Some examples for solving systems of algebraic equations by calculating groebner bases
Journal of Symbolic Computation
The random product homotopy and deficient polynomial systems
Numerische Mathematik
Numerical solution of a class of deficient polynomial systems
SIAM Journal on Numerical Analysis
A homotopy for solving general polynomial systems that respects m-homogenous structures
Applied Mathematics and Computation
Computing all solutions to polynomial systems using homotopy continuation
Applied Mathematics and Computation
Regularity results for solving systems of polynomials by homotopy method
Numerische Mathematik
Homotopy method for general &lgr;-matrix problems
SIAM Journal on Matrix Analysis and Applications
Coefficient-parameter polynomial continuation
Applied Mathematics and Computation
Finding all isolated solutions to polynomial systems using HOMPACK
ACM Transactions on Mathematical Software (TOMS)
A neural network modeled by an adaptive Lotka-Volterra system
SIAM Journal on Applied Mathematics
The cheater's homotopy: an efficient procedure for solving systems of polynomial equations
SIAM Journal on Numerical Analysis
Chemical equilibrium systems as numerical test problems
ACM Transactions on Mathematical Software (TOMS)
Practical determination of the dimension of an algebraic variety
Proceedings of the third conference on Computers and mathematics
Symbolic solution polynomial equation systems with symmetry
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
An optimal condition for determining the exact number of roots of a polynomial system
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
How we proved that there are exactly 924 cyclic 7-roots
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
A new start system for solving deficient polynomial systems using continuation
Applied Mathematics and Computation
Nonlinear homotopies for solving deficient polynomial systems with parameters
SIAM Journal on Numerical Analysis
The GBQ-algorithm for constructing start systems of homotopies for polynomial systems
SIAM Journal on Numerical Analysis
Computing singular solutions to polynomial systems
Advances in Applied Mathematics
The 40 “generic” positions of a parallel robot
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
On the Newton Polytope of the Resultant
Journal of Algebraic Combinatorics: An International Journal
A convex geometric approach to counting the roots of a polynomial system
Selected papers of the workshop on Continuous algorithms and complexity
Homotopies exploiting Newton polytopes for solving sparse polynomial systems
SIAM Journal on Numerical Analysis
Symmetric homotopy construction
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Regular Article: Symmetrical Newton Polytopes for Solving Sparse Polynomial Systems
Advances in Applied Mathematics
A product-decomposition bound for Bezout numbers
SIAM Journal on Numerical Analysis
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
C vs Ada: arguing performance religion
ACM SIGAda Ada Letters
Sparse elimination and applications in kinematics
Sparse elimination and applications in kinematics
Efficient incremental algorithms for the sparse resultant and the mixed volume
Journal of Symbolic Computation
Dynamic Pole Assignment and Schubert Calculus
SIAM Journal on Control and Optimization
Counting affine roots of polynomial systems via pointed Newton polytopes
Journal of Complexity
Note on the end game in homotopy zero curve tracking
ACM Transactions on Mathematical Software (TOMS)
Mathematics of Computation
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Complexity and real computation
Complexity and real computation
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
Systems of algebraic equations with bad reduction
Journal of Symbolic Computation
Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
MARS: a MAPLE/MATLAB/C resultant-based solver
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Some remarks on real and complex output feedback
Systems & Control Letters
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Finding all isolated zeros of polynomial systems in Cn via stable mixed volumes
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
How to count efficiently all affine roots of a polynomial system
Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Box-bisection for solving second-degree systems and the problem of clustering
ACM Transactions on Mathematical Software (TOMS)
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Granularity of Homotopy Algorithms for Polynomial Systems of Equations
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
Homotopy techniques for real-time visualization of geometric tangent problems
Proceedings of the eighteenth annual symposium on Computational geometry
Geometric completion of differential systems using numeric-symbolic continuation
ACM SIGSAM Bulletin
Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Using computer algebra to find nash equilibria
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computer algebra handbook
Numerical factorization of multivariate complex polynomials
Theoretical Computer Science - Algebraic and numerical algorithm
Finding all real zeros of polynomial systems using multi-resultant
Journal of Computational and Applied Mathematics
Symbolic-numeric completion of differential systems by homotopy continuation
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
An intrinsic homotopy for intersecting algebraic varieties
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Algorithm 846: MixedVol: a software package for mixed-volume computation
ACM Transactions on Mathematical Software (TOMS)
Application of numerical algebraic geometry and numerical linear algebra to PDE
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
ACM Transactions on Mathematical Software (TOMS)
On approximate triangular decompositions in dimension zero
Journal of Symbolic Computation
Numerical algebraic geometry and kinematics
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Numerical local rings and local solution of nonlinear systems
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Symbolic-numeric computation of implicit riquier bases for PDE
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
ACM Communications in Computer Algebra
Numerical primary decomposition
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
A numerical elimination method for polynomial computations
Theoretical Computer Science
ApaTools: a software toolbox for approximate polynomial algebra
ACM Communications in Computer Algebra
Incomplete Gröbner basis as a preconditioner for polynomial systems
Journal of Computational and Applied Mathematics
HOM4PS-2.0para: Parallelization of HOM4PS-2.0 for solving polynomial systems
Parallel Computing
Implicit Riquier Bases for PDAE and their semi-discretizations
Journal of Symbolic Computation
Fast and Stable Polynomial Equation Solving and Its Application to Computer Vision
International Journal of Computer Vision
Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm
International Journal of Computational Science and Engineering
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
A method for finding zeros of polynomial equations using a contour integral based eigensolver
Proceedings of the 2009 conference on Symbolic numeric computation
Mixed volume techniques for embeddings of Laman graphs
Computational Geometry: Theory and Applications
Moments and sums of squares for polynomial optimization and related problems
Journal of Global Optimization
Parametric estimation of affine deformations of planar shapes
Pattern Recognition
An intrinsic homotopy for intersecting algebraic varieties
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Counting and locating the solutions of polynomial systems of maximum likelihood equations, I
Journal of Symbolic Computation
Sweeping algebraic curves for singular solutions
Journal of Computational and Applied Mathematics
Enumeration of totally real number fields of bounded root discriminant
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Interrobot transformations in 3-D
IEEE Transactions on Robotics
Polynomial homotopies on multicore workstations
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Solving schubert problems with Littlewood-Richardson homotopies
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Polynomial homotopy continuation with PHCpack
ACM Communications in Computer Algebra
Sampling algebraic sets in local intrinsic coordinates
Computers & Mathematics with Applications
Computing curve intersection by homotopy methods
Journal of Computational and Applied Mathematics
Stability verification for monotone systems using homotopy algorithms
Numerical Algorithms
Parallel homotopy algorithms to solve polynomial systems
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Interfacing with the numerical homotopy algorithms in PHCpack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Sudokus and Gröbner bases: not only a divertimento
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems
ACM Transactions on Mathematical Software (TOMS)
Numerical calculation of H-bases for positive dimensional varieties
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
SIAM Journal on Scientific Computing
Computing Puiseux series for algebraic surfaces
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Computing real solutions of polynomial systems via low-rank moment matrix completion
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Verified error bounds for real solutions of positive-dimensional polynomial systems
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Journal of Computational Physics
Cell decomposition of almost smooth real algebraic surfaces
Numerical Algorithms
Mobility analysis and kinematics of the semi-general 2(3-RPS) series-parallel manipulator
Robotics and Computer-Integrated Manufacturing
Robotics and Computer-Integrated Manufacturing
NAClab: a Matlab toolbox for numerical algebraic computation
ACM Communications in Computer Algebra
| Hi-index | 0.02 |
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 article the structure and design of the software package PHC is described. The main program operates in several modes, is menu driven, and is file oriented. This package features 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.