FLINT3.7.0-dev
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padic_radix_pow_ui, padic_radix_pow_si, padic_radix_pow_fmpz

Synopsis#include <flint/padic_radix.h>
int padic_radix_pow_ui(padic_radix_t res, const padic_radix_t x, ulong n, gr_ctx_t ctx)source
int padic_radix_pow_si(padic_radix_t res, const padic_radix_t x, slong n, gr_ctx_t ctx)source
int padic_radix_pow_fmpz(padic_radix_t res, const padic_radix_t x, const fmpz_t n, gr_ctx_t ctx)source

Set res to xnx^n, computing the power of the unit with truncated multiplications and rounding once. For x=upv+O(pN)x = u p^v + O(p^N) and n≥1n \ge 1 the error term is O(p(n−1)v+N+vp(n))O(p^{(n - 1)v + N + v_p(n)}), which is valid since every term (nk)an−khk\binom{n}{k} a^{n - k} h^k, k≥1k \ge 1, of (a+h)n−an(a + h)^n - a^n has valuation at least (n−1)v+N+vp(n)(n - 1)v + N + v_p(n); for an inexact zero O(pN)O(p^N) it is O(pnN)O(p^{nN}). Negative exponents invert first. An exact input keeps an exact result when it fits the context precision.

Cite this page

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