void
arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, long n, long prec)
{
if (n == 0 || B->length == 0)
{
printf("arb_poly_inv_series: require n > 0 and nonzero input\n");
abort();
}
if (A->length == 0)
{
arb_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
arb_poly_t t;
arb_poly_init(t);
arb_poly_div_series(t, A, B, n, prec);
arb_poly_swap(Q, t);
arb_poly_clear(t);
return;
}
arb_poly_fit_length(Q, n);
_arb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec);
_arb_poly_set_length(Q, n);
_arb_poly_normalise(Q);
}
void
_arb_poly_div(arb_ptr Q,
arb_srcptr A, slong lenA,
arb_srcptr B, slong lenB, slong prec)
{
slong lenQ, lenB2;
arb_ptr Arev, Brev;
lenQ = lenA - lenB + 1;
Arev = _arb_vec_init(2 * lenQ);
Brev = Arev + lenQ;
_arb_poly_reverse(Arev, A + (lenA - lenQ), lenQ, lenQ);
if (lenB >= lenQ)
{
_arb_poly_reverse(Brev, B + (lenB - lenQ), lenQ, lenQ);
lenB2 = lenQ;
}
else
{
_arb_poly_reverse(Brev, B, lenB, lenB);
lenB2 = lenB;
}
_arb_poly_div_series(Q, Arev, lenQ, Brev, lenB2, lenQ, prec);
_arb_poly_reverse(Q, Q, lenQ, lenQ);
_arb_vec_clear(Arev, 2 * lenQ);
}
void
_arb_poly_tan_series(arb_ptr g,
arb_srcptr h, slong hlen, slong len, slong prec)
{
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_tan(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else if (len == 2)
{
arb_t t;
arb_init(t);
arb_tan(g, h, prec);
arb_mul(t, g, g, prec);
arb_add_ui(t, t, 1, prec);
arb_mul(g + 1, t, h + 1, prec); /* safe since hlen >= 2 */
arb_clear(t);
}
else
{
arb_ptr t, u;
t = _arb_vec_init(2 * len);
u = t + len;
NEWTON_INIT(TAN_NEWTON_CUTOFF, len)
NEWTON_BASECASE(n)
_arb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec, 0);
_arb_poly_div_series(g, t, n, u, n, n, prec);
NEWTON_END_BASECASE
NEWTON_LOOP(m, n)
_arb_poly_mullow(u, g, m, g, m, n, prec);
arb_add_ui(u, u, 1, prec);
_arb_poly_atan_series(t, g, m, n, prec);
_arb_poly_sub(t + m, h + m, FLINT_MAX(0, hlen - m), t + m, n - m, prec);
_arb_poly_mullow(g + m, u, n, t + m, n - m, n - m, prec);
NEWTON_END_LOOP
NEWTON_END
_arb_vec_clear(t, 2 * len);
}
}
void
arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, long n, long prec)
{
if (n == 0)
{
arb_poly_zero(Q);
return;
}
if (B->length == 0)
{
arb_poly_fit_length(Q, n);
_arb_vec_indeterminate(Q->coeffs, n);
_arb_poly_set_length(Q, n);
return;
}
if (A->length == 0)
{
arb_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
arb_poly_t t;
arb_poly_init(t);
arb_poly_div_series(t, A, B, n, prec);
arb_poly_swap(Q, t);
arb_poly_clear(t);
return;
}
arb_poly_fit_length(Q, n);
_arb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec);
_arb_poly_set_length(Q, n);
_arb_poly_normalise(Q);
}
void
_arb_poly_cot_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec)
{
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_cot_pi(g, h, prec);
_arb_vec_zero(g + 1, len - 1);
}
else
{
arb_ptr t, u;
t = _arb_vec_init(len);
u = _arb_vec_init(len);
_arb_poly_sin_cos_pi_series(t, u, h, hlen, len, prec);
_arb_poly_div_series(g, u, len, t, len, len, prec);
_arb_vec_clear(t, len);
_arb_vec_clear(u, len);
}
}
