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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of Calcium.
Calcium 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "qqbar.h"
int
qqbar_is_root_of_unity(slong * p, ulong * q, const qqbar_t x)
{
ulong n;
n = fmpz_poly_is_cyclotomic(QQBAR_POLY(x));
if (n == 0)
return 0;
if (q != NULL)
*q = n;
if (n == 1)
{
if (p != NULL) *p = 0;
}
else if (n == 2)
{
if (p != NULL) *p = 1;
}
else if (n == 3)
{
if (p != NULL) *p = (qqbar_sgn_im(x) > 0) ? 1 : 2;
}
else if (n == 4)
{
if (p != NULL) *p = (qqbar_sgn_im(x) > 0) ? 1 : 3;
}
else
{
if (p != NULL)
{
arb_t t, u;
acb_t z;
fmpz_t k;
slong prec;
acb_init(z);
arb_init(t);
arb_init(u);
fmpz_init(k);
prec = 64; /* more than enough */
qqbar_get_acb(z, x, prec);
acb_arg(t, z, prec);
arb_const_pi(u, prec);
arb_div(t, t, u, prec);
arb_mul_2exp_si(t, t, -1);
arb_mul_ui(t, t, n, prec);
if (!arb_get_unique_fmpz(k, t))
{
flint_printf("qqbar_is_root_of_unity: unexpected precision issue\n");
flint_abort();
}
if (fmpz_sgn(k) < 0)
fmpz_add_ui(k, k, n);
*p = fmpz_get_si(k);
acb_clear(z);
arb_clear(t);
arb_clear(u);
fmpz_clear(k);
}
}
return 1;
}
void
qqbar_root_of_unity(qqbar_t res, slong p, ulong q)
{
fmpq_t t;
ulong a, b;
slong prec;
fmpq_init(t);
if (q == 0)
{
flint_printf("qqbar_root_of_unity: q = 0\n");
flint_abort();
}
fmpq_set_si(t, p, q);
fmpz_fdiv_r(fmpq_numref(t), fmpq_numref(t), fmpq_denref(t));
a = fmpz_get_ui(fmpq_numref(t));
b = fmpz_get_ui(fmpq_denref(t));
if (a == 0)
{
qqbar_one(res);
}
else if (a == 1 && b == 2)
{
qqbar_set_si(res, -1);
}
else if (a == 1 && b == 4)
{
qqbar_i(res);
}
else if (a == 3 && b == 4)
{
qqbar_i(res);
qqbar_conj(res, res);
}
else
{
fmpz_poly_cyclotomic(QQBAR_POLY(res), b);
fmpq_mul_2exp(t, t, 1);
for (prec = QQBAR_DEFAULT_PREC / 2; ; prec *= 2)
{
arb_sin_cos_pi_fmpq(acb_imagref(QQBAR_ENCLOSURE(res)),
acb_realref(QQBAR_ENCLOSURE(res)),
t, prec);
/* todo: this is really unnecessary... */
if (_qqbar_validate_uniqueness(QQBAR_ENCLOSURE(res),
QQBAR_POLY(res), QQBAR_ENCLOSURE(res), prec * 2))
{
break;
}
}
}
fmpq_clear(t);
}
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