int main()
{
slong iter;
flint_rand_t state;
flint_printf("psl2z_inv....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
psl2z_t f, g, h, i;
psl2z_init(f);
psl2z_init(g);
psl2z_init(h);
psl2z_init(i);
psl2z_randtest(f, state, n_randint(state, 100));
psl2z_randtest(g, state, n_randint(state, 100));
psl2z_randtest(h, state, n_randint(state, 100));
psl2z_inv(g, f);
psl2z_mul(h, f, g);
psl2z_one(i);
if (!psl2z_equal(h, i) || !psl2z_is_correct(g))
{
flint_printf("FAIL\n");
flint_printf("f = "); psl2z_print(f); flint_printf("\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n");
flint_printf("h = "); psl2z_print(h); flint_printf("\n");
flint_printf("i = "); psl2z_print(i); flint_printf("\n");
abort();
}
psl2z_inv(f, f);
if (!psl2z_equal(f, g) || !psl2z_is_correct(f))
{
flint_printf("FAIL (aliasing)\n");
flint_printf("f = "); psl2z_print(f); flint_printf("\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n");
abort();
}
psl2z_clear(f);
psl2z_clear(g);
psl2z_clear(h);
psl2z_clear(i);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("psl2z_mul....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
psl2z_t f, g, h, u, v;
psl2z_init(f);
psl2z_init(g);
psl2z_init(h);
psl2z_init(u);
psl2z_init(v);
psl2z_randtest(f, state, n_randint(state, 100));
psl2z_randtest(g, state, n_randint(state, 100));
psl2z_randtest(h, state, n_randint(state, 100));
psl2z_randtest(u, state, n_randint(state, 100));
psl2z_randtest(v, state, n_randint(state, 100));
/* test (f*g)*h = f*(g*h) */
psl2z_mul(u, f, g);
psl2z_mul(u, u, h);
psl2z_mul(v, g, h);
psl2z_mul(v, f, v);
if (!psl2z_equal(u, v) || !psl2z_is_correct(u) || !psl2z_is_correct(v))
{
flint_printf("FAIL\n");
flint_printf("f = "); psl2z_print(f); flint_printf("\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n");
flint_printf("h = "); psl2z_print(h); flint_printf("\n");
flint_printf("u = "); psl2z_print(u); flint_printf("\n");
flint_printf("v = "); psl2z_print(v); flint_printf("\n");
abort();
}
psl2z_clear(f);
psl2z_clear(g);
psl2z_clear(h);
psl2z_clear(u);
psl2z_clear(v);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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()
{
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("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()
{
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;
}
