits);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
dirichlet_char_init(psi, G);
/* check number char properties */
for (iter2 = 0; iter2 < 100; iter2++)
{
ulong m, n;
ulong p1, p2, pairing, cm, cn, q2, q3;
dirichlet_group_t G2, G3;
dirichlet_char_t chi2, chi3;
if (iter2 == 50)
dirichlet_group_dlog_precompute(G, 5);
/* one random character */
do
m = n_randint(state, q);
while (n_gcd(q, m) > 1);
dirichlet_char_log(chi, G, m);
p1 = dirichlet_order_ui(G, m);
p2 = dirichlet_order_char(G, chi);
check_eq(p1, p2, q, m, "order m", "order chi");
p1 = dirichlet_conductor_ui(G, m);
p2 = dirichlet_conductor_char(G, chi);
check_eq(p1, p2, q, m, "conductor m", "conductor chi");
p1 = dirichlet_parity_ui(G, m);
p2 = dirichlet_parity_char(G, chi);
check_eq(p1, p2, q, m, "parity m", "parity chi");
p1 = dirichlet_char_is_real(G, chi);
p2 = (dirichlet_order_char(G, chi) <= 2);
check_eq(p1, p2, q, m, "is_real", "(order <= 2)");
/* check index */
p1 = dirichlet_index_char(G, chi);
dirichlet_char_index(psi, G, p1);
if (!dirichlet_char_eq_deep(G, chi, psi))
{
flint_printf("FAIL: index\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("chi = "); dirichlet_char_print(G, chi);
flint_printf("\n\nindex(chi) = %wu\n\n", p1);
flint_printf("psi(index) = %wu\n\n", psi->n);
flint_printf("psi = "); dirichlet_char_print(G, psi);
flint_printf("\n\n");
abort();
}
/* lift to higher modulus */
q2 = q * (1 + n_randint(state, 100));
dirichlet_group_init(G2, q2);
dirichlet_char_init(chi2, G2);
dirichlet_char_lift(chi2, G2, chi, G);
p1 = dirichlet_conductor_char(G, chi);
p2 = dirichlet_conductor_char(G2, chi2);
check_eq(p1, p2, q, m, "conductor chi", "conductor lift");
p1 = dirichlet_order_char(G, chi);
p2 = dirichlet_order_char(G2, chi2);
check_eq(p1, p2, q, m, "order chi", "order lift");
/* and lower */
dirichlet_char_lower(psi, G, chi2, G2);
if (!dirichlet_char_eq_deep(G, chi, psi))
{
flint_printf("FAIL: lift and lower back\n\n");
flint_printf("q = %wu\n\nchi = ", q);
dirichlet_char_print(G, chi);
flint_printf("\n\nq2 = %wu\n\nchi2 = ", q2);
dirichlet_char_print(G2, chi2);
flint_printf("\n\nq = %wu\n\npsi = ", q);
dirichlet_char_print(G, psi);
flint_printf("\n\n");
abort();
}
q3 = dirichlet_conductor_char(G, chi) * random_divisor(state, G);
q3 = n_gcd(q, q3);
dirichlet_group_init(G3, q3);
dirichlet_char_init(chi3, G3);
dirichlet_char_lower(chi3, G3, chi2, G2);
p1 = dirichlet_conductor_char(G, chi);
p2 = dirichlet_conductor_char(G3, chi3);
check_eq(p1, p2, q, m, "conductor chi", "conductor lower");
p1 = dirichlet_order_char(G, chi);
p2 = dirichlet_order_char(G3, chi3);
check_eq(p1, p2, q, m, "order chi", "order lower");
dirichlet_char_clear(chi3);
dirichlet_group_clear(G3);
dirichlet_char_clear(chi2);
dirichlet_group_clear(G2);
/* another random character */
do
n = n_randint(state, q);
while (n_gcd(q, n) > 1);
dirichlet_char_log(psi, G, n);
pairing = dirichlet_pairing(G, m, n);
cn = dirichlet_chi(G, chi, n);
cm = dirichlet_chi(G, psi, m);
if (pairing != cn || pairing != cm)
{
flint_printf("FAIL: pairing\n\n");
flint_printf("q = %wu\n\n", q);
flint_printf("m = %wu\n\n", m);
flint_printf("n = %wu\n\n", n);
flint_printf("chi(m,n) = %wu\n\n", pairing);
flint_printf("chi(m)(n) = %wu\n\n", cn);
flint_printf("chi(n)(m) = %wu\n\n", cm);
abort();
}
}
dirichlet_group_dlog_clear(G);
dirichlet_char_clear(chi);
dirichlet_char_clear(psi);
dirichlet_group_clear(G);
}
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main(void)
{
int i, result;
flint_rand_t state;
printf("powmod_precomp....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 100000; i++)
{
mp_limb_t a, d, r1, r2, bits;
mpz_t a_m, d_m, r2_m;
mp_limb_signed_t exp;
double dpre;
mpz_init(a_m);
mpz_init(d_m);
mpz_init(r2_m);
bits = n_randint(state, FLINT_D_BITS) + 1;
d = n_randbits(state, bits);
do
{
a = n_randint(state, d);
} while (n_gcd(d, a) != 1UL);
exp = n_randtest(state);
dpre = n_precompute_inverse(d);
r1 = n_powmod_precomp(a, exp, d, dpre);
mpz_set_ui(a_m, a);
mpz_set_ui(d_m, d);
if (exp < 0L)
{
mpz_powm_ui(r2_m, a_m, -exp, d_m);
mpz_invert(r2_m, r2_m, d_m);
} else
mpz_powm_ui(r2_m, a_m, exp, d_m);
r2 = mpz_get_ui(r2_m);
result = (r1 == r2);
if (!result)
{
printf("FAIL:\n");
printf("a = %lu, exp = %ld, d = %lu\n", a, exp, d);
printf("r1 = %lu, r2 = %lu\n", r1, r2);
abort();
}
mpz_clear(a_m);
mpz_clear(d_m);
mpz_clear(r2_m);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
flint_randinit(state);
printf("make_monic....");
fflush(stdout);
/* Check new leading coeff = gcd old leading coeff and modulus */
for (i = 0; i < 10000; i++)
{
nmod_poly_t a, b;
mp_limb_t n = n_randtest_not_zero(state);
mp_limb_t l;
nmod_poly_init(a, n);
nmod_poly_init(b, n);
if (n == 1) continue;
do { nmod_poly_randtest(a, state, n_randint(state, 100) + 1); } while (a->length == 0);
nmod_poly_make_monic(b, a);
l = n_gcd(a->mod.n, a->coeffs[a->length - 1]);
result = (l == b->coeffs[b->length - 1]);
if (!result)
{
printf("FAIL:\n");
printf("l = %lu, a->lead = %ld, n = %lu\n",
l, a->coeffs[a->length - 1], a->mod.n);
nmod_poly_print(a), printf("\n\n");
nmod_poly_print(b), printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
}
/* test aliasing */
for (i = 0; i < 10000; i++)
{
nmod_poly_t a;
mp_limb_t n = n_randtest_not_zero(state);
mp_limb_t l;
nmod_poly_init(a, n);
if (n == 1) continue;
do { nmod_poly_randtest(a, state, n_randint(state, 100) + 1); } while (a->length == 0);
l = n_gcd(a->mod.n, a->coeffs[a->length - 1]);
nmod_poly_make_monic(a, a);
result = (l == a->coeffs[a->length - 1]);
if (!result)
{
printf("FAIL:\n");
printf("l = %lu, a->lead = %ld, n = %lu\n",
l, a->coeffs[a->length - 1], a->mod.n);
nmod_poly_print(a), printf("\n\n");
abort();
}
nmod_poly_clear(a);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}