As a compututational mathematician, actively developing software, maintaining central locations for downloads (or up-to-date links), and appropriate communications for questions, installation, and use are important.

I am the co-author of several actively maintained software packages and a developer of Bertini.


paramotopy is a parallel implementation of the so-called coefficient-PARAmeter hoMOTOPY. Often, scientists are interested in solving a polynomial system with the same monomial structure but at many different parameter points of interest.

Over a set of measure 0 in the space of coefficients, the number of complex solutions is constant. We do a costly initial solve at a generic point in our parameter space and use the solutions at this generic point as our new start system. We then 'paramotope' (i.e., perform a coefficient-parameter homotopy) into all the particular systems of interest. Each system can done independently which allows us to highly parallelize this process.

paramotopy is actively developed by Daniel J. Bates, Daniel A. Brake, and Matthew Niemerg.

Download Paramotopy 1.0.1.

galeDuality for Fewnomial Systems

galeDuality for Fewnomial systems is software for studying polynomial systems with `few' mo'nomials'. A scheme-theoretic isomorphism exists between the positive solutions of any polynomial system and the solutions in the interior of the positive chamber of the Gale Dual of the system. Currently, galeDuality will compute the symbolic transformation of a fewnomial system to its corresponding Gale System. By way of the Khovanskii-Rolle Theorem, a completely real-tracking algorithm exists to find only the real solutions.

When the number of monomials exceeds the number of variables by precisely 2, a proof of concept of this real-tracking is implementated in Maple. The goal is to extend this to when excess of the number of monomomials compared to the variables is arbitrary and to design new algorithms as problems are encountered during the development.

galeDuality is currently in alpha and available for download.

galeDuality is actively developed by Daniel J. Bates, Jonathan D. Hauenstein, Matthew Niemerg, and Frank Sottile.


BertiniLab is a MATLAB interface of Bertini.

BertiniLab is actively developed by Daniel J. Bates, Andrew Newell, and Matthew Niemerg.

Download BertiniLab 1.5.

Other Software

Here are links to some other mathematical software packages that you may (or may not!) find useful: