flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2016 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 "arb_poly.h"
#include "arb_hypgeom.h"

void
_arb_hypgeom_airy_series(arb_ptr ai, arb_ptr ai_prime,
    arb_ptr bi, arb_ptr bi_prime, arb_srcptr z, slong zlen, slong len, slong prec)
{
    arb_ptr t, u, v;
    slong tlen = len + ((ai_prime != NULL) || (bi_prime != NULL));

    zlen = FLINT_MIN(zlen, len);

    if (zlen <= 0)
        return;

    if (zlen == 1)
    {
        arb_hypgeom_airy(ai, ai_prime, bi, bi_prime, z, prec);
        return;
    }

    t = _arb_vec_init(tlen);
    u = _arb_vec_init(tlen);
    v = _arb_vec_init(len);

    arb_hypgeom_airy_jet((ai || ai_prime) ? t : NULL,
                         (bi || bi_prime) ? u : NULL, z, tlen, prec);

    /* compose with nonconstant part */
    arb_zero(v);
    _arb_vec_set(v + 1, z + 1, zlen - 1);

    if (ai != NULL) _arb_poly_compose_series(ai, t, len, v, zlen, len, prec);
    if (bi != NULL) _arb_poly_compose_series(bi, u, len, v, zlen, len, prec);

    /* todo: use chain rule to avoid compositions for derivatives? */
    if (ai_prime != NULL)
    {
        _arb_poly_derivative(t, t, len + 1, prec);
        _arb_poly_compose_series(ai_prime, t, len, v, zlen, len, prec);
    }

    if (bi_prime != NULL)
    {
        _arb_poly_derivative(u, u, len + 1, prec);
        _arb_poly_compose_series(bi_prime, u, len, v, zlen, len, prec);
    }

    _arb_vec_clear(t, tlen);
    _arb_vec_clear(u, tlen);
    _arb_vec_clear(v, len);
}

void
arb_hypgeom_airy_series(arb_poly_t ai, arb_poly_t ai_prime,
    arb_poly_t bi, arb_poly_t bi_prime, const arb_poly_t z, slong len, slong prec)
{
    if (len == 0)
    {
        if (ai != NULL) arb_poly_zero(ai);
        if (ai_prime != NULL) arb_poly_zero(ai_prime);
        if (bi != NULL) arb_poly_zero(bi);
        if (bi_prime != NULL) arb_poly_zero(bi_prime);
        return;
    }

    if (z->length <= 1)
        len = 1;

    if (ai != NULL) arb_poly_fit_length(ai, len);
    if (ai_prime != NULL) arb_poly_fit_length(ai_prime, len);
    if (bi != NULL) arb_poly_fit_length(bi, len);
    if (bi_prime != NULL) arb_poly_fit_length(bi_prime, len);

    if (z->length == 0)
    {
        arb_t t;
        arb_init(t);
        _arb_hypgeom_airy_series(
            ai ? ai->coeffs : NULL, ai_prime ? ai_prime->coeffs : NULL,
            bi ? bi->coeffs : NULL, bi_prime ? bi_prime->coeffs : NULL,
            t, 1, len, prec);
        arb_clear(t);
    }
    else
    {
        _arb_hypgeom_airy_series(
            ai ? ai->coeffs : NULL, ai_prime ? ai_prime->coeffs : NULL,
            bi ? bi->coeffs : NULL, bi_prime ? bi_prime->coeffs : NULL,
            z->coeffs, z->length, len, prec);
    }

    if (ai != NULL)
    {
        _arb_poly_set_length(ai, len);
        _arb_poly_normalise(ai);
    }

    if (ai_prime != NULL)
    {
        _arb_poly_set_length(ai_prime, len);
        _arb_poly_normalise(ai_prime);
    }

    if (bi != NULL)
    {
        _arb_poly_set_length(bi, len);
        _arb_poly_normalise(bi);
    }

    if (bi_prime != NULL)
    {
        _arb_poly_set_length(bi_prime, len);
        _arb_poly_normalise(bi_prime);
    }
}