FLINT3.7.0-dev
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_arb_poly_taylor_shift, arb_poly_taylor_shift

Synopsis#include <flint/arb_poly.h>
void _arb_poly_taylor_shift(arb_ptr g, const arb_t c, slong n, slong prec)source
void arb_poly_taylor_shift(arb_poly_t g, const arb_poly_t f, const arb_t c, slong prec)source

Set g to the Taylor shift f(x+c)f(x + c). The underscore version works in place on {g, n}. Wrappers of _gr_poly_taylor_shift.

Over the real ball context the generic function dispatches to _gr_arb_poly_taylor_shift, which uses Horner's scheme (_gr_poly_taylor_shift_horner) if n≤30n \le 30, if n≤100n \le 100 and cc has fewer than prec/100\mathit{prec}/100 bits, or if n≤500n \le 500, cc has a one-bit midpoint and n<30+3precn < 30 + 3\sqrt{\mathit{prec}}; otherwise the convolution algorithm (_gr_poly_taylor_shift_convolution, one polynomial product) if prec>2n\mathit{prec} > 2n, and the divide-and-conquer algorithm (_gr_poly_taylor_shift_divconquer) if not.

Cite this page

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