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 254 articles , 1 standard article )

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  1. Angelini, Elena; Bocci, Cristiano; Chiantini, Luca: Catalecticant intersections and confinement of decompositions of forms (2022)
  2. Chen, Qipin; Hao, Wenrui; He, Juncai: A weight initialization based on the linear product structure for neural networks (2022)
  3. Dahan, Xavier: Lexicographic Gröbner bases of bivariate polynomials modulo a univariate one (2022)
  4. Frohmader, Andrew; Heaton, Alexander: Epsilon local rigidity and numerical algebraic geometry (2022)
  5. Hauenstein, Jonathan D.; Manivel, Laurent; Szendrői, Balázs: On the equations defining some Hilbert schemes (2022)
  6. Arrondo, Enrique; Bernardi, Alessandra; Marques, Pedro Macias; Mourrain, Bernard: Skew-symmetric tensor decomposition (2021)
  7. Ballico, Edoardo; Bernardi, Alessandra; Santarsiero, Pierpaola: Identifiability of rank-3 tensors (2021)
  8. Brysiewicz, Taylor: Necklaces count polynomial parametric osculants (2021)
  9. Cid-Ruiz, Yairon; Homs, Roser; Sturmfels, Bernd: Primary ideals and their differential equations (2021)
  10. Collins, J. B.; Hauenstein, Jonathan D.: A singular value homotopy for finding critical parameter values (2021)
  11. Dufresne, Emilie; Harrington, Heather A.; Hauenstein, Jonathan D.; Kevrekidis, Panayotis G.; Tripoli, Paolo: On some configurations of oppositely charged trapped vortices in the plane (2021)
  12. Frye, Charles G.; Simon, James; Wadia, Neha S.; Ligeralde, Andrew; Deweese, Michael R.; Bouchard, Kristofer E.: Critical point-finding methods reveal gradient-flat regions of deep network losses (2021)
  13. Gross, Elizabeth; Hill, Cvetelina: The steady-state degree and mixed volume of a chemical reaction network (2021)
  14. Hao, Wenrui: A gradient descent method for solving a system of nonlinear equations (2021)
  15. Hao, Wenrui; Zheng, Chunyue: A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations (2021)
  16. Hauenstein, Jonathan D.; Liddell, Alan C. jun.; McPherson, Sanesha; Zhang, Yi: Numerical algebraic geometry and semidefinite programming (2021)
  17. Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Solving determinantal systems using homotopy techniques (2021)
  18. He, Yang-Hui: The Calabi-Yau landscape. From geometry, to physics, to machine learning (2021)
  19. Imbach, Rémi; Pouget, Marc; Yap, Chee: Clustering complex zeros of triangular systems of polynomials (2021)
  20. Labahn, George; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Homotopy techniques for solving sparse column support determinantal polynomial systems (2021)

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