PHCpack swMATH ID: 705 Software Authors: Verschelde, Jan 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; Macaulay2; HOM4PS; SINGULAR; MixedVol; PHoM; NumericalAlgebraicGeometry; HomotopyContinuation; alphaCertified; SageMath; Maple; Matlab; PHClab; Hom4PS-3; NAG4M2; Gfan; ISOLATE; DEMiCs; Mathematica; Magma Cited in: 253 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 352 Authors 35 Verschelde, Jan 21 Sommese, Andrew John 16 Hauenstein, Jonathan D. 15 Leykin, Anton 15 Wampler, Charles W. II 12 Bates, Daniel J. 11 Li, Tien-Yien 9 Rodriguez, Jose Israel 9 Sottile, Frank 9 Wu, Wenyuan 7 Telen, Simon 6 Helmer, Martin 6 Peterson, Chris 5 Bliss, Nathan 5 Breiding, Paul 5 Chen, Tianran 5 Duff, Timothy 5 Hochstenbach, Michiel E. 5 Lasserre, Jean-Bernard 5 Mehta, Dhagash 5 Niemerg, Matthew E. 5 Reid, Greg J. 5 Yu, Bo 5 Zeng, Zhonggang 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 Sturmfels, Bernd 4 Van Barel, Marc 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 Takayama, Nobuki 3 Tsigaridas, Elias P. 3 Yahl, Thomas 3 Zhang, JinTao 3 Zhang, Xuping 3 Zhao, Ailing 2 Banks, Jeffrey W. 2 Brysiewicz, Taylor 2 Datta, Ruchira S. 2 Davis, Brent R. 2 De Lathauwer, Lieven 2 Dong, Bo 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 Heaton, Alexander 2 Henrion, Didier 2 Henshaw, William D. 2 Hill, Cvetelina 2 Huang, Bo 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 Sagraloff, Michael 2 Scott, Robin 2 Su, Hai-Jun 2 Syam, Muhammed I. 2 Takeda, Akiko 2 Theobald, Thorsten 2 Timme, Sascha 2 Vidunas, Raimundas 2 Walker, Elise 2 Wang, Yu 2 Watson, Layne Terry 2 Xia, Bican 2 Yu, Josephine 2 Yu, Xiangcheng 1 Adamer, Michael F. 1 Aghassi, Michele 1 Alaeddini, Adel 1 Albea, Carolina 1 Alber, David M. ...and 252 more Authors all top 5 Cited in 84 Serials 24 Journal of Symbolic Computation 9 Journal of Computational and Applied Mathematics 9 Foundations of Computational Mathematics 7 Applied Mathematics and Computation 6 Theoretical Computer Science 6 Numerical Algorithms 5 Mathematics of Computation 5 SIAM Journal on Numerical Analysis 5 SIAM Journal on Matrix Analysis and Applications 5 Journal of High Energy Physics 4 ACM Transactions on Mathematical Software 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 Journal of Algebra and its Applications 3 The Journal of Software for Algebra and Geometry 2 Automatica 2 Journal of Pure and Applied Algebra 2 Advances in Applied Mathematics 2 Journal of Global Optimization 2 Mathematical Programming. 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Electronic Transactions on Numerical Analysis 1 Bulletin des Sciences Mathématiques 1 Advances in Computational Mathematics 1 Reliable Computing 1 Taiwanese Journal of Mathematics 1 Qualitative Theory of Dynamical Systems 1 Journal of Systems Science and Complexity 1 The IMA Volumes in Mathematics and its Applications 1 Lecture Notes in Computer Science 1 Advances in High Energy Physics 1 Mathematical Programming Computation 1 Journal of Algebraic Statistics 1 Asian Journal of Control 1 Numerical Algebra, Control and Optimization 1 Arnold Mathematical Journal 1 CBMS Regional Conference Series in Mathematics 1 Foundations of Data Science 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 38 Fields 152 Numerical analysis (65-XX) 92 Algebraic geometry (14-XX) 78 Computer science (68-XX) 61 Commutative algebra (13-XX) 29 Field theory and polynomials (12-XX) 21 Operations research, mathematical programming (90-XX) 18 Functions of a complex variable (30-XX) 16 Real functions (26-XX) 14 Convex and discrete geometry (52-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Mechanics of particles and systems (70-XX) 10 Partial differential equations (35-XX) 10 Biology and other natural sciences (92-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Statistics (62-XX) 8 Systems theory; control (93-XX) 7 Combinatorics (05-XX) 6 Ordinary differential equations (34-XX) 6 Quantum theory (81-XX) 5 Number theory (11-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 General and overarching topics; collections (00-XX) 3 Geometry (51-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year