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 212 articles , 1 standard article )

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  1. Bernstein, Daniel Irving; Farnsworth, Cameron; Rodriguez, Jose Israel: The algebraic matroid of the finite unit norm tight frame (funtf) variety (2020)
  2. 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)
  3. Brakhage, Karl-Heinz; Niemeyer, Alice C.; Plesken, Wilhelm; Robertz, Daniel; Strzelczyk, Ansgar: The icosahedra of edge length 1 (2020)
  4. Breiding, Paul; Sturmfels, Bernd; Timme, Sascha: 3264 conics in a second (2020)
  5. Clarke, Oliver; Mohammadi, Fatemeh; Rauh, Johannes: Conditional independence ideals with hidden variables (2020)
  6. Di Rocco, Sandra; Eklund, David; Weinstein, Madeleine: The bottleneck degree of algebraic varieties (2020)
  7. Friedland, Shmuel; Wang, Li: Spectral norm of a symmetric tensor and its computation (2020)
  8. Hao, Wenrui; Hesthaven, Jan; Lin, Guang; Zheng, Bin: A homotopy method with adaptive basis selection for computing multiple solutions of differential equations (2020)
  9. Hao, Wenrui; Zheng, Chunyue: An adaptive homotopy method for computing bifurcations of nonlinear parametric systems (2020)
  10. Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
  11. Hauenstein, Jonathan D.; Regan, Margaret H.: Real monodromy action (2020)
  12. Hauenstein, Jonathan D.; Rodriguez, Jose Israel: Multiprojective witness sets and a trace test (2020)
  13. Jafarloo, Iman Bahmani; Calussi, Gabriele: Weak Hadamard star configurations and apolarity (2020)
  14. Kogan, Irina A.; Ruddy, Michael; Vinzant, Cynthia: Differential signatures of algebraic curves (2020)
  15. Lairez, Pierre: Rigid continuation paths. I: Quasilinear average complexity for solving polynomial systems (2020)
  16. Ovchinnikov, Alexey; Pogudin, Gleb; Scanlon, Thomas: Effective difference elimination and nullstellensatz (2020)
  17. Seigal, Anna: Ranks and symmetric ranks of cubic surfaces (2020)
  18. Telen, Simon: Numerical root finding via Cox rings (2020)
  19. Adamer, Michael F.; Helmer, Martin: Complexity of model testing for dynamical systems with toric steady states (2019)
  20. Améndola, Carlos; Friz, Peter; Sturmfels, Bernd: Varieties of signature tensors (2019)

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