DEMiCs: A Software Package for Computing the Mixed Volume Via Dynamic Enumeration of all Mixed Cells

  • Tomohiko Mizutani
  • Akiko Takeda
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 148)


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

Key words

mixed volume mixed cell polyhedral homotopy polynomial system semi-mixed structure dynamic enumeration 


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Copyright information

© Springer Science + Business Media, LLC 2008

Authors and Affiliations

  • Tomohiko Mizutani
    • 1
  • Akiko Takeda
    • 1
  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan

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