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. Bartzos, Evangelos; Emiris, Ioannis Z.; Legerský, Jan; Tsigaridas, Elias: On the maximal number of real embeddings of minimally rigid graphs in (\mathbbR^2,\mathbbR^3) and (S^2) (2021)
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  3. Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Solving determinantal systems using homotopy techniques (2021)
  4. Mourrain, Bernard; Telen, Simon; Van Barel, Marc: Truncated normal forms for solving polynomial systems: generalized and efficient algorithms (2021)
  5. Bartzos, Evangelos; Emiris, Ioannis Z.; Schicho, Josef: On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs (2020)
  6. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  7. Bozorgmanesh, Hassan; Hajarian, Masoud: Solving tensor E-eigenvalue problem faster (2020)
  8. Bozorgmanesh, Hassan; Hajarian, Masoud; Chronopoulos, Anthony Theodore: Interval tensors and their application in solving multi-linear systems of equations (2020)
  9. 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)
  10. Cheng, Jin-San; Dou, Xiaojie; Wen, Junyi: A new deflation method for verifying the isolated singular zeros of polynomial systems (2020)
  11. Hao, Wenrui; Zheng, Chunyue: An adaptive homotopy method for computing bifurcations of nonlinear parametric systems (2020)
  12. Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
  13. Hauenstein, Jonathan D.; Rodriguez, Jose Israel: Multiprojective witness sets and a trace test (2020)
  14. Krause, Andrew L.; Klika, Václav; Halatek, Jacob; Grant, Paul K.; Woolley, Thomas E.; Dalchau, Neil; Gaffney, Eamonn A.: Turing patterning in stratified domains (2020)
  15. Menini, Laura; Possieri, Corrado; Tornambè, Antonio: A symbolic algorithm to compute immersions of polynomial systems into linear ones up to an output injection (2020)
  16. Shirinkam, Sara; Alaeddini, Adel; Gross, Elizabeth: Identifying the number of components in Gaussian mixture models using numerical algebraic geometry (2020)
  17. Telen, Simon: Numerical root finding via Cox rings (2020)
  18. Telen, Simon; Van Barel, Marc; Verschelde, Jan: A robust numerical path tracking algorithm for polynomial homotopy continuation (2020)
  19. Vidunas, Raimundas; He, Yang-Hui: Genus one Belyi maps by quadratic correspondences (2020)
  20. Zhu, Lailai; Stone, Howard A.: Harnessing elasticity to generate self-oscillation via an electrohydrodynamic instability (2020)

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