FLINT3.7.0-dev
/

_arb_poly_pow_arb_series, arb_poly_pow_arb_series

Synopsis#include <flint/arb_poly.h>
void _arb_poly_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec)source
void arb_poly_pow_arb_series(arb_poly_t h, const arb_poly_t f, const arb_t g, slong len, slong prec)source

Set h to fg=exp⁡(glog⁡f)f^g = \exp(g \log f) for a constant exponent gg, truncated to length len. The underscore version requires positive lengths with flen≤len\mathit{flen} \le \mathit{len} and no aliasing.

Special cases: if gg is an exact integer with ∣g∣<263|g| < 2^{63}, binary exponentiation is used (followed by an inversion if g<0g < 0); if f=a+bxdf = a + bx^d is a binomial, the coefficients come from the binomial series (_arb_poly_binomial_pow_arb_series); if g=±1/2g = \pm 1/2 exactly, _arb_poly_sqrt_series or _arb_poly_rsqrt_series is used; otherwise exp⁡(glog⁡f)\exp(g \log f).

Cite this page

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