acb_dirichlet_roots_init, acb_dirichlet_roots_clear
Synopsis
#include <flint/acb_dirichlet.h>void acb_dirichlet_roots_init(acb_dirichlet_roots_t t, ulong order, slong num, slong prec)sourcevoid acb_dirichlet_roots_clear(acb_dirichlet_roots_t t)sourceInitialise t for the roots of unity of order n = order, optimised for num evaluations at precision prec, and free it.
For very small num, only e^{2\pi i/n} is precomputed and then raised to powers; for small prec and large n even this may be skipped if evaluating each root from scratch is estimated to be faster. For large num, all roots in the first quadrant are precomputed, unless this would use too much memory, and for intermediate num a baby-step giant-step table is built.
Cite this page
The FLINT team, “acb_dirichlet_roots_init, acb_dirichlet_roots_clear (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_roots_init.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-roots-init,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_roots\_init, acb\_dirichlet\_roots\_clear (acb\_dirichlet.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_roots_init.html},
note = {Generated 2026-10-20}
}