Abstract
DEMiCs is a software package written in C++ for computing the mixed volume of the Newton polytopes of a general semi-mixed polynomial system through dynamic enumeration of all mixed cells. The underlying mixed cells play an essential role for computing all isolated zeros of a polynomial system by polyhedral homotopy continuation method. A notable feature of DEMiCs is in the construction of a dynamic enumeration tree for finding all mixed cells. The dynamic enumeration method, proposed by Mizutani, Takeda and Kojima for fully mixed polynomial systems, is extended to semi-mixed systems and incorporated in the package. Numerical results show that DEMiCs significantly is faster than existing software packages for semi-mixed polynomial systems with many distinct supports. The software package DEMiCs is available at http://www.is.titech.ac.jp/~mizutan8/DEMiCs/.
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Mizutani, T., Takeda, A. (2008). DEMiCs: A Software Package for Computing the Mixed Volume Via Dynamic Enumeration of all Mixed Cells. In: Stillman, M., Verschelde, J., Takayama, N. (eds) Software for Algebraic Geometry. The IMA Volumes in Mathematics and its Applications, vol 148. Springer, New York, NY. https://doi.org/10.1007/978-0-387-78133-4_5
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DOI: https://doi.org/10.1007/978-0-387-78133-4_5
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