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. Kim, S.; Kojima, M.: Numerical stability of path tracing in polyhedral homotopy continuation methods (2004)
  2. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Homotopies for intersecting solution components of polynomial systems (2004)
  3. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Numerical factorization of multivariate complex polynomials (2004)
  4. Syam, Muhammed I.: Finding all real zeros of polynomial systems using multi-resultant (2004)
  5. Datta, Ruchira S.: Using computer algebra to find Nash equilibria (2003)
  6. Gao, Tangan; Li, T. Y.: Mixed volume computation for semi-mixed systems (2003)
  7. Georg, Kurt: A new exclusion test. (2003)
  8. Hazaveh, K.; Jeffrey, D. J.; Reid, G. J.; Watt, S. M.; Wittkopf, A. D.: An exploration of homotopy solving in Maple (2003)
  9. Henrion, Didier; Lasserre, Jean-Bernard: Solving global optimization problems over polynomials with GloptiPoly 2.1 (2003)
  10. Hochstenbach, Michiel E.; van der Vorst, Henk A.: Alternatives to the Rayleigh quotient for the quadratic eigenvalue problem (2003)
  11. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Numerical irreducible decomposition (2003)
  12. Haas, Bertrand: A simple counterexample to Kouchnirenko’s conjecture (2002)
  13. Schreiber, H.; Meer, K.; Schmitt, B. J.: Dimensional synthesis of planar Stephenson mechanisms for motion generation using circlepoint search and homotopy methods (2002)
  14. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: A method for tracking singular paths with application to the numerical irreducible decomposition (2002)
  15. Sturmfels, Bernd: Solving systems of polynomial equations (2002)
  16. Takeda, Akiko; Kojima, Masakazu; Fujisawa, Katsuki: Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method (2002)
  17. Theobald, Thorsten: An enumerative geometry framework for algorithmic line problems in (\mathbbR^3) (2002)
  18. Ceberio, Martine; Granvilliers, Laurent: Solving nonlinear systems by constraint inversion and interval arithmetic (2001)
  19. Georg, Kurt: Improving the efficiency of exclusion algorithms (2001)
  20. Granvilliers, Laurent: On the combination of interval constraint solvers (2001)

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