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 137 articles , 1 standard article )

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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. Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes: Certifying solutions to overdetermined and singular polynomial systems over $\mathbbQ$ (2018)
  3. Bernardi, Alessandra; Gimigliano, Alessandro; Idà, Monica: Singularities of plane rational curves via projections (2018)
  4. Baharev, Ali; Domes, Ferenc; Neumaier, Arnold: A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations (2017)
  5. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  6. Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard: Tensor decomposition and homotopy continuation (2017)
  7. Boralevi, Ada; van Doornmalen, Jasper; Draisma, Jan; Hochstenbach, Michiel E.; Plestenjak, Bor: Uniform determinantal representations (2017)
  8. Breiding, Paul: The expected number of eigenvalues of a real Gaussian tensor (2017)
  9. Brown, David A.; Zingg, David W.: Design and evaluation of homotopies for efficient and robust continuation (2017)
  10. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  11. Cifuentes, Diego; Parrilo, Pablo A.: Sampling algebraic varieties for sum of squares programs (2017)
  12. Compagnoni, Marco; Notari, Roberto; Antonacci, Fabio; Sarti, Augusto: On the statistical model of source localization based on range difference measurements (2017)
  13. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
  14. Hauenstein, Jonathan D.; Levandovskyy, Viktor: Certifying solutions to square systems of polynomial-exponential equations (2017)
  15. Hein, Nickolas; Sottile, Frank: A lifted square formulation for certifiable Schubert calculus (2017)
  16. Helmer, Martin: A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties (2017)
  17. Imbach, Rémi; Moroz, Guillaume; Pouget, Marc: A certified numerical algorithm for the topology of resultant and discriminant curves (2017)
  18. Kileel, Joe: Minimal problems for the calibrated trifocal variety (2017)
  19. Mahdi, Adam; Pessoa, Claudio; Hauenstein, Jonathan D.: A hybrid symbolic-numerical approach to the center-focus problem (2017)
  20. Martín del Campo, Abraham; Rodriguez, Jose Israel: Critical points via monodromy and local methods (2017)

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