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.

References in zbMATH (referenced in 15 articles )

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  1. Angelini, Elena; Galuppi, Francesco; Mella, Massimiliano; Ottaviani, Giorgio: On the number of Waring decompositions for a generic polynomial vector (2018)
  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. Krone, Robert; Leykin, Anton: Numerical algorithms for detecting embedded components (2017)
  5. Leykin, Anton; Plaumann, Daniel: Determinantal representations of hyperbolic curves via polynomial homotopy continuation (2017)
  6. Martín del Campo, Abraham; Rodriguez, Jose Israel: Critical points via monodromy and local methods (2017)
  7. Hauenstein, Jonathan D.; Liddell, Alan C.: Certified predictor-corrector tracking for Newton homotopies (2016)
  8. Leykin, Anton: Polynomial homotopy continuation in Macaulay2 (2016)
  9. Bates, Daniel J.; Niemerg, Matthew: Using monodromy to avoid high precision in homotopy continuation (2014)
  10. Beltrán, Carlos; Leykin, Anton: Robust certified numerical homotopy tracking (2013)
  11. Beltrán, Carlos; Pardo, Luis Miguel: Fast linear homotopy to find approximate zeros of polynomial systems (2011)
  12. Guan, Yun; Verschelde, Jan: Sampling algebraic sets in local intrinsic coordinates (2011)
  13. Leykin, Anton: Numerical algebraic geometry (2011)
  14. Anton Leykin: Numerical Algebraic Geometry for Macaulay2 (2009) arXiv
  15. Leykin, Anton: Numerical algebraic geometry for macaulay2 (2009) ioport