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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ca.h"
truth_t
ca_check_is_imaginary(const ca_t x, ca_ctx_t ctx)
{
if (CA_IS_SPECIAL(x))
{
if (ca_is_unknown(x, ctx))
return T_UNKNOWN;
return T_FALSE;
}
else if (CA_IS_QQ(x, ctx))
{
if (fmpq_is_zero(CA_FMPQ(x)))
return T_TRUE;
else
return T_FALSE;
}
else if (CA_IS_QQ_I(x, ctx))
{
const fmpz *n;
n = QNF_ELEM_NUMREF(CA_NF_ELEM(x));
if (fmpz_is_zero(n))
return T_TRUE;
return T_FALSE;
}
else
{
acb_t t;
truth_t res;
slong prec, prec_limit;
res = T_UNKNOWN;
acb_init(t);
prec_limit = ctx->options[CA_OPT_PREC_LIMIT];
prec_limit = FLINT_MAX(prec_limit, 64);
for (prec = 64; (prec <= prec_limit) && (res == T_UNKNOWN); prec *= 2)
{
ca_get_acb_raw(t, x, prec, ctx);
if (arb_is_zero(acb_realref(t)))
{
res = T_TRUE;
break;
}
if (!arb_contains_zero(acb_realref(t)))
{
res = T_FALSE;
break;
}
/* try conjugation */
/* todo: precision to do this should depend on complexity of the polynomials, degree of the elements... */
if (prec == 64)
{
ca_t t;
ca_init(t, ctx);
ca_conj_deep(t, x, ctx);
ca_neg(t, t, ctx);
res = ca_check_equal(t, x, ctx);
ca_clear(t, ctx);
if (res != T_UNKNOWN)
break;
}
/* try qqbar computation */
/* todo: precision to do this should depend on complexity of the polynomials, degree of the elements... */
if (prec == 64)
{
qqbar_t a;
qqbar_init(a);
if (ca_get_qqbar(a, x, ctx))
res = (qqbar_sgn_re(a) == 0) ? T_TRUE : T_FALSE;
qqbar_clear(a);
}
}
acb_clear(t);
return res;
}
}