/*
    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 2.1 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);
    }
}