acb_theta_reduce_z
Synopsis
#include <flint/acb_theta.h>int acb_theta_reduce_z(acb_ptr new_zs, arb_ptr rs, acb_ptr cs, acb_srcptr zs, slong nb, const acb_mat_t tau, slong prec)sourceReduces the nb vectors in zs with respect to the lattice \mathbb{Z}^g + \tau \mathbb{Z}^g. For each z, Y^{-1} y is rounded to the nearest even integral vector r (stored in rs), and z' = z - \tau r minus the nearest even integral vector to its real part is stored in new_zs; then \theta_{a,b}(z',\tau) = e^{-\pi i r^T (z + z')} \theta_{a,b}(z,\tau) for all characteristics, and the exponential factor is stored in cs. Returns 0 (with undefined outputs) if the rounding fails because of extreme values, and 1 otherwise.
Cite this page
The FLINT team, “acb_theta_reduce_z (acb_theta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_theta/acb_theta_reduce_z.html (generated 2026-10-20).
@misc{flint-doc-acb-theta-acb-theta-reduce-z,
author = {{The FLINT team}},
title = {{acb\_theta\_reduce\_z (acb\_theta.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_theta/acb_theta_reduce_z.html},
note = {Generated 2026-10-20}
}