int main()
{
slong iter;
flint_rand_t state;
flint_printf("eisenstein....");
fflush(stdout);
flint_randinit(state);
/* Test functional equation */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
acb_t tau1, tau2, t;
acb_ptr r1, r2;
slong e0, prec0, prec1, prec2, len1, len2, i;
psl2z_t g;
psl2z_init(g);
acb_init(tau1);
acb_init(tau2);
acb_init(t);
e0 = 1 + n_randint(state, 200);
prec0 = 2 + n_randint(state, 2000);
prec1 = 2 + n_randint(state, 2000);
prec2 = 2 + n_randint(state, 2000);
len1 = n_randint(state, 20);
len2 = n_randint(state, 20);
r1 = _acb_vec_init(len1);
r2 = _acb_vec_init(len2);
acb_randtest(tau1, state, prec0, e0);
acb_randtest(tau2, state, prec0, e0);
psl2z_randtest(g, state, 1 + n_randint(state, 200));
acb_modular_transform(tau2, g, tau1, prec0);
acb_modular_eisenstein(r1, tau1, len1, prec1);
acb_modular_eisenstein(r2, tau2, len2, prec2);
for (i = 0; i < FLINT_MIN(len1, len2); i++)
{
acb_mul_fmpz(t, tau1, &g->c, prec1);
acb_add_fmpz(t, t, &g->d, prec1);
acb_pow_ui(t, t, 2 * i + 4, prec1);
acb_mul(t, t, r1 + i, prec1);
if (!acb_overlaps(t, r2 + i))
{
flint_printf("FAIL (overlap)\n");
flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n");
flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
flint_printf("r1 = "); acb_printd(r1 + i, 15); flint_printf("\n\n");
flint_printf("r2 = "); acb_printd(r2 + i, 15); flint_printf("\n\n");
flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n");
flint_abort();
}
}
acb_clear(tau1);
acb_clear(tau2);
acb_clear(t);
_acb_vec_clear(r1, len1);
_acb_vec_clear(r2, len2);
psl2z_clear(g);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("fundamental_domain_approx....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_t x, y;
psl2z_t g;
arf_t one_minus_eps, tol;
acb_t z, w, w2;
arb_t t;
slong prec;
fmpq_init(x);
fmpq_init(y);
psl2z_init(g);
acb_init(z);
acb_init(w);
acb_init(w2);
arf_init(one_minus_eps);
arf_init(tol);
arb_init(t);
/* pick an exact point in the upper half plane */
fmpq_randtest(x, state, 1 + n_randint(state, 500));
do {
fmpq_randtest(y, state, 1 + n_randint(state, 500));
} while (fmpz_sgn(fmpq_numref(y)) <= 0);
/* pick a tolerance */
arf_set_ui_2exp_si(tol, 1, -(slong) n_randint(state, 500));
/* now increase the precision until convergence */
for (prec = 32; ; prec *= 2)
{
if (prec > 16384)
{
flint_printf("FAIL (no convergence)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
arb_set_fmpq(acb_realref(z), x, prec);
arb_set_fmpq(acb_imagref(z), y, prec);
arf_set_ui_2exp_si(one_minus_eps, 1, -prec / 4);
arf_sub_ui(one_minus_eps, one_minus_eps, 1, prec, ARF_RND_DOWN);
arf_neg(one_minus_eps, one_minus_eps);
acb_modular_fundamental_domain_approx(w, g, z, one_minus_eps, prec);
acb_modular_transform(w2, g, z, prec);
if (!psl2z_is_correct(g) || !acb_overlaps(w, w2))
{
flint_printf("FAIL (incorrect transformation)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
/* success */
if (acb_modular_is_in_fundamental_domain(w, tol, prec))
break;
}
/* check that g^(-1) * w contains x+yi */
psl2z_inv(g, g);
acb_modular_transform(w2, g, w, 2 + n_randint(state, 1000));
if (!arb_contains_fmpq(acb_realref(w2), x) ||
!arb_contains_fmpq(acb_imagref(w2), y))
{
flint_printf("FAIL (inverse containment)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
psl2z_clear(g);
acb_clear(z);
acb_clear(w);
acb_clear(w2);
arf_clear(one_minus_eps);
arf_clear(tol);
arb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("transform....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
psl2z_t g;
acb_t z, w1, w2, t;
slong prec;
psl2z_init(g);
acb_init(z);
acb_init(w1);
acb_init(w2);
acb_init(t);
psl2z_randtest(g, state, n_randint(state, 20));
acb_randtest(z, state, 1 + n_randint(state, 200), 1 + n_randint(state, 20));
acb_randtest(w1, state, 1 + n_randint(state, 200), 1 + n_randint(state, 20));
acb_randtest(w2, state, 1 + n_randint(state, 200), 1 + n_randint(state, 20));
acb_modular_transform(w1, g, z, 2 + n_randint(state, 200));
prec = 2 + n_randint(state, 200);
acb_mul_fmpz(t, z, &g->a, prec);
acb_add_fmpz(t, t, &g->b, prec);
acb_mul_fmpz(w2, z, &g->c, prec);
acb_add_fmpz(w2, w2, &g->d, prec);
acb_div(w2, t, w2, prec);
if (!acb_overlaps(w1, w2))
{
flint_printf("FAIL\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n");
flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n");
abort();
}
psl2z_clear(g);
acb_clear(z);
acb_clear(w1);
acb_clear(w2);
acb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("eta....");
fflush(stdout);
flint_randinit(state);
/* Test functional equation */
for (iter = 0; iter < 10000; iter++)
{
acb_t tau1, tau2, z1, z2, z3, t;
fmpq_t arg;
long e0, prec0, prec1, prec2;
psl2z_t g;
psl2z_init(g);
fmpq_init(arg);
acb_init(tau1);
acb_init(tau2);
acb_init(z1);
acb_init(z2);
acb_init(z3);
acb_init(t);
e0 = 1 + n_randint(state, 200);
prec0 = 2 + n_randint(state, 2000);
prec1 = 2 + n_randint(state, 2000);
prec2 = 2 + n_randint(state, 2000);
acb_randtest(tau1, state, prec0, e0);
acb_randtest(tau2, state, prec0, e0);
acb_randtest(z1, state, prec0, e0);
acb_randtest(z2, state, prec0, e0);
psl2z_randtest(g, state, 1 + n_randint(state, 200));
acb_modular_transform(tau2, g, tau1, prec0);
acb_modular_eta(z1, tau1, prec1);
acb_modular_eta(z2, tau2, prec2);
/* apply transformation */
fmpq_set_si(arg, acb_modular_epsilon_arg(g), 12);
arb_sin_cos_pi_fmpq(acb_imagref(t), acb_realref(t), arg, prec1);
acb_mul(z3, z1, t, prec1);
acb_mul_fmpz(t, tau1, &g->c, prec1);
acb_add_fmpz(t, t, &g->d, prec1);
acb_sqrt(t, t, prec1);
acb_mul(z3, z3, t, prec1);
if (!acb_overlaps(z3, z2))
{
printf("FAIL (overlap)\n");
printf("tau1 = "); acb_printd(tau1, 15); printf("\n\n");
printf("tau2 = "); acb_printd(tau2, 15); printf("\n\n");
printf("g = "); psl2z_print(g); printf("\n\n");
printf("z1 = "); acb_printd(z1, 15); printf("\n\n");
printf("z2 = "); acb_printd(z2, 15); printf("\n\n");
printf("z3 = "); acb_printd(z3, 15); printf("\n\n");
abort();
}
acb_modular_eta(tau1, tau1, prec2);
if (!acb_overlaps(z1, tau1))
{
printf("FAIL (aliasing)\n");
printf("tau1 = "); acb_print(tau1); printf("\n\n");
printf("tau2 = "); acb_print(tau2); printf("\n\n");
printf("z1 = "); acb_print(z1); printf("\n\n");
printf("z2 = "); acb_print(z2); printf("\n\n");
abort();
}
acb_clear(tau1);
acb_clear(tau2);
acb_clear(z1);
acb_clear(z2);
acb_clear(z3);
acb_clear(t);
psl2z_clear(g);
fmpq_clear(arg);
}
/* Test special values */
for (iter = 0; iter < 100; iter++)
{
acb_t tau, z;
arb_t t, u;
long prec;
acb_init(tau);
acb_init(z);
arb_init(t);
arb_init(u);
prec = 2 + n_randint(state, 2000);
acb_randtest(z, state, prec, 10);
acb_onei(tau);
acb_modular_eta(z, tau, prec);
arb_one(t);
arb_mul_2exp_si(t, t, -2);
arb_gamma(t, t, prec);
arb_const_pi(u, prec);
arb_root(u, u, 4, prec);
arb_pow_ui(u, u, 3, prec);
arb_div(t, t, u, prec);
arb_mul_2exp_si(t, t, -1);
if (!arb_overlaps(acb_realref(z), t) ||
!arb_contains_zero(acb_imagref(z)))
{
printf("FAIL (value 1)\n");
printf("tau = "); acb_print(tau); printf("\n\n");
printf("z = "); acb_print(z); printf("\n\n");
abort();
}
acb_clear(tau);
acb_clear(z);
arb_clear(t);
arb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("j....");
fflush(stdout);
flint_randinit(state);
/* Test SL2Z invariance */
for (iter = 0; iter < 10000; iter++)
{
acb_t tau1, tau2, z1, z2;
slong e0, prec0, prec1, prec2;
psl2z_t g;
psl2z_init(g);
acb_init(tau1);
acb_init(tau2);
acb_init(z1);
acb_init(z2);
e0 = 1 + n_randint(state, 100);
prec0 = 2 + n_randint(state, 2000);
prec1 = 2 + n_randint(state, 2000);
prec2 = 2 + n_randint(state, 2000);
acb_randtest(tau1, state, prec0, e0);
acb_randtest(tau2, state, prec0, e0);
acb_randtest(z1, state, prec0, e0);
acb_randtest(z2, state, prec0, e0);
psl2z_randtest(g, state, 1 + n_randint(state, 200));
acb_modular_transform(tau2, g, tau1, prec0);
acb_modular_j(z1, tau1, prec1);
acb_modular_j(z2, tau2, prec2);
if (!acb_overlaps(z1, z2))
{
flint_printf("FAIL (overlap)\n");
flint_printf("tau1 = "); acb_print(tau1); flint_printf("\n\n");
flint_printf("tau2 = "); acb_print(tau2); flint_printf("\n\n");
flint_printf("z1 = "); acb_print(z1); flint_printf("\n\n");
flint_printf("z2 = "); acb_print(z2); flint_printf("\n\n");
abort();
}
acb_modular_j(tau1, tau1, prec2);
if (!acb_overlaps(z1, tau1))
{
flint_printf("FAIL (aliasing)\n");
flint_printf("tau1 = "); acb_print(tau1); flint_printf("\n\n");
flint_printf("tau2 = "); acb_print(tau2); flint_printf("\n\n");
flint_printf("z1 = "); acb_print(z1); flint_printf("\n\n");
flint_printf("z2 = "); acb_print(z2); flint_printf("\n\n");
abort();
}
acb_clear(tau1);
acb_clear(tau2);
acb_clear(z1);
acb_clear(z2);
psl2z_clear(g);
}
/* Test special values */
for (iter = 0; iter < 100; iter++)
{
acb_t tau, z;
slong prec;
acb_init(tau);
acb_init(z);
prec = 2 + n_randint(state, 2000);
acb_randtest(z, state, prec, 10);
acb_onei(tau);
acb_modular_j(z, tau, prec);
acb_sub_ui(z, z, 1728, prec);
if (!acb_contains_zero(z))
{
flint_printf("FAIL (value 1)\n");
flint_printf("tau = "); acb_print(tau); flint_printf("\n\n");
flint_printf("z = "); acb_print(z); flint_printf("\n\n");
abort();
}
acb_set_ui(tau, 2);
acb_div_ui(tau, tau, 3, prec);
acb_exp_pi_i(tau, tau, prec);
acb_modular_j(z, tau, prec);
if (!acb_contains_zero(z))
{
flint_printf("FAIL (value 2)\n");
flint_printf("tau = "); acb_print(tau); flint_printf("\n\n");
flint_printf("z = "); acb_print(z); flint_printf("\n\n");
abort();
}
acb_clear(tau);
acb_clear(z);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}