FLINT3.7.0-dev
/

_padic_log, _padic_log_rectangular, _padic_log_satoh, _padic_log_balanced

Synopsis#include <flint/padic.h>
void _padic_log(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)source
void _padic_log_rectangular(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)source
void _padic_log_satoh(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)source
void _padic_log_balanced(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N)source

Set z to

\log(1 - y) = -\sum_{i = 1}^{\infty} \frac{y^i}{i} \bmod p^N

for an integer y \ne 0 with v = \operatorname{ord}_p(y) and 1 \le v < N; the logarithm of x is obtained with y = 1 - x. Do not allow aliasing between y and z. _padic_log uses the rectangular version for N < 512 / b, where b is the bit length of p, and the balanced version otherwise. The balanced version does not use v.

Cite this page

The FLINT team, “_padic_log, _padic_log_rectangular, _padic_log_satoh, _padic_log_balanced (padic.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/padic/_padic_log.html (generated 2026-10-20).