Computing Theta Functions with Julia
Mathematical Software
2021-04-21 v2 Algebraic Geometry
Complex Variables
Abstract
We present a new package Theta.jl for computing with the Riemann theta function. It is implemented in Julia and offers accurate numerical evaluation of theta functions with characteristics and their derivatives of arbitrary order. Our package is optimized for multiple evaluations of theta functions for the same Riemann matrix, in small dimensions. As an application, we report on experimental approaches to the Schottky problem in genus five.
Cite
@article{arxiv.1906.06507,
title = {Computing Theta Functions with Julia},
author = {Daniele Agostini and Lynn Chua},
journal= {arXiv preprint arXiv:1906.06507},
year = {2021}
}
Comments
v2: to appear in the Journal of Software for Algebra and Geometry. Content reorganized according to the published version