padic_poly_inv_series
#include <flint/padic_poly.h>void padic_poly_inv_series(padic_poly_t g, const padic_poly_t f, slong n, const padic_ctx_t ctx)sourceSets g to the power series inverse of f modulo x^n, n \ge 1, reduced to the precision of g. The constant coefficient of f must have the minimal valuation of all coefficients, that is, the constant coefficient of the stored integer polynomial must be a p-adic unit; otherwise, and if it is zero, the function throws. If -v \ge N the result is zero.
The result has valuation -v. Its integer part is computed modulo p^{N + v} by Newton iteration (Newton iteration for power series and division), starting from the inverse of the constant coefficient computed by _padic_inv and using middle products over \mathbb{Z} followed by reduction.
The FLINT team, “padic_poly_inv_series (padic_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/padic_poly/padic_poly_inv_series.html (generated 2026-10-20).
@misc{flint-doc-padic-poly-padic-poly-inv-series,
author = {{The FLINT team}},
title = {{padic\_poly\_inv\_series (padic\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/padic_poly/padic_poly_inv_series.html},
note = {Generated 2026-10-20}
}