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,
optimal control, image processing, pattern recognition,
global optimization, and computational physics:

M. Abdullahi, B.I. Mshelia, and S. Hamma:
Solution of polynomial system using PHCpack.
Journal of Physical Sciences and Innovation, 4:4453, 2012.

MinHo Ahn, DongOh Nam and ChungNim Lee:
SelfCalibration with Varying Focal Lengths Using
the Infinity Homography. In Proceedings of the
4th Asian Conference on Computer Vision (ACCV2000),
pages 140145, 2000.

Gianni Amisano and Oreste Tristani:
Exact likelihood computation for nonlinear DSGE models with
heteroskedastic innovations.
Journal of Economic Dynamics and Control 35:21672185, 2011.

D. Arzelier, C. Louembet, A. Rondepierre, and M. KaraZaitri:
A New Mixed Iterative Algorithm to Solve the FuelOptimal Linear
Impulsive Rendezvous Problem.
Journal of Optimization Theory and Applications, 2013.

Bassi, I.G., Abdullahi Mohammed, and Okechukwu C.E.:
Analysis Of Solving Polynomial Equations Using Homotopy Continuation
Method.
International Journal of Engineering Research &
Technology (IJERT) 2(8):14011411, 2013.

Daniel J. Bates and Frank Sottile:
KhovanskiiRolle Continuation for Real Solutions.
Foundations of Computational Mathematics 11:563587, 2011.

Jahan Bayat and Carl D. Crane III:
ClosedForm Equilibrium Analysis of Planar Tensegrity Mechanisms.
In 2006 Florida Conference on Recent Advances in Robotics, FCRAR 2006.

Genevieve Belanger, Kristjan Kannike, Alexander Pukhov, and Martti Raidal:
Minimal semiannihilating Z_n scalar dark matter.
Journal of Cosmology and Astroparticle Physics,
June 2014 (Open Access).

Ivo W.M. Bleylevens, Michiel E. Hostenbach, and Ralf L.M. Peeters:
Polynomial Optimization and a JacobiDavidson type method for
commuting matrices.
Applied Mathematics and Computation 224(1): 564580, 2013.

Guy Bresler, Dustin Cartwright, David Tse:
Feasibility of Interference Alignment for the MIMO interference channel.
IEEE Transactions on Information Theory 60(9):55735586, 2014.

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): 234244, 2005.

MaxLouis G. Buot, Serkan Hosten and Donald St. P. Richards:
Counting and locating the solutions of polynomial systems of maximum
likelihood equations, II: The BehrensFisher problem.
Statistica Sinica 17(4):13431354, 2007.

Enric Celaya, Tom Creemers, Lluis Ros:
Exact interval propagation for the efficient solution of position
analysis problems on planar linkages.
Mechanism and Machine Theory 54: 116131, 2012.

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.

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 7479, ACM 2003.

R.S. Datta: Finding all Nash equilibria of a finite game using
polynomial algebra. Economic Theory 42(1):5596, 2009.

B.H. Dayton: Numerical Local Rings and Local Solution of Nonlinear
Systems. In Proceedings of the 2007 International Workshop on
SymbolicNumeric Computation (SNC'07), pages 7986, ACM 2007.

Max Demenkov:
Estimating region of attraction for polynomial vector fields
by homotopy methods.
ACM Communications in Computer Algebra 46(3):8485, 2012.

Max Demenkov:
A Matlab Tool for Regions of Attraction Estimation
via Numerical Algebraic Geometry.
In the 2015 International Conference on Mechanics  Seventh
Polyakhov's Reading, February 26, 2015, Russia,
Saint Petersburg State University,
Proceedings Edited by A.A. Tikhonov. IEEE 2015.

Ian H. Dinwoodie, Emily Gamundi, and Ed Mosteig:
Multiple Solutions for Blocking Probabilities in Asymmetric Networks.
Open Systems and Information Dynamics 12(3):273288, 2005.

Csaba Domokos and Zoltan Kato:
Parametric Estimation of Affine Deformations of Planar Shapes.
Pattern Recognition, 2009. In press.

C. Durand and C.M. Hoffmann: Variational Constraints in 3D.
In Proceedings of the International Conference on Shape Modeling
and Applications, AizuWakamatsu, Japan, pages 9098, IEEE Computer
Society, 1999.

C. Durand and C.M. Hoffmann: A systematic framework for solving
geometric constraints analytically.
J. Symbolic Computation 30(5):493520, 2000.

I.Z. Emiris, E. Tsigaridas, G. Tzoumas:
The predicates for the Voronoi diagram of ellipses.
Proc. ACM Symp. Comput. Geom. 2006.

Jonathan P. Epperlein and Bassam Bamieh:
A Frequency Domain Method for Optimal Periodic Control.
2012 American Control Conference (ACC), pages 55015506, IEEE 2012.

F. Ferrari:
On the geometry of super YangMills theories: phases and
irreducible polynomials.
Journal of High Energy Physics 1, paper 26, 2009.

Jaime GallardoAlvarado:
A simple method to solve the forward displacement analysis of
the general sixlegged parallel manipulator.
Robotics and ComputerIntegrated Manufacturing 30:5561, 2014.

Jaime GallardoAlvarado and JuandeDios PosadasGarcia:
Mobility analysis and kinematics of the semigeneral 2(3RPS)
seriesparallel manipulator.
Robotics and ComputerIntegrated Manufactoring
29(6): 463472, 2013.

Bertrand Haas: A Simple Counterexample to Kouchnirenko's Conjecture.
Beitraege zur Algebra und Geometrie/Contributions to Algebra
and Geometry, 43(1):18, 2002.

Adlane Habed and Boubakeur Boufama:
Camera selfcalibration from bivariate polynomial equations and
the coplanarity constraint.
Image and Vision Computing, 24(5):498514, 2006.

Marshall Hampton and Richard Moeckel:
Finiteness of stationary configurations of the fourvortex problem.
Transactions of the American Mathematical Society,
361(3): 13171332, 2009.

Jonathan Hauenstein, Jose Israel Rodriguez, and Bernd Sturmfels:
Maximum Likelihood for Matrices with Rank Constraints.
Journal of Algebraic Statistics 5(1): 1838, 2014.

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 1619, Berlin, Germany, pages 8895.

Gabor Horvath:
Moment MatchingBased Distribution Fitting with Generalized
HyperErlang Distributions
In Analytical and Stochastic Modeling Techniques and Applications,
Lecture Notes in Computer Science, Volume 7984, pages 232246, 2013.

X.G. Huang: Forward Kinematics for a Parallel Platform Robot.
Communications in Computer and Information Sciences
86:529532, 2011.

Xiguang Huang, Qizheng Liao, Shimin Wei, and Qiang Xu:
Five precision pointpath synthesis of planar fourbar linkage
using algebraic method.
Frontiers of Electrical and Electronic Engineering in China
3(4):470474, 2008.

Xiguang Huang, Qizheng Liao, Shimin Wei, Qiang Xu, and Shuguang Huang:
The 4SPS2CCS generalized StewartGough Platform mechanisms and its
direct kinematics.
In Proceedings of the 2007 IEEE International Conference on
Mechatronics and Automation, August 58, 2007, Harbin, China.
Pages 24722477, 2007.

Hamadi Jamali, Tokunbo Ogunfunmi:
Stationary points of the finite length constant modulus optimization.
Signal Processing 82(4): 625641, 2002.

Libin Jiao, Bo Dong, Jintao Zhang, and Bo Yu:
Polynomial Homotopy Methods for the Sparse Interpolation Problem Part I:
Equally Spaced Sampling.
SIAM J. Numer. Anal. 54(1): 462480, 2016.

Bjorn Johansson, Magnus Oskarsson, and Kalle Astrom:
Structure and motion estimation from complex features
in three views.
In the Online ICVGIP2002 Proceedings
(Indian Conference on Computer Vision, Graphics and Image Processing).

M. KaraZaitri, D. Arzelier, and C. Louembet:
Mixed iterative algorithm for solving optimal implusive timefixed
rendezvous problem.
American Institute of Aeronautics and Astronautics Guidance, Navigation,
and Control Conference, Toronto, Canada, 0205 August 2010.

P.U. Lamalle, A. Messiaen, P. Dumortier, F. Durodie, M. Evrard, F. Louche:
Study of mutual coupling effects in the antenna array of the ICRH plugin
for ITER.
Fusion Engineering and Design 74:359365, 2005.

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):652661, 2002.
 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 1821, 2003, Tianjin, China.
China Machinery Press, edited by Tian Huang.
 E. Lee and C. Mavroidis: Geometric Design of 3R Manipulators for
Reaching Four EndEffector Spatial Poses.
International Journal for Robotics Research, 23(3):247254, 2004.

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 710, 2002.

Dimitri Leggas and Oleg V. Tsodikov: Determination of small crystal
structures from a minimum set of diffraction intensities by homotopy
continuation.
Acta Crystallographica Section A 71(3): 319324, 2015.

Dawei Leng and Weidong Sun: Finding All the Solutions of PnP Problem.
In
IST 2009  International Workshop on Imaging Systems and Techniques,
Shenzhen, China, May 1112, 2009. Pages 348352, IEEE, 2009.

Anton Leykin: Numerical Primary Decomposition.
In Proceedings of ISSAC 2008, edited by David Jeffrey,
pages 165164, ACM 2008.

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 9798, ACM 2007. (on CDROM)

Anton Leykin and Frank Sottile: Galois groups of Schubert problems
via homotopy computation.
Mathematics of Computation 78: 17491765, 2009.
 Shaobai Li, Srinandan Dasmahapatra, and Koushik Maharatna:
Dynamical System Approach for Edge Detection Using Coupled
FitzHughNaguma Neurons.
IEEE Transactions on Image Processing 24(12), 52065219, 2015.
 Ross A. Lippert:
Fixing multiple eigenvalues by a minimal perturbation.
Linear Algebra Appl. 432(7): 17851817, 2010.
 M. Maniatis and O. Nachtmann:
Stability and symmetry breaking in the general threeHiggsdouble
model.
Journal of High Energy Physics 2015:58, February 2015.
 Hyosang Moon and Nina P. Robson:
Design of spatial nonanthropomorphic articulated systems based on
arm joint constraint kinematic data for human interactive robotics
applications. DETC201546530. In the Proceedings of the ASME 2015
International Design Engineering Technical Conferences & Computers
and Information in Engineering Conference. IDETC/CIE 2015.
August 25, 2015, Boston Massachusetts.
 Marc Moreno Maza, Greg Reid, Robin Scott, and Wenyuan Wu:
On Approximate Triangular Decompositions I. Dimension Zero.
In SNC 2005 Proceedings.
International Workshop on SymbolicNumeric Computation.
Xi'an, China, July 1921, 2005.
Edited by Dongming Wang and Lihong Zhi.
Pages 250275, 2005.

Andrew J. Newell: Transition to supermagnetism in chains of
magnetosome crystals.
Geochemistry Geophysics Geosystems 10(11):119, 2009.

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.

P.A. Parrilo and B. Sturmfels.
Minimizing polynomial functions.
In S. Basu and L. GonzalezVega, editors,
Algorithmic and quantitative real algebraic geometry,
volume 60 of DIMACS Series in Discrete Mathematics and
Theoretical Computer Science, pages 8399. AMS, 2003.

Alba Perez and J.M. McCarthy: Dual Quaternion Synthesis of
Constrained Robotic Systems.
Journal of Mechanical Design 126(3): 425435, 2004.

Nina PatarinskyRobson, J. Michael McCarthy, and Irem Y. Tumer:
The algebraic synthesis of a spatial TS chain for a prescribed
acceleration task.
Mechanism and Machine Theory 43(10): 12681280, 2008.

Nina PatarinskyRobson, J. Michael McCarthy, and Irem Y. Tumer:
Failure Recovery Planning for an Arm Mounted on an
Exploratory Rover.
IEEE Transactions on Robotics 25(6):14481453, 2009.

Jose Israel Rodriguez:
Combinatorial excess intersection.
Journal of Symbolic Computation 68(2): 297307, 2015.

Roger E. SanchezAlonso, JoseJoel GonzalezBarbosa, Eduardo
CastiloCastaneda, and Jaime GallardoAlvarado:
Kinematic analysis of a novel 2(3RUS) parallel manipulator.
Robotica, available on CJO2015.

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):717737, 2002.

Ben ShirtEdiss, Ricard V. Sole, and Kepa RuizMirazo:
Emergent Chemical Behavior in VariableVolume Protocells.
Life 5: 181121, 2015.

Frank Sottile: Real Schubert Calculus: Polynomial systems and a conjecture
of Shapiro and Shapiro. Experimental Mathematics
9(2): 161182, 2000.

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 1114, 2004.
Proceedings, Part III. Edited by T. Pajdla and J. Matas.
Lecture Notes in Computer Science 3023, pages 252263, Springer, 2004.

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/DAC48813. Chicago, IL, Sept. 0206, 2003.

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 200585085. Long Beach, CA, Sept. 2428 2005.

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):757775, 2005

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): 776786, 2006.

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 26, 2003.

Attila Tanács and Joakim Lindblad and Nataša Sladoje and Zoltan Ka:
Estimation of linear deformations of 2D and 3D fuzzy objects,
Pattern Recognition 48(4):13911403, 2015.

N. Trawny, X.S. Zhou, K.X. Zhou, S.I. Roumeliotis:
3D Relative Pose Estimation from DistanceOnly Measurements.
Proceedings of the 2007/IEEE/RSJ International Conference
on intelligent Robots and Systems. San Diego, CA, Oct 29Nov 2, 2007,
pages 10711078, IEEE, 2007.

T. Turocy:
Towards a blackbox solver for finite games: Computing all equilibria
with Gambit and PHCpack.
In Software for Algebraic Geometry, volume 148 of the IMA
volumes in Mathematics and its Applications, edited by M.E. Stillman,
N. Takayama, and J. Verschelde, pages 133148, SpringerVerlag, 2008.

Konstantin Usevich and Ivan Markovsky:
Structured lowrank approximation as a rational function minimization.
In 16th IFAC Symposium on System Identification Brussels,
11  13 Jul 2012, pages 722727.

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 1822, 1996. Available on CDROM.
 Wenyuan Wu and Greg Reid:
Symbolicnumeric 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 377385, ACM 2007.
 Jonathan Widger and Daniel Grosu:
Parallel Computation of Nash Equilibria in NPlayer Games.
In Proc. of the 12th IEEE International Conference on Computational
Science and Engineering (CSE 2009), August 2931, 2009, Vancouver,
Canada, pages 209215.

F. Xie, G. Reid, and S. Valluri: A numerical method for the
one dimensional action functional for FBG structures.
Can J. Phys. 76: 121, 2002.

Hong Bing Xin, Qiang Huang, and Yueqing Yu:
Position and Orientation Analyses of Mechanism by PHCpack Solver
of Homotopy Continuation.
Applied Mechanics and Materials152254: 17791784, 2012.

K. Yang and R. Orsi:
Static output feedback pole placement via a trust region approach.
IEEE Transactions on Automatic Control 52(11): 21462150, 2007.

Yan Yang, Yao Zhang, Fangxing Li, and Haoyong Chen:
Computing All Nash Equilibria of Multiplayer Games in Electricity
Markets by Solving Polynomial Equations.
IEEE Transactions on Power Systems 27(1): 8191, 2012.

Jun Zhang and Mohan Sarovar:
Identification of open quantum systems from observable time traces.
Physical Review A 91, 052121, 2015.

Shiqiang Zhang, Shufang Zhang, and Yan Wan:
Biorthogonal Wavelet Construction Using Homotopy Method.
Chinese Journal of Electronics 24(4), pages 772775, 2015.

Xun S. Zhou and Stergios I. Roumeliotis:
Determining 3D Relative Transformations for Any Combination of
Range and Bearing Measurements.
IEEE Transactions on Robotics 29(2):458474, 2013.
In addition to the publications listed above, PHCpack was used as a
benchmark to measure the progress of new algorithms in the following
papers:

T. Gao and T.Y. Li:
Mixed volume computation via linear programming.
Taiwanese Journal of Mathematics 4(4): 599619, 2000.

T. Gao and T.Y. Li:
Mixed volume computation for semimixed systems.
Discrete Comput. Geom. 29(2):257277, 2003.

L. Granvilliers:
On the Combination of Interval Constraint Solvers.
Reliable Computing 7(6): 467483, 2001.

Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler:
Regeneration Homotopies for Solving Systems of Polynomials.
Mathematics of Computation 80(273): 345377, 2011.

S. Kim and M. Kojima:
Numerical Stability of Path Tracing in Polyhedral Homotopy
Continuation Methods.
Computing 73(4): 329348, 2004.

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):20762097, 2005.

T.L. Lee, T.Y. Li, and C.H. Tsai:
HOM4PS2.0: a software package for solving polynomial systems
by the polyhedral homotopy continuation method.
Computing 83(23): 109133, 2008.

Anton Leykin:
Numerical Algebraic Geometry.
The Journal of Software for Algebra and Geometry
volume 3, pages 510, 2011.

T.Y. Li and X. Li:
Finding Mixed Cells in the Mixed Volume Computation.
Foundations of Computational Mathematics 1(2): 161181, 2001.

T.Y. Li, X. Wang, and M. Wu:
Numerical Schubert Calculus by the Pieri Homotopy Algorithm.
SIAM J. Numer Anal. 40(2): 578600, 2002.

J.M. Porta, L. Ros, T. Creemers, and F. Thomas:
Box approximations of planar linkage configuration spaces.
Journal of Mechanical Design 129(4):397405, 2007.

Laurent Sorber, Marc Van Barel, and Lieven De Lathauwer:
Numerical solution of bivariate and polyanalytic polynomial systems.
SIAM J. Numer. Anal. 52(4):15511572, 2014.

Yang Sun, YuHui Tao, FengShan Bai:
Incomplete Groebner basis as a preconditioner for polynomial systems.
Journal of Computational and Applied Mathematics 226(1):29, 2009.
PHCpack was used to develop new homotopy algorithms:

Bo Dong, Bo Yu, and Yan Yu:
A symmetric and hybrid polynomial system solving method for mixed
trigonometric polynomial systems.
Mathematics of Computation 83(288): 18471868, 2014.

Bo Yu and Bo Dong:
A hybrid polynomial system solving method for mixed
trigonometric polynomial systems.
SIAM J. Numer. Anal. 46(3): 15031518, 2008.

Xuping Zhang, Jintao Zhang, and Bo Yu:
Eigenfunction expansion method for multiple solutions
of semilinear elliptic equations with polynomial nonlinearity.
SIAM J. Numer. Anal. 51(5): 26802699, 2013.
Last, but certainly not least, there is the wonderful book of
Bernd Sturmfels which contains a section on computing Nash
equilibria with PHCpack.

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!