### Abstract

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 language | English (US) |
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Article number | 10 |

Journal | ACM Transactions on Mathematical Software |

Volume | 44 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2017 |

### All Science Journal Classification (ASJC) codes

- Software
- Applied Mathematics

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## Cite this

*ACM Transactions on Mathematical Software*,

*44*(1), [10]. https://doi.org/10.1145/3056528