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 243 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. Arrondo, Enrique; Bernardi, Alessandra; Marques, Pedro Macias; Mourrain, Bernard: Skew-symmetric tensor decomposition (2021)
  3. Ballico, Edoardo; Bernardi, Alessandra; Santarsiero, Pierpaola: Identifiability of rank-3 tensors (2021)
  4. Brysiewicz, Taylor: Necklaces count polynomial parametric osculants (2021)
  5. Collins, J. B.; Hauenstein, Jonathan D.: A singular value homotopy for finding critical parameter values (2021)
  6. 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)
  7. 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)
  8. Gross, Elizabeth; Hill, Cvetelina: The steady-state degree and mixed volume of a chemical reaction network (2021)
  9. Hao, Wenrui: A gradient descent method for solving a system of nonlinear equations (2021)
  10. Hao, Wenrui; Zheng, Chunyue: A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations (2021)
  11. Hauenstein, Jonathan D.; Liddell, Alan C. jun.; McPherson, Sanesha; Zhang, Yi: Numerical algebraic geometry and semidefinite programming (2021)
  12. Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Solving determinantal systems using homotopy techniques (2021)
  13. Imbach, Rémi; Pouget, Marc; Yap, Chee: Clustering complex zeros of triangular systems of polynomials (2021)
  14. Labahn, George; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Homotopy techniques for solving sparse column support determinantal polynomial systems (2021)
  15. Mourrain, Bernard; Telen, Simon; Van Barel, Marc: Truncated normal forms for solving polynomial systems: generalized and efficient algorithms (2021)
  16. Pun, Chi Seng: (G)-expected utility maximization with ambiguous equicorrelation (2021)
  17. Subramanian, P.; Kevrekidis, I. G.; Kevrekidis, P. G.: Exploring critical points of energy landscapes: from low-dimensional examples to phase field crystal PDEs (2021)
  18. Bernardi, Alessandra; Taufer, Daniele: Waring, tangential and cactus decompositions (2020)
  19. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  20. Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas: Identifying the parametric occurrence of multiple steady states for some biological networks (2020)

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