HOM4PS swMATH ID: 410 Software Authors: Lee, T.L.; Li, T.Y.; Tsai, C.H. Description: HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method. HOM4PS-2.0 is a software package in FORTRAN 90 which implements the polyhedral homotopy continuation method for solving polynomial systems. It updates its original version HOM4PS in three key aspects: (1) a new method for finding mixed cells; (2) combining the polyhedral and linear homotopies in one step; (3) a new way of dealing with curve jumping. Numerical results show that this revision leads to a spectacular speed-up, ranging up to 1950s, over its original version on all benchmark systems, especially for large ones. It surpasses the existing packages in finding isolated zeros, such as PHCpack [J. Verschelde, ACM Trans. Math. Softw. 25, No. 2, 251–276 (1999; Zbl 0961.65047)] PHoM [T. Gunji et al., Computing 73, No. 1, 57–77 (2004; Zbl 1061.65041)] and Bertini [D. J. Bates et al., in: Stillman, Michael E. (ed.) et al., Software for algebraic geometry. Papers of a workshop, Minneapolis, MN, USA, October 23–27, 2006. New York, NY: Springer. The IMA Volumes in Mathematics and its Applications 148, 1–14 (2008; Zbl 1143.65344), available at http://www.nd.edu/ sommese/bertini], in speed by big margins. Homepage: http://www.math.nsysu.edu.tw/~leetsung/works/HOM4PS_soft.htm Related Software: PHCpack; Bertini; alphaCertified; PHoM; Macaulay2; MixedVol; NumericalAlgebraicGeometry; SINGULAR; NAG4M2; DEMiCs; Hom4PS-3; HomotopyContinuation; HOMPACK90; PoSSo; STRINGVACUA; CoCoA; Paramotopy; Matlab; ISOLATE; Gfan Cited in: 82 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method. Zbl 1167.65366Lee, T. L.; Li, T. Y.; Tsai, C. H. 2008 all top 5 Cited by 127 Authors 8 Hauenstein, Jonathan D. 7 Bates, Daniel J. 7 Chen, Tianran 6 Lee, Tsung-Lin 6 Li, Tien-Yien 6 Wu, Wenyuan 5 Mehta, Dhagash 5 Sommese, Andrew John 4 Leykin, Anton 4 Luo, Zhongxuan 4 Niemerg, Matthew E. 4 Wampler, Charles W. II 4 Yu, Bo 3 Beltrán, Carlos 3 Chen, Changbo 3 Dayar, Tugrul 3 Di Rocco, Sandra 3 Eklund, David 3 Feng, Erbao 3 Feng, Yong 3 He, Yang-Hui Evariste 3 Imbach, Rémi 3 Peterson, Chris 3 Sottile, Frank 2 Breiding, Paul 2 Dong, Bo 2 Gross, Elizabeth 2 Hill, Cvetelina 2 Hu, Wenyu 2 Newell, Andrew J. 2 Pouget, Marc 2 Santoprete, Manuele 2 Staub, Florian 2 Su, Hai-Jun 2 Tari, Hafez 2 Verschelde, Jan 2 Zhang, JinTao 2 Zhang, Xuping 1 Adrovic, Danko 1 Alaeddini, Adel 1 Awange, Joseph L. 1 Besana, Gian Mario 1 Bozóki, Sándor 1 Camargo-Molina, José Eliel 1 Castañeda-Sheissa, Roberto 1 Chen, Jingwei 1 Chen, Liping 1 Chrysikos, Ioannis 1 Davis, Brent R. 1 Decker, Wolfram 1 Duff, Timothy 1 Filobello-Nino, Uriel A. 1 Frohmader, Andrew 1 Führ, Hartmut 1 Han, Lixing 1 Hao, Wenrui 1 Heaton, Alexander 1 Hermanns, Holger 1 Huang, Lihua 1 Jensen, Anders Nedergaard 1 Jiao, Libin 1 Jimenez-Fernandez, Victor Manuel 1 Khan, Yasir 1 Kim, Sunyoung 1 Kojima, Masakazu 1 Lee, Kisun 1 Li, Zhe 1 Liddell, Alan C. jun. 1 Lin, Song-Sun 1 Lin, Wen-Wei 1 Luo, Xinlong 1 Lv, Jiahui 1 Mahmoud, Abdrhaman 1 Marigliano, Orlando 1 Marin-Hernandez, A. 1 Mathis, Pascal 1 Mevissen, Martin 1 Morais, António P. 1 Moroz, Guillaume 1 Oeding, Luke 1 Orhan, M. 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