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 233 articles , 1 standard article )

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  1. Arrondo, Enrique; Bernardi, Alessandra; Marques, Pedro Macias; Mourrain, Bernard: Skew-symmetric tensor decomposition (2021)
  2. Brysiewicz, Taylor: Necklaces count polynomial parametric osculants (2021)
  3. Collins, J. B.; Hauenstein, Jonathan D.: A singular value homotopy for finding critical parameter values (2021)
  4. 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)
  5. Hao, Wenrui: A gradient descent method for solving a system of nonlinear equations (2021)
  6. Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Solving determinantal systems using homotopy techniques (2021)
  7. Mourrain, Bernard; Telen, Simon; Van Barel, Marc: Truncated normal forms for solving polynomial systems: generalized and efficient algorithms (2021)
  8. Subramanian, P.; Kevrekidis, I. G.; Kevrekidis, P. G.: Exploring critical points of energy landscapes: from low-dimensional examples to phase field crystal PDEs (2021)
  9. Bernardi, Alessandra; Taufer, Daniele: Waring, tangential and cactus decompositions (2020)
  10. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  11. 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)
  12. Brakhage, Karl-Heinz; Niemeyer, Alice C.; Plesken, Wilhelm; Robertz, Daniel; Strzelczyk, Ansgar: The icosahedra of edge length 1 (2020)
  13. Breiding, Paul; Sturmfels, Bernd; Timme, Sascha: 3264 conics in a second (2020)
  14. Brysiewicz, Taylor: Numerical software to compute Newton polytopes and tropical membership (2020)
  15. Clarke, Oliver; Mohammadi, Fatemeh; Rauh, Johannes: Conditional independence ideals with hidden variables (2020)
  16. DiPasquale, Michael; Flores, Zachary; Peterson, Chris: On the apolar algebra of a product of linear forms (2020)
  17. Di Rocco, Sandra; Eklund, David; Weinstein, Madeleine: The bottleneck degree of algebraic varieties (2020)
  18. Friedland, Shmuel; Wang, Li: Spectral norm of a symmetric tensor and its computation (2020)
  19. Gäfvert, Oliver: Computational complexity of learning algebraic varieties (2020)
  20. Hao, Wenrui; Hesthaven, Jan; Lin, Guang; Zheng, Bin: A homotopy method with adaptive basis selection for computing multiple solutions of differential equations (2020)

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