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. (Source:

References in zbMATH (referenced in 210 articles , 1 standard article )

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  1. Zeng, Zhonggang: ApaTools: a software toolbox for approximate polynomial algebra (2008)
  2. Zeng, Zhonggang: A numerical elimination method for polynomial computations (2008)
  3. Leykin, Anton; Verschelde, Jan; Zhao, Ailing: Evaluation of Jacobian matrices for Newton’s method with deflation to approximate isolated singular solutions of polynomial systems (2007)
  4. Mizutani, Tomohiko; Takeda, Akiko; Kojima, Masakazu: Dynamic enumeration of all mixed cells (2007)
  5. Moreno Maza, Marc; Reid, Greg J.; Scott, Robin; Wu, Wenyuan: On approximate linearized triangular decompositions (2007)
  6. Moreno Maza, Marc; Reid, Greg; Scott, Robin; Wu, Wenyuan: On approximate triangular decompositions in dimension zero (2007)
  7. Wu, Wenyuan; Reid, Greg: Symbolic-numeric computation of implicit Riquier bases for PDE (2007)
  8. Aghassi, Michele; Bertsimas, Dimitris: Robust game theory (2006)
  9. Buot, Max-Louis G.; Richards, Donald St. P.: Counting and locating the solutions of polynomial systems of maximum likelihood equations. I. (2006)
  10. Gunji, T.; Kim, S.; Fujisawa, K.; Kojima, M.: PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems (2006)
  11. Iglesias, Andrés (ed.); Takayama, Nobuki (ed.): Mathematical software -- ICMS 2006. Second international congress on mathematical software, Castro Urdiales, Spain, September 1--3, 2006. Proceedings (2006)
  12. Leykin, Anton; Verschelde, Jan: Interfacing with the numerical homotopy algorithms in PHCpack (2006)
  13. Leykin, Anton; Verschelde, Jan; Zhao, Ailing: Newton’s method with deflation for isolated singularities of polynomial systems (2006)
  14. Leykin, Anton; Verschelde, Jan; Zhuang, Yan: Parallel homotopy algorithms to solve polynomial systems (2006)
  15. Su, Hai-Jun; Mccarthy, J. Michael; Sosonkina, Masha; Watson, Layne T.: Algorithm 857: POLSYS(_-)GLP -- a parallel general linear product homotopy code for solving polynomial systems of equations. (2006)
  16. Wu, Wenyuan; Reid, Greg: Application of numerical algebraic geometry and numerical linear algebra to PDE (2006)
  17. Gao, Tangan; Li, T. Y.; Wu, Mengnien: Algorithm 846: MixedVol: a software package for mixed-volume computation. (2005)
  18. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Introduction to numerical algebraic geometry (2005)
  19. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: An intrinsic homotopy for intersecting algebraic varieties (2005)
  20. Syam, Muhammed I.: Nonlinear optimization exclusion tests for finding all solutions of nonlinear equations (2005)

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