FLINT3.7.0-dev
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padic_teichmuller

Synopsis#include <flint/padic.h>
void padic_teichmuller(padic_t rop, const padic_t op, const padic_ctx_t ctx)source

Sets rop to the Teichmüller lift of op, reduced. If op is zero or divisible by pp the result is zero (which satisfies tp=tt^p = t but is not a root of unity). Throws if op has negative valuation.

The lift is the root of tp−tt^p - t congruent to op modulo pp, computed by Newton iteration. Since the derivative at the root is p−1p - 1, the iteration t←t−(tp−t)/(p−1)t \gets t - (t^p - t)/(p - 1), with an inverse of p−1p - 1 lifted alongside, suffices (Hensel lifting of inverses, square roots and Teichmüller lifts).

Cite this page

The FLINT team, “padic_teichmuller (padic.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/padic/padic_teichmuller.html (generated 2026-11-02).