Bertini_real

silviana amethyst
2025

Bertini_real is a numerical decomposer for algebraic surfaces and curves. From polynomials in a text input file, the program ultimately will provide you with a STL file you can supply to a thickening program and 3D print. It is written in C++, using Bertini, MPICH, and Boost. Its interface is through the command line, and a Matlab suite is provided for processing the plain text output into something useable by a human.

The project homepage is at bertinireal.com, and you can find sourcecode at github.com

We have three papers on the topic – two extended abstracts summarizing the theoretical advancements (one on the implementation, and another on the decomposition of surfaces including singular curves, and one submitted paper on the software itself.

My coauthors for the project are Dan Bates, Wenrui Hao, Jon Hauenstein, Andrew Sommese, and Charles Wampler. I later worked with a bunch of students on the project, both at Notre Dame and then at UWEC.

My 3d printed surfaces in my galleries have almost all been generated from Bertini_real.