/* F = 1 + U + U^2 + ... = 1/(1-U) assuming that U[0] is positive;
indeterminate if not convergent */
static void
arb_poly_geometric_sum(arb_poly_t F, const arb_poly_t U, long len, long prec)
{
if (U->length == 0)
{
arb_poly_one(F);
return;
}
arb_poly_add_si(F, U, -1, prec);
arb_poly_neg(F, F);
if (F->length > 0 && arb_is_positive(F->coeffs))
{
arb_poly_inv_series(F, F, len, prec);
}
else
{
arb_poly_fit_length(F, len);
_arb_vec_indeterminate(F->coeffs, len);
_arb_poly_set_length(F, len);
}
}
/* F = 1 + U + U^2 + U^3 + ... = 1/(1-U)
U = product of (1 + |A-B|/(|B[0] - |B[1:]|)
product of (1 / (|B[0] - |B[1:]|))
* |Z|
*/
void
acb_hypgeom_pfq_series_bound_factor(arb_poly_t F,
const acb_poly_struct * a, long p,
const acb_poly_struct * b, long q,
const acb_poly_t z,
long n, long len, long prec)
{
long i;
arb_poly_t T, U, V;
acb_poly_t BN, AB;
/* not convergent */
if (p > q)
{
arb_poly_fit_length(F, len);
_arb_vec_indeterminate(F->coeffs, len);
_arb_poly_set_length(F, len);
return;
}
arb_poly_init(T);
arb_poly_init(U);
arb_poly_init(V);
acb_poly_init(BN);
acb_poly_init(AB);
acb_poly_majorant(U, z, prec);
for (i = 0; i < q; i++)
{
acb_poly_add_si(BN, b + i, n, prec);
if (acb_poly_length(BN) != 0 &&
arb_is_positive(acb_realref(BN->coeffs)))
{
if (i < p)
{
/* 1 + |a-b|/reciprocal_majorant(b + n) */
acb_poly_sub(AB, a + i, b + i, prec);
acb_poly_majorant(T, AB, prec);
acb_poly_reciprocal_majorant(V, BN, prec);
arb_poly_div_series(T, T, V, len, prec);
arb_poly_add_si(T, T, 1, prec);
arb_poly_mullow(U, U, T, len, prec);
}
else
{
acb_poly_reciprocal_majorant(T, BN, prec);
arb_poly_div_series(U, U, T, len, prec);
}
}
else
{
arb_poly_fit_length(U, len);
_arb_vec_indeterminate(U->coeffs, len);
_arb_poly_set_length(U, len);
break;
}
}
/* F = 1/(1-U) */
arb_poly_geometric_sum(F, U, len, prec);
arb_poly_clear(T);
arb_poly_clear(U);
arb_poly_clear(V);
acb_poly_clear(BN);
acb_poly_clear(AB);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("digamma_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
slong m, n1, n2, rbits1, rbits2, rbits3;
arb_poly_t a, b, c, d;
rbits1 = 2 + n_randint(state, 300);
rbits2 = 2 + n_randint(state, 300);
rbits3 = 2 + n_randint(state, 300);
m = n_randint(state, 25);
n1 = n_randint(state, 25);
n2 = n_randint(state, 25);
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
arb_poly_randtest(a, state, m, rbits1, 10);
arb_poly_digamma_series(b, a, n1, rbits2);
arb_poly_digamma_series(c, a, n2, rbits3);
arb_poly_set(d, b);
arb_poly_truncate(d, FLINT_MIN(n1, n2));
arb_poly_truncate(c, FLINT_MIN(n1, n2));
if (!arb_poly_overlaps(c, d))
{
flint_printf("FAIL\n\n");
flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3);
flint_printf("a = "); arb_poly_printd(a, 50); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 50); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 50); flint_printf("\n\n");
abort();
}
/* check psi(a) + 1/a = psi(a+1) */
arb_poly_inv_series(c, a, n1, rbits2);
arb_poly_add(c, b, c, rbits2);
arb_poly_add_si(d, a, 1, rbits2);
arb_poly_digamma_series(d, d, n1, rbits2);
if (!arb_poly_overlaps(c, d))
{
flint_printf("FAIL (functional equation)\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
arb_poly_digamma_series(a, a, n1, rbits2);
if (!arb_poly_overlaps(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rgamma_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
slong m, n1, n2, qbits, rbits1, rbits2, rbits3;
fmpq_poly_t A;
arb_poly_t a, b, c, d;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 400);
rbits2 = 2 + n_randint(state, 400);
rbits3 = 2 + n_randint(state, 400);
m = 1 + n_randint(state, 30);
n1 = 1 + n_randint(state, 30);
n2 = 1 + n_randint(state, 30);
fmpq_poly_init(A);
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
fmpq_poly_randtest_not_zero(A, state, m, qbits);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_rgamma_series(b, a, n1, rbits2);
arb_poly_rgamma_series(c, a, n2, rbits3);
arb_poly_set(d, b);
arb_poly_truncate(d, FLINT_MIN(n1, n2));
arb_poly_truncate(c, FLINT_MIN(n1, n2));
if (!arb_poly_overlaps(c, d))
{
flint_printf("FAIL\n\n");
flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3);
flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
abort();
}
/* check rgamma(a) = a gamma(a+1) */
arb_poly_add_si(d, a, 1, rbits2);
arb_poly_rgamma_series(d, d, n1, rbits2);
arb_poly_mullow(c, d, a, n1, rbits2);
if (!arb_poly_overlaps(b, c))
{
flint_printf("FAIL (functional equation, n1 = %wd)\n\n", n1);
flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
arb_poly_rgamma_series(a, a, n1, rbits2);
if (!arb_poly_overlaps(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
fmpq_poly_clear(A);
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
