MixedVol swMATH ID: 581 Software Authors: Gao, Tangan; Li, T. Y.; Wu, Mengnien Description: Algorithm 846: MixedVol: a software package for mixed-volume computation. MixedVol is a C++ software package that computes the mixed volume of n finite subsets of ℤn or the support of a system of n polynomials in n variables. The software produces the mixed volume as well as the mixed cells. The mixed cells are crucial for solving polynomial systems by the polyhedral homotopy continuation method. The software leads existing codes for mixed-volume computation in speed by a substantial margin and its memory requirement is very low. Homepage: http://dl.acm.org/citation.cfm?id=1114274 Related Software: PHCpack; DEMiCs; HOM4PS; PHoM; Bertini; Gfan; Hom4PS-3; STRINGVACUA; Macaulay2; CoCoA; SINGULAR; alphaCertified; Magma; CUDA; VortexCalculations; PoSSo; Binomials.m2; Stony Brook; SageMath; Mathematica Cited in: 29 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Mixed volume computation in solving polynomial systems. Zbl 1416.65145Lee, Tsung-Lin; Li, Tien-Yien 2011 Algorithm 846: MixedVol: a software package for mixed-volume computation. Zbl 1136.65320Gao, Tangan; Li, T. Y.; Wu, Mengnien 2005 all top 5 Cited by 38 Authors 7 Chen, Tianran 7 Li, Tien-Yien 6 Mehta, Dhagash 5 Lee, Tsung-Lin 4 Verschelde, Jan 3 He, Yang-Hui Evariste 2 Hauenstein, Jonathan D. 2 Rummel, Markus 2 Sommars, Jeff 1 Adrovic, Danko 1 AlAdwani, Mohammad 1 Bliss, Nathan 1 Dong, Bo 1 Gao, Tangan 1 Gurvits, Leonid 1 Helmke, Uwe R. 1 Horigome, Noriyuki 1 Jensen, Anders Nedergaard 1 Jiao, Libin 1 Lageman, Christian 1 Malajovich, Gregorio 1 Martínez-Pedrera, Danny 1 McCarthy, J. Michael 1 Mikawa, Masahiko 1 Niemerg, Matthew E. 1 Saavedra, Serguei 1 Santoprete, Manuele 1 Sosonkina, Masha 1 Su, Hai-Jun 1 Terui, Akira 1 Valeanu, Alexandru 1 Wang, Xiaoshen 1 Watson, Layne Terry 1 Westphal, Alexander 1 Wu, Mengnien 1 Yu, Bo 1 Yu, Xiangcheng 1 Zeng, Zhonggang all top 5 Cited in 13 Serials 4 Journal of High Energy Physics 2 ACM Transactions on Mathematical Software 2 Journal of Symbolic Computation 2 Discrete & Computational Geometry 2 Communications in Information and Systems 1 Mathematical Biosciences 1 Computing 1 MCSS. Mathematics of Control, Signals, and Systems 1 Celestial Mechanics and Dynamical Astronomy 1 Taiwanese Journal of Mathematics 1 Foundations of Computational Mathematics 1 Journal of Systems Science and Complexity 1 Advances in High Energy Physics all top 5 Cited in 17 Fields 15 Numerical analysis (65-XX) 11 Computer science (68-XX) 9 Commutative algebra (13-XX) 7 Algebraic geometry (14-XX) 7 Convex and discrete geometry (52-XX) 4 Quantum theory (81-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year