Users of PHCpack

The papers listed below report the use of PHCpack in the fields of algebraic statistics, communication networks, geometric constraint solving, real algebraic geometry, computation of Nash equilibria, signal processing, magnetism, mechanical design, computational geometry, computer vision, pattern recognition, global optimization, and computational physics:
  1. Min-Ho Ahn, Dong-Oh Nam and Chung-Nim Lee: Self-Calibration with Varying Focal Lengths Using the Infinity Homography. In Proceedings of the 4th Asian Conference on Computer Vision (ACCV2000), pages 140-145, 2000.
  2. Jahan Bayat and Carl D. Crane III: Closed-Form Equilibrium Analysis of Planar Tensegrity Mechanisms. In 2006 Florida Conference on Recent Advances in Robotics, FCRAR 2006.
  3. M.-L. G. Buot and D. St. P. Richards: Counting and Locating the Solutions of Polynomial Systems of Maximum Likelihood Equations I. Journal of Symbolic Computation 41(2): 234-244, 2005.
  4. Max-Louis G. Buot, Serkan Hosten and Donald St. P. Richards: Counting and locating the solutions of polynomial systems of maximum likelihood equations, II: The Behrens-Fisher problem. Statistica Sinica 17(4):1343-1354, 2007.
  5. Tom Creemers, Josep M. Porta, Lluis Ros, and Federico Thomas: Fast Multiresolutive Approximations of Planar Linkage Configuration Spaces. IEEE 2006 International Conference on Robotics and Automation.
  6. R.S. Datta: Using Computer Algebra To Compute Nash Equilibria. In Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation (ISSAC 2003), pages 74-79, ACM 2003.
  7. R.S. Datta: Finding all Nash equilibria of a finite game using polynomial algebra. Enonomic Theory 42(1):55-96, 2009.
  8. B.H. Dayton: Numerical Local Rings and Local Solution of Nonlinear Systems. In Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation (SNC'07), pages 79-86, ACM 2007.
  9. Ian H. Dinwoodie, Emily Gamundi, and Ed Mosteig: Multiple Solutions for Blocking Probabilities in Asymmetric Networks. Open Systems and Information Dynamics 12(3):273-288, 2005.
  10. Csaba Domokos and Zoltan Kato: Parametric Estimation of Affine Deformations of Planar Shapes. Pattern Recognition, 2009. In press.
  11. C. Durand and C.M. Hoffmann: Variational Constraints in 3D. In Proceedings of the International Conference on Shape Modeling and Applications, Aizu-Wakamatsu, Japan, pages 90-98, IEEE Computer Society, 1999.
  12. C. Durand and C.M. Hoffmann: A systematic framework for solving geometric constraints analytically. J. Symbolic Computation 30(5):493-520, 2000.
  13. I.Z. Emiris, E. Tsigaridas, G. Tzoumas: The predicates for the Voronoi diagram of ellipses. Proc. ACM Symp. Comput. Geom. 2006.
  14. F. Ferrari: On the geometry of super Yang-Mills theories: phases and irreducible polynomials. Journal of High Energy Physics 1, paper 26, 2009.
  15. Bertrand Haas: A Simple Counterexample to Kouchnirenko's Conjecture. Beitraege zur Algebra und Geometrie/Contributions to Algebra and Geometry, 43(1):1-8, 2002.
  16. Adlane Habed and Boubakeur Boufama: Camera self-calibration from bivariate polynomial equations and the coplanarity constraint. Image and Vision Computing, 24(5):498-514, 2006.
  17. Marshall Hampton and Richard Moeckel: Finiteness of stationary configurations of the four-vortex problem. Transactions of the American Mathematical Society, 361(3): 1317-1332, 2009.
  18. Christoph Hellings, David A. Schmidt, and Wolfgang Utschick: Optimized beamforming for the two stream MIMO interference channel at high SNR In 2009 Internatial ITG workshop on smart antennas - WSA 2009, February 16-19, Berlin, Germany, pages 88-95.
  19. Xiguang Huang, Qizheng Liao, Shimin Wei, and Qiang Xu: Five precision point-path synthesis of planar four-bar linkage using algebraic method. Frontiers of Electrical and Electronic Engineering in China 3(4):470-474, 2008.
  20. Xiguang Huang, Qizheng Liao, Shimin Wei, Qiang Xu, and Shuguang Huang: The 4SPS-2CCS generalized Stewart-Gough Platform mechanisms and its direct kinematics. In Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, August 5-8, 2007, Harbin, China. Pages 2472-2477, 2007.
  21. Hamadi Jamali, Tokunbo Ogunfunmi: Stationary points of the finite length constant modulus optimization. Signal Processing 82(4): 625-641, 2002.
  22. Bjorn Johansson, Magnus Oskarsson, and Kalle Astrom: Structure and motion estimation from complex features in three views. In the Online ICVGIP-2002 Proceedings (Indian Conference on Computer Vision, Graphics and Image Processing).
  23. M. Kara-Zaitri, D. Arzelier, and C. Louembet: Mixed iterative algorithm for solving optimal implusive time-fixed rendezvoud problem. American Institute of Aeronautics and Astronautics Guidance, Navigation, and Control Conference, Toronto, Canada, 02-05 August 2010.
  24. P.U. Lamalle, A. Messiaen, P. Dumortier, F. Durodié, M. Evrard, F. Louche: Study of mutual coupling effects in the antenna array of the ICRH plug-in for ITER. Fusion Engineering and Design 74:359-365, 2005.
  25. E. Lee and C. Mavroidis: Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Continuation. Journal of Mechanical Design, Transactions of the ASME, 124(4):652-661, 2002.
  26. E. Lee and C. Mavroidis: Four Precision Points Geometric Design of Spatial 3R Manipulators. Proceedings of the 11th World Congress in Mechanism and Machine Sciences, August 18-21, 2003, Tianjin, China. China Machinery Press, edited by Tian Huang.
  27. E. Lee and C. Mavroidis: Geometric Design of 3R Manipulators for Reaching Four End-Effector Spatial Poses. International Journal for Robotics Research, 23(3):247-254, 2004.
  28. E. Lee, C. Mavroidis, and J. Morman: Geometric Design of Spatial 3R Manipulators. Proceedings of the 2002 NSF Design, Service, and Manufacturing Grantees and Research Conference, San Juan, Puerto Rico, January 7-10, 2002.
  29. Anton Leykin: Numerical Primary Decomposition In Proceedings of ISSAC 2008, edited by David Jeffrey, pages 165-164, ACM 2008.
  30. Anton Leykin and Frank Sottile: Computing Monodromy via Parallel Homotopy Continuation. In Proceedings of the 2007 International Workshop on Parallel Symbolic Computation (PASCO'07), pages 97-98, ACM 2007. (on CDROM)
  31. Anton Leykin and Frank Sottile: Galois groups of Schubert problems via homotopy computation. Mathematics of Computation 78: 1749-1765, 2009.
  32. Marc Moreno Maza, Greg Reid, Robin Scott, and Wenyuan Wu: On Approximate Triangular Decompositions I. Dimension Zero. In SNC 2005 Proceedings. International Workshop on Symbolic-Numeric Computation. Xi'an, China, July 19-21, 2005. Edited by Dongming Wang and Lihong Zhi. Pages 250-275, 2005.
  33. Andrew J. Newell: Transition to supermagnetism in chains of magnetosome crystals. Geochemistry Geophysics Geosystems 10(11):1-19, 2009.
  34. M. Oskarsson, A. Zisserman and K. Astrom: Minimal Projective Reconstruction for combinations of Points and Lines in Three Views. Electronic Proceedings of BMVC2002 - The 13th British Machine Vision Conference 2002, pages 63 - 72.
  35. P.A. Parrilo and B. Sturmfels. Minimizing polynomial functions. In S. Basu and L. Gonzalez-Vega, editors, Algorithmic and quantitative real algebraic geometry, volume 60 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 83-99. AMS, 2003.
  36. Alba Perez and J.M. McCarthy: Dual Quaternion Synthesis of Constrained Robotic Systems. Journal of Mechanical Design 126(3): 425-435, 2004.
  37. N.P. Robson, J.M. McCarthy, and I.Y. Tumer: The algebraic synthesis of a spatial TS chain for a prescribed acceleration task. Mechanism and Machine Theory 43(10): 1268-1280, 2008.
  38. H. Schreiber, K. Meer, and B.J. Schmitt: Dimensional synthesis of planar Stephenson mechanisms for motion generation using circlepoint search and homotopy methods. Mechanism and Machine Theory 37(7):717-737, 2002.
  39. F. Sottile: Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro. Experimental Mathematics 9(2): 161-182, 2000.
  40. H. Stewenius and K. Astrom: Structure and Motion Problems for Multiple Rigidly Moving Cameras. In Computer Vision - ECCV 2004: 8th European Conference on Computer Vision, Prague, Czech Republic, May 11-14, 2004. Proceedings, Part III. Edited by T. Pajdla and J. Matas. Lecture Notes in Computer Science 3023, pages 252-263, Springer, 2004.
  41. H.-J. Su and J.M. McCarthy: Kinematic Synthesis of RPS Serial Chains. In Proceedings of the ASME Design Engineering Technical Conferences (CDROM). Paper DETC03/DAC-48813. Chicago, IL, Sept. 02-06, 2003.
  42. H.-J. Su and J.M. McCarthy: Synthesis of Compliant Mechanisms with Specified Equilibrium Positions. In Proceedings of the ASME International Design Engineering Technical Conferences. Paper DETC 2005-85085. Long Beach, CA, Sept. 24-28 2005.
  43. H.-J. Su and J.M. McCarthy: Kinematic Synthesis of RPS Serial Chains for a Given Set of Task Positions. Mechanism and Machine Theory, 40(7):757-775, 2005
  44. H.-J. Su and J.M. McCarthy: A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms ASME Journal of Mechanical Design128(4): 776-786, 2006.
  45. H.-J. Su, C.W. Wampler, and J.M. McCarthy: Geometric Design of Cylindric PRS Serial Chains. ASME Design Engineering Technical Conferences, Chicago, IL, Sep 2-6, 2003.
  46. N. Trawny, X.S. Zhou, K.X. Zhou, S.I. Roumeliotis: 3D Relative Pose Estimation from Distance-Only Measurements. Proceedings of the 2007/IEEE/RSJ International Conference on intelligent Robots and Systems. San Diego, CA, Oct 29-Nov 2, 2007, pages 1071-1078, IEEE, 2007.
  47. C.W. Wampler: Isotropic coordinates, circularity and Bezout numbers: planar kinematics from a new perspective. Proceedings of the 1996 ASME Design Engineering Technical Conference. Irvine, CA, Aug 18-22, 1996. Available on CD-ROM.
  48. Wenyuan Wu and Greg Reid: Symbolic-numeric computation of implicit Riquier bases for PDE. In Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, edited by C.W. Brown, pages 377-385, ACM 2007.
  49. Jonathan Widger and Daniel Grosu: Parallel Computation of Nash Equilibria in N-Player Games. In Proc. of the 12th IEEE International Conference on Computational Science and Engineering (CSE 2009), August 29-31, 2009, Vancouver, Canada, pages 209-215.
  50. F. Xie, G. Reid, and S. Valluri: A numerical method for the one dimensional action functional for FBG structures. Can J. Phys. 76: 1-21, 2002.
  51. K. Yang and R. Orsi. Static output feedback pole placement via a trust region approach. IEEE Transactions on Automatic Control 52(11): 2146-2150, 2007.
In addition to the publications listed above, PHCpack was used as a benchmark to measure the progress of new algorithms in the following papers:
  1. T. Gao and T.Y. Li: Mixed volume computation via linear programming. Taiwanese Journal of Mathematics 4(4): 599-619, 2000.
  2. T. Gao and T.Y. Li: Mixed volume computation for semi-mixed systems. Discrete Comput. Geom. 29(2):257-277, 2003.
  3. L. Granvilliers: On the Combination of Interval Constraint Solvers. Reliable Computing 7(6): 467-483, 2001.
  4. S. Kim and M. Kojima: Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods. Computing 73(4): 329-348, 2004.
  5. Y. Lebbah, C. Michel, M. Rueher, D. Daney, and J.P. Merlet: Efficient and safe global constraints for handling numerical constraint systems. SIAM J. Numer. Anal. 42(5):2076-2097, 2005.
  6. T.L. Lee, T.Y. Li, and C.H. Tsai: HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method. Computing 83(2-3): 109-133, 2008.
  7. T.Y. Li and X. Li: Finding Mixed Cells in the Mixed Volume Computation. Foundations of Computational Mathematics 1(2): 161-181, 2001.
  8. T.Y. Li, X. Wang, and M. Wu: Numerical Schubert Calculus by the Pieri Homotopy Algorithm. SIAM J. Numer Anal. 40(2): 578-600, 2002.
  9. J.M. Porta, L. Ros, T. Creemers, and F. Thomas: Box approximations of planar linkage configuration spaces. Journal of Mechanical Design 129(4):397-405, 2007.
  10. Yang Sun, Yu-Hui Tao, Feng-Shan Bai: Incomplete Gröbner basis as a preconditioner for polynomial systems. Journal of Computational and Applied Mathematics 226(1):2-9, 2009.
PHCpack was used to develop new homotopy algorithms:
  1. Bo Yu and Bo Dong: A hybrid polynomial system solving method for mixed trigonometric polynomial systems. SIAM J. Numer. Anal. 46(3): 1503-1518, 2008.
Last, but certainly not least, there is the wonderful book of Bernd Sturmfels which contains a section on computing Nash equilibria with PHCpack.
  1. B. Sturmfels: Solving Systems of Polynomial Equations. CBMS Regional Conference Series of the AMS, Number 97, 2002.
If you achieved some nice results with PHCpack, please let me know!