arb/acb_poly/div_series.c

/*=============================================================================

    This file is part of ARB.

    ARB is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    ARB is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with ARB; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2012, 2013 Fredrik Johansson

******************************************************************************/

#include "acb_poly.h"

void 
_acb_poly_div_series(acb_ptr Q, acb_srcptr A, long Alen,
    acb_srcptr B, long Blen, long n, long prec)
{
    Alen = FLINT_MIN(Alen, n);
    Blen = FLINT_MIN(Blen, n);

    if (Blen == 1)
    {
        _acb_vec_scalar_div(Q, A, Alen, B, prec);
        _acb_vec_zero(Q + Alen, n - Alen);
    }
    else if (n == 2)
    {
        if (Alen == 1)
        {
            acb_div(Q, A, B, prec);
            acb_div(Q + 1, Q, B, prec);
            acb_mul(Q + 1, Q + 1, B + 1, prec);
            acb_neg(Q + 1, Q + 1);
        }
        else
        {
            acb_div(Q, A, B, prec);
            acb_mul(Q + 1, Q, B + 1, prec);
            acb_sub(Q + 1, A + 1, Q + 1, prec);
            acb_div(Q + 1, Q + 1, B, prec);
        }
    }
    else
    {
        acb_ptr Binv;
        Binv = _acb_vec_init(n);
        _acb_poly_inv_series(Binv, B, Blen, n, prec);
        _acb_poly_mullow(Q, Binv, n, A, Alen, n, prec);
        _acb_vec_clear(Binv, n);
    }
}

void
acb_poly_div_series(acb_poly_t Q, const acb_poly_t A, const acb_poly_t B, long n, long prec)
{
    if (n == 0)
    {
        acb_poly_zero(Q);
        return;
    }

    if (B->length == 0)
    {
        acb_poly_fit_length(Q, n);
        _acb_vec_indeterminate(Q->coeffs, n);
        _acb_poly_set_length(Q, n);
        return;
    }

    if (A->length == 0)
    {
        acb_poly_zero(Q);
        return;
    }

    if (Q == A || Q == B)
    {
        acb_poly_t t;
        acb_poly_init(t);
        acb_poly_div_series(t, A, B, n, prec);
        acb_poly_swap(Q, t);
        acb_poly_clear(t);
        return;
    }

    acb_poly_fit_length(Q, n);
    _acb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec);
    _acb_poly_set_length(Q, n);
    _acb_poly_normalise(Q);
}