padic_teichmuller
Synopsis
#include <flint/padic.h>void padic_teichmuller(padic_t rop, const padic_t op, const padic_ctx_t ctx)sourceSets rop to the Teichmüller lift of op, reduced. If op is zero or divisible by p the result is zero (which satisfies t^p = t but is not a root of unity). Throws if op has negative valuation.
The lift is the root of t^p - t congruent to op modulo p, computed by Newton iteration. Since the derivative at the root is p - 1, the iteration t \gets t - (t^p - t)/(p - 1), with an inverse of p - 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 2026-10-20).
@misc{flint-doc-padic-padic-teichmuller,
author = {{The FLINT team}},
title = {{padic\_teichmuller (padic.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/padic/padic_teichmuller.html},
note = {Generated 2026-10-20}
}