Numerical algebraic geometry. Numerical algebraic geometry uses numerical data to describe algebraic varieties. It is based on numerical polynomial homotopy continuation, which is an alternative to the classical symbolic approaches of computational algebraic geometry. We present a package, whose primary purpose is to interlink the existing symbolic methods of Macaulay2 and the powerful engine of numerical approximate computations. The core procedures of the package exhibit performance competitive with the other homotopy continuation software.

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  1. Duff, Timothy; Hein, Nickolas; Sottile, Frank: Certification for polynomial systems via square subsystems (2022)
  2. Hao, Wenrui; Zheng, Chunyue: A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations (2021)
  3. Leykin, Anton; Del Campo, Abraham Martín; Sottile, Frank; Vakil, Ravi; Verschelde, Jan: Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm (2021)
  4. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  5. 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)
  6. Hauenstein, Jonathan D.; Rodriguez, Jose Israel: Multiprojective witness sets and a trace test (2020)
  7. Duff, Timothy; Hill, Cvetelina; Jensen, Anders; Lee, Kisun; Leykin, Anton; Sommars, Jeff: Solving polynomial systems via homotopy continuation and monodromy (2019)
  8. Kosta, Dimitra; Kubjas, Kaie: Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry (2019)
  9. Angelini, Elena; Galuppi, Francesco; Mella, Massimiliano; Ottaviani, Giorgio: On the number of Waring decompositions for a generic polynomial vector (2018)
  10. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  11. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
  12. Krone, Robert; Leykin, Anton: Numerical algorithms for detecting embedded components (2017)
  13. Leykin, Anton; Plaumann, Daniel: Determinantal representations of hyperbolic curves via polynomial homotopy continuation (2017)
  14. Martín del Campo, Abraham; Rodriguez, Jose Israel: Critical points via monodromy and local methods (2017)
  15. Hauenstein, Jonathan D.; Liddell, Alan C.: Certified predictor-corrector tracking for Newton homotopies (2016)
  16. Leykin, Anton: Polynomial homotopy continuation in Macaulay2 (2016)
  17. Bates, Daniel J.; Niemerg, Matthew: Using monodromy to avoid high precision in homotopy continuation (2014)
  18. Beltrán, Carlos; Leykin, Anton: Robust certified numerical homotopy tracking (2013)
  19. Beltrán, Carlos; Pardo, Luis Miguel: Fast linear homotopy to find approximate zeros of polynomial systems (2011)
  20. Guan, Yun; Verschelde, Jan: Sampling algebraic sets in local intrinsic coordinates (2011)

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