FLINT3.7.0-dev
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padic_poly_inv_series

Synopsis#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)source

Sets gg to the power series inverse of ff modulo xnx^n, n≥1n \ge 1, reduced to the precision of gg. The constant coefficient of ff must have the minimal valuation of all coefficients, that is, the constant coefficient of the stored integer polynomial must be a pp-adic unit; otherwise, and if it is zero, the function throws. If −v≥N-v \ge N the result is zero.

The result has valuation −v-v. Its integer part is computed modulo pN+vp^{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 Z\mathbb{Z} followed by reduction.

Cite this page

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 2026-11-02).