_arb_poly_inv_series, arb_poly_inv_series
#include <flint/arb_poly.h>void arb_poly_inv_series(arb_poly_t Q, const arb_poly_t A, slong n, slong prec)sourceSet Q to the power series inverse 1/A truncated to length n (len). The result is finite only if the constant term of A excludes zero; it is indeterminate if A is zero. The underscore version requires positive lengths and no aliasing.
The first coefficients are computed by the recurrence q_i = -q_0 \sum_{j=1}^{i} a_j q_{i-j} with arb_dot (all of them if n \le 8 or A has length 2, otherwise the first 4), and the rest by the Newton iteration Q \leftarrow Q - Q(AQ - 1), which doubles the length at each step and computes only the unknown part of AQ - 1 by a middle product. The recurrence is faster up to much larger lengths but gives worse error bounds (Power series in ball arithmetic).
Guides#
The FLINT team, “_arb_poly_inv_series, arb_poly_inv_series (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_inv_series.html (generated 2026-10-20).
@misc{flint-doc-arb-poly-arb-poly-inv-series,
author = {{The FLINT team}},
title = {{\_arb\_poly\_inv\_series, arb\_poly\_inv\_series (arb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_poly/_arb_poly_inv_series.html},
note = {Generated 2026-10-20}
}