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 is significantly faster than existing software packages for semi-mixed polynomial systems with many distinct supports. The software package DEMiCs is available at \url{ mizutan8/DEMiCs/}.

References in zbMATH (referenced in 16 articles , 1 standard article )

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  1. Anders Jensen, Jeff Sommars, Jan Verschelde: Computing Tropical Prevarieties in Parallel (2017) arXiv
  2. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  3. Chen, Tianran; Mehta, Dhagash: Parallel degree computation for binomial systems (2017)
  4. Malajovich, Gregorio: Computing mixed volume and all mixed cells in quermassintegral time (2017)
  5. Jensen, Anders Nedergaard: An implementation of exact mixed volume computation (2016)
  6. Sommars, Jeff; Verschelde, Jan: Pruning algorithms for pretropisms of Newton polytopes (2016)
  7. Chen, Tianran; Li, Tien-Yien: Homotopy continuation method for solving systems of nonlinear and polynomial equations (2015)
  8. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed volume computation in parallel (2014)
  9. Chen, Tianran; Li, Tien-Yien; Wang, Xiaoshen: Theoretical aspects of mixed volume computation via mixed subdivision (2014)
  10. Herrero, María Isabel; Jeronimo, Gabriela; Sabia, Juan: Elimination for generic sparse polynomial systems (2014)
  11. Herrero, María Isabel; Jeronimo, Gabriela; Sabia, Juan: Computing isolated roots of sparse polynomial systems in affine space (2010)
  12. Lee, Tsung-Lin; Santoprete, Manuele: Central configurations of the five-body problem with equal masses (2009)
  13. Lee, T.L.; Li, T.Y.; Tsai, C.H.: HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method (2008)
  14. Mizutani, Tomohiko; Takeda, Akiko: DEMiCs: a software package for computing the mixed volume via dynamic enumeration of all mixed cells (2008)
  15. Stillman, Michael E. (ed.); Takayama, Nobuki (ed.); Verschelde, Jan (ed.): Software for algebraic geometry. Papers of a workshop, Minneapolis, MN, USA, October 23--27, 2006 (2008)
  16. Mizutani, Tomohiko; Takeda, Akiko; Kojima, Masakazu: Dynamic enumeration of all mixed cells (2007)