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; PHClab; Matlab; SageMath; NumericalAlgebraicGeometry; Maple; Gfan; NAG4M2; DEMiCs; ISOLATE; Mathematica; HomotopyContinuation; Hom4PS-3; Magma
Cited in: 229 Publications
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Cited by 317 Authors

34 Verschelde, Jan
21 Sommese, Andrew John
15 Hauenstein, Jonathan D.
15 Wampler, Charles W. II
14 Leykin, Anton
12 Bates, Daniel J.
9 Li, Tien-Yien
8 Wu, Wenyuan
7 Sottile, Frank
6 Lasserre, Jean-Bernard
6 Peterson, Chris
6 Rodriguez, Jose Israel
5 Bliss, Nathan
5 Chen, Tianran
5 Helmer, Martin
5 Hochstenbach, Michiel E.
5 Mehta, Dhagash
5 Reid, Greg J.
5 Telen, Simon
5 Zeng, Zhonggang
4 Emiris, Ioannis Z.
4 Gross, Elizabeth
4 He, Yang-Hui Evariste
4 Kojima, Masakazu
4 Lee, Tsung-Lin
4 Niemerg, Matthew E.
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
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 Breiding, Paul
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 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 Watson, Layne Terry
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
1 Åström, Kalle
1 Awange, Joseph L.
1 Baharev, Ali
...and 217 more Authors
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Cited in 78 Serials

22 Journal of Symbolic Computation
9 Journal of Computational and Applied Mathematics
7 Applied Mathematics and Computation
7 Foundations of Computational Mathematics
6 Theoretical Computer Science
5 SIAM Journal on Numerical Analysis
5 Numerical Algorithms
4 Mathematics of Computation
4 ACM Transactions on Mathematical Software
4 SIAM Journal on Matrix Analysis and Applications
4 Linear Algebra and its Applications
4 Experimental Mathematics
4 SIAM Journal on Scientific Computing
4 Mechanism and Machine Theory
4 Journal of High Energy Physics
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 Scientific Computing
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. Series A. 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
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. Series B (English Edition)
1 Numerical Linear Algebra with Applications
1 Economic Theory
1 ETNA. Electronic Transactions on Numerical Analysis
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 Asian Journal of Control
1 CBMS Regional Conference Series in Mathematics
1 SIAM Journal on Applied Algebra and Geometry
1 Foundations of Data Science
1 SIAM Journal on Mathematics of Data Science

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