Algorithm 976: Bertini-real: Numerical decomposition of real algebraic curves and surfaces

Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Bertini-real is a compiled command line program for numerically decomposing the real portion of a positivedimensional complex component of an algebraic set. The software uses homotopy continuation to solve a series of systems via regeneration from a witness set to compute a cell decomposition. The implemented decomposition algorithms are similar to the well-known cylindrical algebraic decomposition (CAD) first established by Collins in that they produce a set of connected cells. In contrast to the CAD, Bertini-real produces cells with midpoints connected to boundary points by homotopies, which can easily be numerically tracked. Furthermore, the implemented decomposition for surfaces naturally yields a triangulation. This CAD-like decomposition captures the topological information and permits further computation on the real sets, such as sampling, visualization, and three-dimensional printing.

Original languageEnglish (US)
Article number10
JournalACM Transactions on Mathematical Software
Issue number1
StatePublished - Jul 2017

All Science Journal Classification (ASJC) codes

  • Software
  • Applied Mathematics


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