PHCpack
PHCpack is a software package to solve polynomial systems by homotopy continuation methods.
A polynomial system is given as a sequence of polynomials in several variables. Homotopy continuation methods operate in two stages. In the first stage, a family of polynomial systems (the so-called homotopy) is constructed. This homotopy contains a polynomial system with known solutions. In the second stage, numerical continuation methods are applied to track the solution paths defined by the homotopy, starting at the known solutions and leading to the solutions of the given polynomial system.
Version 1.0 of PHCpack has been archived by ACM Transactions of Mathematical Software (ACM TOMS) as Algorithm 795. PHCpack incorporates MixedVol (Algorithm 846 of ACM TOMS by T. Gao, T.Y. Li, and M. Wu) to compute mixed volumes fast. DEMiCs (Dynamic Enumeration of all Mixed Cells, by T. Mizutani, A. Takeda, and M. Kojima), computes mixed volumes at a faster pace than MixedVol for larger systems with many different supports. DEMiCs is also integrated into PHCpack. For its double double and quad double arithmetic, PHCpack contains QDlib of Y. Hida, X.S. Li, and D.H. Bailey. For triple double, and other multiple doubles (penta, octo, deca), code generated from the CAMPARY software is used. CAMPARY is the CudA Multiple Precision ARithmetic librarY, by Mioara Joldes, Olivier Marty, Jean-Michel Muller, Valentina Popescu and Warwick Tucker.
This material is based upon work supported by the National Science Foundation under Grants No. 9804846, 0105739, 0134611, 0410036, 0713018, 1115777, 1440534, and 1854513. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Executable versions of the code for Linux, MacOS X, and Windows are available at http://www.math.uic.edu/~jan/download.html. Other links:
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The documentation of PHCpack in html format is at http://www.math.uic.edu/~jan/phcpack_doc_html and its pdf version is at http://www.math.uic.edu/~jan/PHCpack.pdf.
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The documentation of phcpy in html format is at http://www.math.uic.edu/~jan/phcpy_doc_html and its pdf version is at http://www.math.uic.edu/~jan/phcpydoc.pdf.
The restructured text source for the documentation for PHCpack starts at https://github.com/janverschelde/PHCpack/tree/master/src/doc/source and for phcpy at https://github.com/janverschelde/PHCpack/tree/master/src/Python/PHCpy3/doc/source.
To try phcpy in a python or SageMath kernel of a jupyter notebook, visit http://www.phcpack.org.