FLINT3.7.0-dev
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_arb_poly_inv_series, arb_poly_inv_series

Synopsis#include <flint/arb_poly.h>
void _arb_poly_inv_series(arb_ptr Q, arb_srcptr A, slong Alen, slong len, slong prec)source
void arb_poly_inv_series(arb_poly_t Q, const arb_poly_t A, slong n, slong prec)source

Set Q to the power series inverse 1/A1/A truncated to length n (len). The result is finite only if the constant term of AA excludes zero; it is indeterminate if AA is zero. The underscore version requires positive lengths and no aliasing.

The first coefficients are computed by the recurrence qi=−q0∑j=1iajqi−jq_i = -q_0 \sum_{j=1}^{i} a_j q_{i-j} with arb_dot (all of them if n≤8n \le 8 or AA has length 2, otherwise the first 4), and the rest by the Newton iteration Q←Q−Q(AQ−1)Q \leftarrow Q - Q(AQ - 1), which doubles the length at each step and computes only the unknown part of AQ−1AQ - 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#

Cite this page

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 2026-11-02).