_acb_poly_taylor_shift, acb_poly_taylor_shift
#include <flint/acb_poly.h>void acb_poly_taylor_shift(acb_poly_t g, const acb_poly_t f, const acb_t c, slong prec)sourceSet g to the Taylor shift f(x + c). The underscore version works in place on {g, n}. Wrappers of _gr_poly_taylor_shift.
Over the complex ball context the generic function dispatches to _gr_acb_poly_taylor_shift, which uses Horner's scheme (_gr_poly_taylor_shift_horner) if n \le 30, if n \le 100 and c has fewer than \mathit{prec}/100 bits, or if n \le 500, c has a one-bit midpoint and n < 30 + 3\sqrt{\mathit{prec}}; otherwise the convolution algorithm (_gr_poly_taylor_shift_convolution, one polynomial product) if \mathit{prec} > 2n, and the divide-and-conquer algorithm (_gr_poly_taylor_shift_divconquer) if not.
The FLINT team, “_acb_poly_taylor_shift, acb_poly_taylor_shift (acb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_poly/_acb_poly_taylor_shift.html (generated 2026-10-20).
@misc{flint-doc-acb-poly-acb-poly-taylor-shift,
author = {{The FLINT team}},
title = {{\_acb\_poly\_taylor\_shift, acb\_poly\_taylor\_shift (acb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_poly/_acb_poly_taylor_shift.html},
note = {Generated 2026-10-20}
}