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, mechanical design, computational geometry, computer vision, 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. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. C. Durand and C.M. Hoffmann: A systematic framework for solving geometric constraints analytically. J. Symbolic Computation 30(5):493-520, 2000.
  10. I.Z. Emiris, E. Tsigaridas, G. Tzoumas: The predicates for the Voronoi diagram of ellipses. Proc. ACM Symp. Comput. Geom. 2006.
  11. Bertrand Haas: A Simple Counterexample to Kouchnirenko's Conjecture. Beitraege zur Algebra und Geometrie/Contributions to Algebra and Geometry, 43(1):1-8, 2002.
  12. 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.
  13. 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.
  14. Hamadi Jamali, Tokunbo Ogunfunmi: Stationary points of the finite length constant modulus optimization. Signal Processing 82(4): 625-641, 2002.
  15. 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).
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. Anton Leykin: Numerical Primary Decomposition In Proceedings of ISSAC 2008, edited by David Jeffrey, pages 165-164, ACM 2008.
  22. 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)
  23. Anton Leykin and Frank Sottile: Galois groups of Schubert problems via homotopy computation. ArXiV:0710.4607.
  24. 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.
  25. 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.
  26. P.A. Parillo and B. Sturmfels: Minimizing Polynomial Functions. presented at the Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, held at DIMACS, Rutgers University, March 12-16, 2001.
  27. Alba Perez and J.M. McCarthy: Dual Quaternion Synthesis of Constrained Robotic Systems. Journal of Mechanical Design 126(3): 425-435, 2004.
  28. 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.
  29. F. Sottile: Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro. Experimental Mathematics 9(2): 161-182, 2000.
  30. 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.
  31. 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.
  32. 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.
  33. 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
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
  39. 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.Y. Li and X. Li: Finding Mixed Cells in the Mixed Volume Computation. Foundations of Computational Mathematics 1(2): 161-181, 2001.
  7. 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.
  8. 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.
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!