PHCpack swMATH ID: 705 Software Authors: Jan Verschelde Description: Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. Polynomial systems occur in a wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade considerable progress has been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this paper the structure and design of the software package PHC is described. The main program operates in several modes, is menu-driven and file-oriented. This package features a great variety of root-counting methods among its tools. The outline of one black-box solver is sketched and a report is given on its performance on a large database of test problems. The software has been developed on four different machine architectures. Its portability is ensured by the gnu-ada compiler. Homepage: http://homepages.math.uic.edu/~jan/PHCpack/phcpack.html Source Code: https://github.com/janverschelde/PHCpack Programming Languages: Ada 95 Operating Systems: Linux, Mac OS X, SunOS, AIX, Windows Dependencies: PHC Related Software: Bertini; HOM4PS; Macaulay2; SINGULAR; PHoM; MixedVol; alphaCertified; NumericalAlgebraicGeometry; HomotopyContinuation; Matlab; PHClab; Maple; SageMath; Gfan; NAG4M2; Mathematica; DEMiCs; SeDuMi; Hom4PS-3; ISOLATE Cited in: 239 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. Zbl 0961.65047Verschelde, Jan 1999 all top 5 Cited by 333 Authors 35 Verschelde, Jan 21 Sommese, Andrew John 15 Hauenstein, Jonathan D. 15 Wampler, Charles W. II 14 Leykin, Anton 12 Bates, Daniel J. 11 Li, Tien-Yien 9 Sottile, Frank 9 Wu, Wenyuan 6 Lasserre, Jean-Bernard 6 Peterson, Chris 6 Rodriguez, Jose Israel 6 Telen, Simon 5 Bliss, Nathan 5 Chen, Tianran 5 Helmer, Martin 5 Hochstenbach, Michiel E. 5 Mehta, Dhagash 5 Niemerg, Matthew E. 5 Reid, Greg J. 5 Zeng, Zhonggang 4 Breiding, Paul 4 Emiris, Ioannis Z. 4 Gross, Elizabeth 4 He, Yang-Hui Evariste 4 Kojima, Masakazu 4 Lee, Tsung-Lin 4 Plestenjak, Bor 4 Sommars, Jeff 4 Van Barel, Marc 4 Yu, Bo 3 Adrovic, Danko 3 Bartzos, Evangelos 3 Batselier, Kim 3 Beltrán, Carlos E. 3 Bozorgmanesh, Hassan 3 De Moor, Bart L. R. 3 Di Rocco, Sandra 3 Dreesen, Philippe 3 Eklund, David 3 Gao, Tangan 3 Hajarian, Masoud 3 Laurent, Monique 3 Mourrain, Bernard 3 Rostalski, Philipp 3 Sturmfels, Bernd 3 Takayama, Nobuki 3 Zhao, Ailing 2 Banks, Jeffrey W. 2 Brysiewicz, Taylor 2 Datta, Ruchira S. 2 Davis, Brent R. 2 Dong, Bo 2 Duff, Timothy 2 Feng, Erbao 2 Fujisawa, Katsuki 2 Gallardo-Alvarado, Jaime 2 Georg, Kurt 2 Granvilliers, Laurent 2 Guan, Yun 2 Hampton, Marshall 2 Hao, Wenrui 2 Henrion, Didier 2 Henshaw, William D. 2 Hill, Cvetelina 2 Jensen, Anders Nedergaard 2 Kim, Sunyoung 2 Lee, Kisun 2 Luo, Zhongxuan 2 McCarthy, J. Michael 2 Moreno Maza, Marc 2 Newell, Andrew J. 2 Petrović, Sonja 2 Rummel, Markus 2 Scott, Robin 2 Su, Hai-Jun 2 Syam, Muhammed I. 2 Takeda, Akiko 2 Theobald, Thorsten 2 Timme, Sascha 2 Tsigaridas, Elias P. 2 Vidunas, Raimundas 2 Wang, Yu 2 Watson, Layne Terry 2 Xia, Bican 2 Yahl, Thomas 2 Yu, Josephine 2 Yu, Xiangcheng 2 Zhang, JinTao 2 Zhang, Xuping 1 Adamer, Michael F. 1 Aghassi, Michele 1 Alaeddini, Adel 1 Albea, Carolina 1 Alber, David M. 1 Améndola, Carlos 1 Amisano, Gianni 1 Angel, Jordan B. 1 Antonacci, Fabio 1 Arzelier, Denis ...and 233 more Authors all top 5 Cited in 79 Serials 22 Journal of Symbolic Computation 9 Journal of Computational and Applied Mathematics 8 Foundations of Computational Mathematics 7 Applied Mathematics and Computation 6 Theoretical Computer Science 5 Mathematics of Computation 5 SIAM Journal on Numerical Analysis 5 Numerical Algorithms 5 Journal of High Energy Physics 4 ACM Transactions on Mathematical Software 4 SIAM Journal on Matrix Analysis and Applications 4 Journal of Scientific Computing 4 Linear Algebra and its Applications 4 Experimental Mathematics 4 SIAM Journal on Scientific Computing 4 Mechanism and Machine Theory 4 ACM Communications in Computer Algebra 3 Computers & Mathematics with Applications 3 Journal of Computational Physics 3 Bulletin of Mathematical Biology 3 Computing 3 Journal of Complexity 3 Discrete & Computational Geometry 3 The Journal of Software for Algebra and Geometry 2 Journal of Pure and Applied Algebra 2 Advances in Applied Mathematics 2 Journal of Global Optimization 2 Mathematical Programming. 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Series B 2 International Journal of Computer Vision 2 Mathematical Problems in Engineering 2 Advances in Geometry 2 Communications in Information and Systems 2 Journal of Algebra and its Applications 2 Mathematics in Computer Science 2 SIAM Journal on Applied Algebra and Geometry 1 Computer Physics Communications 1 IMA Journal of Numerical Analysis 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Beiträge zur Algebra und Geometrie 1 Automatica 1 Compositio Mathematica 1 Journal of Economic Theory 1 Journal of the Operations Research Society of Japan 1 Journal of Optimization Theory and Applications 1 Meccanica 1 SIAM Journal on Computing 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Journal of Economic Dynamics & Control 1 Applied Mathematics Letters 1 International Journal of Mathematics 1 International Journal of Computational Geometry & Applications 1 Computational Geometry 1 Differential Geometry and its Applications 1 Pattern Recognition 1 Celestial Mechanics and Dynamical Astronomy 1 Applicable Algebra in Engineering, Communication and Computing 1 SIAM Journal on Optimization 1 Applied Mathematics. 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