void
fmpz_poly_complex_roots_squarefree(const fmpz_poly_t poly,
slong initial_prec,
slong target_prec,
slong print_digits)
{
slong i, j, prec, deg, deg_deflated, isolated, maxiter, deflation;
acb_poly_t cpoly, cpoly_deflated;
fmpz_poly_t poly_deflated;
acb_ptr roots, roots_deflated;
int removed_zero;
if (fmpz_poly_degree(poly) < 1)
return;
fmpz_poly_init(poly_deflated);
acb_poly_init(cpoly);
acb_poly_init(cpoly_deflated);
/* try to write poly as poly_deflated(x^deflation), possibly multiplied by x */
removed_zero = fmpz_is_zero(poly->coeffs);
if (removed_zero)
fmpz_poly_shift_right(poly_deflated, poly, 1);
else
fmpz_poly_set(poly_deflated, poly);
deflation = fmpz_poly_deflation(poly_deflated);
fmpz_poly_deflate(poly_deflated, poly_deflated, deflation);
deg = fmpz_poly_degree(poly);
deg_deflated = fmpz_poly_degree(poly_deflated);
flint_printf("searching for %wd roots, %wd deflated\n", deg, deg_deflated);
roots = _acb_vec_init(deg);
roots_deflated = _acb_vec_init(deg_deflated);
for (prec = initial_prec; ; prec *= 2)
{
acb_poly_set_fmpz_poly(cpoly_deflated, poly_deflated, prec);
maxiter = FLINT_MIN(FLINT_MAX(deg_deflated, 32), prec);
TIMEIT_ONCE_START
flint_printf("prec=%wd: ", prec);
isolated = acb_poly_find_roots(roots_deflated, cpoly_deflated,
prec == initial_prec ? NULL : roots_deflated, maxiter, prec);
flint_printf("%wd isolated roots | ", isolated);
TIMEIT_ONCE_STOP
if (isolated == deg_deflated)
{
if (!check_accuracy(roots_deflated, deg_deflated, target_prec))
continue;
if (deflation == 1)
{
_acb_vec_set(roots, roots_deflated, deg_deflated);
}
else /* compute all nth roots */
{
acb_t w, w2;
acb_init(w);
acb_init(w2);
acb_unit_root(w, deflation, prec);
acb_unit_root(w2, 2 * deflation, prec);
for (i = 0; i < deg_deflated; i++)
{
if (arf_sgn(arb_midref(acb_realref(roots_deflated + i))) > 0)
{
acb_root_ui(roots + i * deflation,
roots_deflated + i, deflation, prec);
}
else
{
acb_neg(roots + i * deflation, roots_deflated + i);
acb_root_ui(roots + i * deflation,
roots + i * deflation, deflation, prec);
acb_mul(roots + i * deflation,
roots + i * deflation, w2, prec);
}
for (j = 1; j < deflation; j++)
{
acb_mul(roots + i * deflation + j,
roots + i * deflation + j - 1, w, prec);
}
}
acb_clear(w);
acb_clear(w2);
}
/* by assumption that poly is squarefree, must be just one */
if (removed_zero)
acb_zero(roots + deg_deflated * deflation);
if (!check_accuracy(roots, deg, target_prec))
continue;
acb_poly_set_fmpz_poly(cpoly, poly, prec);
if (!acb_poly_validate_real_roots(roots, cpoly, prec))
continue;
for (i = 0; i < deg; i++)
{
if (arb_contains_zero(acb_imagref(roots + i)))
arb_zero(acb_imagref(roots + i));
}
flint_printf("done!\n");
break;
}
}
if (print_digits != 0)
{
_acb_vec_sort_pretty(roots, deg);
for (i = 0; i < deg; i++)
{
acb_printn(roots + i, print_digits, 0);
flint_printf("\n");
}
}
fmpz_poly_clear(poly_deflated);
acb_poly_clear(cpoly);
acb_poly_clear(cpoly_deflated);
_acb_vec_clear(roots, deg);
_acb_vec_clear(roots_deflated, deg_deflated);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("pow_ui_trunc_binexp....");
fflush(stdout);
flint_randinit(state);
/* compare with fmpz_poly */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong zbits1, rbits1, rbits2, trunc;
ulong e;
fmpz_poly_t A, B;
acb_poly_t a, b;
zbits1 = 2 + n_randint(state, 100);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
e = n_randint(state, 50);
trunc = n_randint(state, 40);
fmpz_poly_init(A);
fmpz_poly_init(B);
acb_poly_init(a);
acb_poly_init(b);
fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), zbits1);
fmpz_poly_pow_trunc(B, A, e, trunc);
acb_poly_set_fmpz_poly(a, A, rbits1);
acb_poly_pow_ui_trunc_binexp(b, a, e, trunc, rbits2);
if (!acb_poly_contains_fmpz_poly(b, B))
{
flint_printf("FAIL\n\n");
flint_printf("bits2 = %wd\n", rbits2);
flint_printf("e = %wu\n", e);
flint_printf("trunc = %wd\n", trunc);
flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n");
flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n");
abort();
}
acb_poly_pow_ui_trunc_binexp(a, a, e, trunc, rbits2);
if (!acb_poly_equal(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
fmpz_poly_clear(A);
fmpz_poly_clear(B);
acb_poly_clear(a);
acb_poly_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("get_unique_fmpz_poly....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong prec, c;
fmpz_poly_t A, B, C;
acb_poly_t a, b;
fmpz_poly_init(A);
fmpz_poly_init(B);
fmpz_poly_init(C);
acb_poly_init(a);
acb_poly_init(b);
fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000));
fmpz_poly_randtest(B, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000));
fmpz_poly_randtest(C, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000));
c = 1 + n_randint(state, 1000);
prec = 2 + n_randint(state, 100);
for ( ; ; )
{
acb_poly_set_fmpz_poly(a, A, prec);
acb_poly_set2_fmpz_poly(b, B, C, prec);
acb_poly_scalar_mul_2exp_si(b, b, -c);
acb_poly_add(a, a, b, prec);
acb_poly_sub(a, a, b, prec);
if (acb_poly_get_unique_fmpz_poly(B, a))
{
if (!fmpz_poly_equal(A, B))
{
flint_printf("FAIL\n\n");
flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n");
flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n");
flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n");
abort();
}
break;
}
else
{
prec *= 2;
}
}
fmpz_poly_clear(A);
fmpz_poly_clear(B);
fmpz_poly_clear(C);
acb_poly_clear(a);
acb_poly_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}