We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
This paper is gives a short introduction into HomotopyContinuation.jl, a polynomial equations solver for Julia [1]. It present excerpts from the comprehensive documentation available at juliahomotopycontinuation.github.io/latest/.
The aim of this project is twofold: establishing a fast numerical polynomial solver in Julia and at the same time providing a highly customizable algorithmic environment for researchers for designing and performing individual experiments.
[1] J. Bezanson, A. Edelman, S. Karpinski and V. Shah: Julia: A fresh approach to numerical computing, SIAM Review, 59(1) (2017), 65-98.