ApaTools: a software toolbox for approximate polynomial algebra Approximate polynomial algebra becomes an emerging area of study in recent years with a broad spectrum of applications. In this paper, we present a software toolbox ApaTools for approximate polynomial algebra. This package includes Maple and Matlab functions implementing advanced numerical algorithms for practical applications, as well as basic utility routines that can be used as building blocks for developing other numerical and symbolic methods in computational algebra.

References in zbMATH (referenced in 17 articles , 2 standard articles )

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  1. Moir, Robert H. C.; Corless, Robert M.; Maza, Marc Moreno; Xie, Ning: Symbolic-numeric integration of rational functions (2020)
  2. Usevich, Konstantin; Markovsky, Ivan: Variable projection methods for approximate (greatest) common divisor computations (2017)
  3. Wu, Wenyuan; Zeng, Zhonggang: The numerical factorization of polynomials (2017)
  4. Robert Krone: Numerical Hilbert functions for Macaulay2 (2014) arXiv
  5. Hao, Wenrui; Sommese, Andrew J.; Zeng, Zhonggang: Algorithm 931, an algorithm and software for computing multiplicity structures at zeros of nonlinear systems (2013)
  6. Terui, Akira: GPGCD: an iterative method for calculating approximate GCD of univariate polynomials (2013)
  7. Dayton, Barry H.; Li, Tien-Yien; Zeng, Zhonggang: Multiple zeros of nonlinear systems (2011)
  8. Di Rocco, Sandra; Eklund, David; Peterson, Chris; Sommese, Andrew J.: Chern numbers of smooth varieties via homotopy continuation and intersection theory (2011)
  9. Zeng, Zhonggang: The numerical greatest common divisor of univariate polynomials (2011)
  10. Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J.: A numerical local dimension test for points on the solution set of a system of polynomial equations (2009)
  11. Zeng, Zhonggang: The approximate irreducible factorization of a univariate polynomial. Revisited (2009)
  12. Zeng, Zhonggang: The closedness subspace method for computing the multiplicity structure of a polynomial system (2009)
  13. Zeng, Zhonggang: Regularization and matrix computation in numerical polynomial algebra (2009)
  14. Stillman, Michael E. (ed.); Takayama, Nobuki (ed.); Verschelde, Jan (ed.): Software for algebraic geometry. Papers of a workshop, Minneapolis, MN, USA, October 23--27, 2006 (2008)
  15. Zeng, Zhonggang: A numerical elimination method for polynomial computations (2008)
  16. Zeng, Zhonggang: ApaTools: a software toolbox for approximate polynomial algebra (2008)
  17. Zeng, Zhonggang: ApaTools: a software toolbox for approximate polynomial algebra (2008)