  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.
