HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)


We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software on an illustrative example. We motivate our choice of Julia and how its features allow us to improve upon existing software packages with respect to usability, modularity and performance. Furthermore, we compare the performance of HomotopyContinuation.jl to the existing packages Bertini and PHCpack.


Numerical algebraic geometry Solving polynomial equations Homotopy continuation Julia 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Technische Universität BerlinBerlinGermany

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