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/*
Copyright (C) 2012 Sebastian Pancratz
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 "qadic.h"
void _qadic_trace(fmpz_t rop, const fmpz *op, slong len,
const fmpz *a, const slong *j, slong lena, const fmpz_t pN)
{
const slong d = j[lena - 1];
slong i, l;
fmpz *t;
t = _fmpz_vec_init(d);
fmpz_set_ui(t + 0, d);
for (i = 1; i < len; i++) /* simple Newton identities to */
/* compute power sums = traces of basis elements */
/* we don't need them past len */
{
for (l = lena - 2; l >= 0 && j[l] >= d - (i - 1); l--)
{
fmpz_addmul(t + i, t + (j[l] + i - d), a + l);
}
if (l >= 0 && j[l] == d - i)
{
fmpz_addmul_ui(t + i, a + l, i);
}
fmpz_neg(t + i, t + i);
fmpz_mod(t + i, t + i, pN);
}
fmpz_zero(rop);
for (i = 0; i < len; i++)
{
fmpz_addmul(rop, op + i, t + i);
}
fmpz_mod(rop, rop, pN);
_fmpz_vec_clear(t, d);
}
void qadic_trace(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
const slong N = padic_prec(rop);
if (qadic_is_zero(op) || op->val >= N)
{
padic_zero(rop);
}
else
{
fmpz_t pN;
int alloc;
alloc = _padic_ctx_pow_ui(pN, N - op->val, &ctx->pctx);
_qadic_trace(padic_unit(rop), op->coeffs, op->length,
ctx->a, ctx->j, ctx->len, pN);
padic_val(rop) = op->val;
_padic_canonicalise(rop, &ctx->pctx);
if (alloc)
fmpz_clear(pN);
}
}