Homotopy Continuation in Macaulay2

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


We describe the design and relationships of several Macaulay2 packages that use numerical polynomial homotopy continuation as their engine. Macaulay2 is a computer algebra system built around the classical symbolic computation tools such as Gröbner bases. However, recent Macaulay2 versions include its own fast implementation of homotopy continuation, interfaces to external numerical algebraic geometry software (Bertini and PHCpack), and a unified data structures design that allows the use of the internal and external capabilities interchangeably. The resulting numerical and hybrid tools are of general interest to Macaulay2 users interested in computational experimentation.


Polynomial homotopy continuation Numerical algebraic geometry Macaulay2 



Research of AL is supported in part by DMS-1719968 award from NSF.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Georgia Institute of TechnologyAtlantaUSA

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