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/*
Copyright (C) 2013 Mike Hansen
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 "ulong_extras.h"
#include "fmpz.h"
#include "fq_zech.h"
void
fq_zech_trace(fmpz_t rop, const fq_zech_t op, const fq_zech_ctx_t ctx)
{
ulong p_i, trace;
fq_zech_t t, op_p_i;
double qm1inv;
if (fq_zech_is_zero(op, ctx))
{
fmpz_zero(rop);
return;
}
fq_zech_zero(t, ctx);
qm1inv = n_precompute_inverse(ctx->qm1);
for (p_i = 1; p_i <= ctx->qm1; p_i *= ctx->p)
{
/* op_q_i = op ^ (p ^ i) */
op_p_i->value = n_mulmod_precomp(op->value, p_i, ctx->qm1, qm1inv);
/* t += op_p_i */
fq_zech_add(t, t, op_p_i, ctx);
}
if (fq_zech_is_zero(t, ctx))
{
fmpz_zero(rop);
}
else
{
trace = t->value / ctx->qm1opm1;
trace = n_powmod(ctx->prime_root, trace, ctx->p);
fmpz_set_ui(rop, trace);
}
}