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 220 articles , 1 standard article )

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  1. Adamer, Michael F.; Helmer, Martin: Complexity of model testing for dynamical systems with toric steady states (2019)
  2. Améndola, Carlos; Bliss, Nathan; Burke, Isaac; Gibbons, Courtney R.; Helmer, Martin; Hoşten, Serkan; Nash, Evan D.; Rodriguez, Jose Israel; Smolkin, Daniel: The maximum likelihood degree of toric varieties (2019)
  3. Chen, Justin; Kileel, Joe: Numerical implicitization: a Macaulay2 package (2019)
  4. Chen, Tianran: Unmixing the mixed volume computation (2019)
  5. Duff, Timothy; Hill, Cvetelina; Jensen, Anders; Lee, Kisun; Leykin, Anton; Sommars, Jeff: Solving polynomial systems via homotopy continuation and monodromy (2019)
  6. Gallardo-Alvarado, Jaime: An application of the Newton-homotopy continuation method for solving the forward kinematic problem of the 3-RRS parallel manipulator (2019)
  7. Kosta, Dimitra; Kubjas, Kaie: Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry (2019)
  8. Leykin, Anton; Yu, Josephine: Beyond polyhedral homotopies (2019)
  9. Obatake, Nida; Shiu, Anne; Tang, Xiaoxian; Torres, Angélica: Oscillations and bistability in a model of ERK regulation (2019)
  10. Paudel, Danda Pani; Habed, Adlane; Demonceaux, Cédric; Vasseur, Pascal: Robust and optimal registration of image sets and structured scenes via sum-of-squares polynomials (2019)
  11. Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.: High-order upwind schemes for the wave equation on overlapping grids: Maxwell’s equations in second-order form (2018)
  12. Bliss, Nathan; Duff, Timothy; Leykin, Anton; Sommars, Jeff: Monodromy solver. Sequential and parallel (2018)
  13. Bliss, Nathan; Verschelde, Jan: The method of Gauss-Newton to compute power series solutions of polynomial homotopies (2018)
  14. Breiding, Paul; Timme, Sascha: HomotopyContinuation.jl: a package for homotopy continuation in Julia (2018)
  15. Charles, Zachary; Boston, Nigel: Exploiting algebraic structure in global optimization and the Belgian chocolate problem (2018)
  16. Kang, Weirui; Zeng, Jiani; Liu, Qinghua; Huang, Zhengdong: Generating the isocurve representation for configuration space of mechanisms (2018)
  17. Leykin, Anton: Homotopy continuation in Macaulay2 (2018)
  18. Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping: Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity (2018)
  19. Telen, Simon; Mourrain, Bernard; Barel, Marc Van: Solving polynomial systems via truncated normal forms (2018)
  20. Telen, Simon; Van Barel, Marc: A stabilized normal form algorithm for generic systems of polynomial equations (2018)

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