Bertini

Bertini™: Software for Numerical Algebraic Geometry Software for solving polynomial systems Finds isolated solutions using total-degree start systems, multihomogeneous-degree start systems, and also user defined homotopies. Implements parameter continuation for families of systems, such as the inverse kinematics of six-revolute serial-link arms, or the forward kinematics of Stewart-Gough parallel-link robots. Adaptive multiprecision implemented for finding isolated solutions and for the numerical irreducible decomposition. Treats positive-dimensional solutions by computing witness sets. Has automatic differentiation which preserves the straightline quality of an input system. Uses homogenization to accurately compute solutions ”at infinity.” Provides a fractional power-series endgame to accurately compute singular roots Allows for subfunctions. Allows for witness set manipulation via both sampling and membership testing. Accepts square or nonsquare systems.


References in zbMATH (referenced in 121 articles , 1 standard article )

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  1. Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes: Certifying solutions to overdetermined and singular polynomial systems over $\mathbbQ$ (2018)
  2. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  3. Breiding, Paul: The expected number of eigenvalues of a real Gaussian tensor (2017)
  4. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  5. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
  6. Hauenstein, Jonathan D.; Levandovskyy, Viktor: Certifying solutions to square systems of polynomial-exponential equations (2017)
  7. Hein, Nickolas; Sottile, Frank: A lifted square formulation for certifiable Schubert calculus (2017)
  8. Imbach, Rémi; Moroz, Guillaume; Pouget, Marc: A certified numerical algorithm for the topology of resultant and discriminant curves (2017)
  9. Mahdi, Adam; Pessoa, Claudio; Hauenstein, Jonathan D.: A hybrid symbolic-numerical approach to the center-focus problem (2017)
  10. Martín del Campo, Abraham; Rodriguez, Jose Israel: Critical points via monodromy and local methods (2017)
  11. Oeding, Luke: The quadrifocal variety (2017)
  12. Plestenjak, Bor: Minimal determinantal representations of bivariate polynomials (2017)
  13. Sturmfels, Bernd: The Hurwitz form of a projective variety (2017)
  14. Wu, Wenyuan; Zeng, Zhonggang: The numerical factorization of polynomials (2017)
  15. Zhang, Xuping; Zhang, Jintao; Yu, Bo: Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities (2017)
  16. Bates, Daniel J.; Hauenstein, Jonathan D.; Niemerg, Matthew E.; Sottile, Frank: Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials (2016)
  17. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew: BertiniLab: a MATLAB interface for solving systems of polynomial equations (2016)
  18. Boyd, John P.: Tracing multiple solution branches for nonlinear ordinary differential equations: Chebyshev and Fourier spectral methods and a degree-increasing spectral homotopy [DISH] (2016)
  19. Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. jun.: Decomposing solution sets of polynomial systems using derivatives (2016)
  20. Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.: Numerical local irreducible decomposition (2016)

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