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 138 articles , 1 standard article )

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  1. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  2. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  3. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
  4. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew: BertiniLab: a MATLAB interface for solving systems of polynomial equations (2016)
  5. Chen, Liping; Han, Lixing; Zhou, Liangmin: Computing tensor eigenvalues via homotopy methods (2016)
  6. De Loera, Jesús A.; Petrović, Sonja; Stasi, Despina: Random sampling in computational algebra: Helly numbers and violator spaces (2016)
  7. Gross, Elizabeth; Harrington, Heather A.; Rosen, Zvi; Sturmfels, Bernd: Algebraic systems biology: a case study for the Wnt pathway (2016)
  8. Hauenstein, Jonathan D.; Liddell, Alan C.: Certified predictor-corrector tracking for Newton homotopies (2016)
  9. Helmer, Martin: Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties (2016)
  10. Jensen, Anders; Leykin, Anton; Yu, Josephine: Computing tropical curves via homotopy continuation (2016)
  11. Jiao, Libin; Dong, Bo; Zhang, Jintao; Yu, Bo: Polynomial homotopy method for the sparse interpolation problem. I: Equally spaced sampling (2016)
  12. Plestenjak, Bor; Hochstenbach, Michiel E.: Roots of bivariate polynomial systems via determinantal representations (2016)
  13. Bliss, Nathan; Sommars, Jeff; Verschelde, Jan; Yu, Xiangcheng: Solving polynomial systems in the cloud with polynomial homotopy continuation (2015)
  14. Feng, Yong; Wu, Wenyuan; Zhang, Jingzhong; Chen, Jingwei: Exact bivariate polynomial factorization over $\mathbb Q$ by approximation of roots (2015)
  15. Hochstenbach, Michiel E.; Muhič, Andrej; Plestenjak, Bor: Jacobi-Davidson methods for polynomial two-parameter eigenvalue problems (2015)
  16. Rodriguez, Jose Israel: Combinatorial excess intersection (2015)
  17. Bates, Daniel J.; Davis, Brent; Eklund, David; Hanson, Eric; Peterson, Chris: Perturbed homotopies for finding all isolated solutions of polynomial systems (2014)
  18. Bates, Daniel J.; Niemerg, Matthew: Using monodromy to avoid high precision in homotopy continuation (2014)
  19. Batselier, Kim; Dreesen, Philippe; De Moor, Bart: The canonical decomposition of $\mathcalC^n_d$ and numerical Gröbner and border bases (2014)
  20. Batselier, Kim; Dreesen, Philippe; De Moor, Bart: On the null spaces of the Macaulay matrix (2014)

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