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
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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
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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. 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
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. Series B (English Edition)
1 Applied and Computational Harmonic Analysis
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 Foundations of Data Science
1 SIAM Journal on Mathematics of Data Science
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Cited in 38 Fields

147 Numerical analysis (65-XX)
85 Algebraic geometry (14-XX)
72 Computer science (68-XX)
57 Commutative algebra (13-XX)
30 Field theory and polynomials (12-XX)
20 Operations research, mathematical programming (90-XX)
18 Functions of a complex variable (30-XX)
16 Real functions (26-XX)
13 Linear and multilinear algebra; matrix theory (15-XX)
13 Convex and discrete geometry (52-XX)
13 Mechanics of particles and systems (70-XX)
10 Biology and other natural sciences (92-XX)
9 Partial differential equations (35-XX)
8 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
7 Combinatorics (05-XX)
7 Systems theory; control (93-XX)
6 Statistics (62-XX)
6 Quantum theory (81-XX)
5 Ordinary differential equations (34-XX)
4 General and overarching topics; collections (00-XX)
4 Number theory (11-XX)
4 Dynamical systems and ergodic theory (37-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)

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