acb_theta_ql_exact
#include <flint/acb_theta.h>void acb_theta_ql_exact(acb_ptr th, acb_srcptr zs, slong nb, const acb_mat_t tau, const slong * pattern, int all, int shifted_prec, slong prec)sourceRuns the quasi-linear algorithm for the nb exact, reduced pairs (z, \tau), with the duplication and dimension-lowering pattern pattern, and sets th to the normalised values \widetilde{\theta}_{a,b}(z,\tau) for all characteristics (all nonzero) or \widetilde{\theta}_{a,0}(z,\tau). With shifted_prec nonzero, the precision of each value takes the distances into account, as in acb_theta_sum. Inexact input gives correct but possibly useless results.
With no duplication steps, acb_theta_sum is called. Otherwise acb_theta_ql_setup prepares the steps; the theta values at 2^m \tau are computed by summation, or with acb_theta_ql_lower_dim, a recursive call in dimension s on a longer list of vectors, and acb_theta_ql_recombine; and the duplication formulas with square roots are applied m times.
Guides#
The FLINT team, “acb_theta_ql_exact (acb_theta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_theta/acb_theta_ql_exact.html (generated 2026-10-20).
@misc{flint-doc-acb-theta-acb-theta-ql-exact,
author = {{The FLINT team}},
title = {{acb\_theta\_ql\_exact (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_ql_exact.html},
note = {Generated 2026-10-20}
}