sp2gz_nb_fundamental, sp2gz_fundamental
#include <flint/acb_theta.h>void sp2gz_fundamental(fmpz_mat_t mat, slong j)sourcesp2gz_nb_fundamental returns the number of fundamental symplectic matrices used in the reduction algorithm, and sp2gz_fundamental sets mat to the j-th of them. For g = 1 there is one (J) and for g = 2 there are 19, which define the boundary of Gottschling's fundamental domain [Got1959]. For g > 2 no such complete set is known; the module uses the 19 g(g-1)/2 matrices obtained by applying the g = 2 matrices to any pair of coordinates and the 2^g embeddings of a lower-dimensional J on any subset of coordinates.
References#
- [Got1959] E. Gottschling, "Explizite Bestimmung der Randflächen es Fundamentalbereiches der Modulgruppe zweiten Grades'', Math. Annalen 138 (1959), 103–124. https://doi.org/10.1007/BF01342938
The FLINT team, “sp2gz_nb_fundamental, sp2gz_fundamental (acb_theta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_theta/sp2gz_nb_fundamental.html (generated 2026-10-20).
@misc{flint-doc-acb-theta-sp2gz-nb-fundamental,
author = {{The FLINT team}},
title = {{sp2gz\_nb\_fundamental, sp2gz\_fundamental (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/sp2gz_nb_fundamental.html},
note = {Generated 2026-10-20}
}