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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"
void
ca_sqrt_factor(ca_t res, const ca_t x, ulong flags, ca_ctx_t ctx)
{
if (CA_IS_SPECIAL(x))
{
if (CA_IS_SIGNED_INF(x))
{
ca_sgn(res, x, ctx);
ca_sqrt_factor(res, res, flags, ctx);
if (!ca_is_unknown(res, ctx))
res->field |= CA_INF;
}
else
{
ca_set(res, x, ctx);
}
}
else
{
slong i;
ca_factor_t fac;
ca_t A, B, t;
if (CA_IS_QQ(x, ctx))
{
qqbar_t t;
qqbar_init(t);
qqbar_fmpq_root_ui(t, CA_FMPQ(x), 2);
ca_set_qqbar(res, t, ctx);
qqbar_clear(t);
return;
}
ca_factor_init(fac, ctx);
ca_init(A, ctx);
ca_init(B, ctx);
ca_init(t, ctx);
ca_factor(fac, x, flags, ctx);
ca_one(A, ctx);
ca_one(B, ctx);
for (i = 0; i < fac->length; i++)
{
if (CA_IS_QQ(fac->exp + i, ctx) && fmpz_is_one(CA_FMPQ_DENREF(fac->exp + i)))
{
if (!fmpz_is_zero(CA_FMPQ_DENREF(fac->exp + i)))
{
fmpz_t e;
ca_ext_ptr ext;
ext = ca_is_gen_as_ext(fac->base + i, ctx);
if (ext != NULL && CA_EXT_HEAD(ext) == CA_Exp)
{
/* sqrt(exp(a)^n) = +/- exp(a*n/2) */
ca_mul_fmpz(t, CA_EXT_FUNC_ARGS(ext), CA_FMPQ_NUMREF(fac->exp + i), ctx);
ca_div_ui(t, t, 2, ctx);
ca_exp(t, t, ctx);
ca_mul(A, A, t, ctx);
continue;
}
/* todo: assert a != 0? */
if (ext != NULL && CA_EXT_HEAD(ext) == CA_Sqrt)
{
/* sqrt(sqrt(a)^n) = +/- a^(n/4) */
ca_set_fmpz(t, CA_FMPQ_NUMREF(fac->exp + i), ctx);
ca_div_ui(t, t, 4, ctx);
ca_pow(t, CA_EXT_FUNC_ARGS(ext), t, ctx);
ca_mul(A, A, t, ctx);
continue;
}
/* todo: assert a != 0? */
if (ext != NULL && CA_EXT_HEAD(ext) == CA_Pow)
{
/* sqrt((a^b)^n) = +/- a^(n*b/2) */
ca_mul_fmpz(t, CA_EXT_FUNC_ARGS(ext) + 1, CA_FMPQ_NUMREF(fac->exp + i), ctx);
ca_div_ui(t, t, 2, ctx);
ca_pow(t, CA_EXT_FUNC_ARGS(ext), t, ctx);
ca_mul(A, A, t, ctx);
continue;
}
fmpz_init(e);
if (fmpz_is_odd(CA_FMPQ_NUMREF(fac->exp + i)))
ca_mul(B, B, fac->base + i, ctx);
fmpz_fdiv_q_2exp(e, CA_FMPQ_NUMREF(fac->exp + i), 1);
ca_pow_fmpz(t, fac->base + i, e, ctx);
ca_mul(A, A, t, ctx);
fmpz_clear(e);
}
}
else
{
ca_pow(t, fac->base + i, fac->exp + i, ctx);
ca_mul(B, B, t, ctx);
}
}
/*
printf("factors:\n");
ca_factor_print(fac, ctx); printf("\n");
ca_print(A, ctx); printf("\n");
ca_print(B, ctx); printf("\n");
*/
ca_sqrt_nofactor(B, B, ctx);
ca_mul(A, A, B, ctx);
/* check sign (todo: much improvable) */
{
acb_t sA, sA2, sB;
int success;
slong prec, prec_limit, low_prec;
low_prec = ctx->options[CA_OPT_LOW_PREC];
prec_limit = ctx->options[CA_OPT_PREC_LIMIT];
prec_limit = FLINT_MAX(prec_limit, low_prec);
ca_sqrt_inert(B, x, ctx);
acb_init(sA);
acb_init(sA2);
acb_init(sB);
success = 0;
for (prec = low_prec; prec <= prec_limit; prec *= 2)
{
ca_get_acb_raw(sA, A, prec, ctx);
ca_get_acb_raw(sB, B, prec, ctx);
acb_neg(sA2, sA);
if (acb_overlaps(sA, sB) && !acb_overlaps(sA2, sB))
{
ca_set(res, A, ctx);
success = 1;
break;
}
if (acb_overlaps(sA2, sB) && !acb_overlaps(sA, sB))
{
ca_neg(res, A, ctx);
success = 1;
break;
}
}
if (!success)
{
if (ca_check_is_zero(A, ctx) == T_TRUE)
ca_zero(res, ctx);
else
ca_set(res, B, ctx);
}
acb_clear(sA);
acb_clear(sA2);
acb_clear(sB);
}
ca_factor_clear(fac, ctx);
ca_clear(A, ctx);
ca_clear(B, ctx);
ca_clear(t, ctx);
}
}