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 203 articles , 1 standard article )

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  1. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  2. Bozorgmanesh, Hassan; Hajarian, Masoud: Solving tensor E-eigenvalue problem faster (2020)
  3. Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas: Identifying the parametric occurrence of multiple steady states for some biological networks (2020)
  4. Cheng, Jin-San; Dou, Xiaojie; Wen, Junyi: A new deflation method for verifying the isolated singular zeros of polynomial systems (2020)
  5. Hao, Wenrui; Zheng, Chunyue: An adaptive homotopy method for computing bifurcations of nonlinear parametric systems (2020)
  6. Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
  7. Menini, Laura; Possieri, Corrado; Tornambè, Antonio: A symbolic algorithm to compute immersions of polynomial systems into linear ones up to an output injection (2020)
  8. Telen, Simon: Numerical root finding via Cox rings (2020)
  9. Vidunas, Raimundas; He, Yang-Hui: Genus one Belyi maps by quadratic correspondences (2020)
  10. Zhu, Lailai; Stone, Howard A.: Harnessing elasticity to generate self-oscillation via an electrohydrodynamic instability (2020)
  11. Adamer, Michael F.; Helmer, Martin: Complexity of model testing for dynamical systems with toric steady states (2019)
  12. 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)
  13. Chen, Justin; Kileel, Joe: Numerical implicitization: a Macaulay2 package (2019)
  14. Chen, Tianran: Unmixing the mixed volume computation (2019)
  15. Gallardo-Alvarado, Jaime: An application of the Newton-homotopy continuation method for solving the forward kinematic problem of the 3-RRS parallel manipulator (2019)
  16. Kosta, Dimitra; Kubjas, Kaie: Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry (2019)
  17. Leykin, Anton; Yu, Josephine: Beyond polyhedral homotopies (2019)
  18. Obatake, Nida; Shiu, Anne; Tang, Xiaoxian; Torres, Angélica: Oscillations and bistability in a model of ERK regulation (2019)
  19. 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)
  20. Bliss, Nathan; Verschelde, Jan: The method of Gauss-Newton to compute power series solutions of polynomial homotopies (2018)

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