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 197 articles , 1 standard article )

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  1. 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)
  2. Breiding, Paul; Sturmfels, Bernd; Timme, Sascha: 3264 conics in a second (2020)
  3. Hao, Wenrui; Hesthaven, Jan; Lin, Guang; Zheng, Bin: A homotopy method with adaptive basis selection for computing multiple solutions of differential equations (2020)
  4. Hao, Wenrui; Zheng, Chunyue: An adaptive homotopy method for computing bifurcations of nonlinear parametric systems (2020)
  5. Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
  6. Hauenstein, Jonathan D.; Regan, Margaret H.: Real monodromy action (2020)
  7. Lairez, Pierre: Rigid continuation paths. I: Quasilinear average complexity for solving polynomial systems (2020)
  8. Adamer, Michael F.; Helmer, Martin: Complexity of model testing for dynamical systems with toric steady states (2019)
  9. Améndola, Carlos; Friz, Peter; Sturmfels, Bernd: Varieties of signature tensors (2019)
  10. Angelini, Elena: Waring decompositions and identifiability via Bertini and Macaulay2 software (2019)
  11. Boyd, John: Strongly nonlinear perturbation theory for solitary waves and bions (2019)
  12. Brake, Danielle A.; Hauenstein, Jonathan D.; Vinzant, Cynthia: Computing complex and real tropical curves using monodromy (2019)
  13. Chen, Justin; Kileel, Joe: Numerical implicitization: a Macaulay2 package (2019)
  14. Christandl, Matthias; Gesmundo, Fulvio; Jensen, Asger Kjærulff: Border rank is not multiplicative under the tensor product (2019)
  15. Conradi, Carsten; Iosif, Alexandru; Kahle, Thomas: Multistationarity in the space of total concentrations for systems that admit a monomial parametrization (2019)
  16. Hao, Wenrui; Yang, Yong: Convergence of a homotopy finite element method for computing steady states of Burgers’ equation (2019)
  17. Hauenstein, Jonathan D.; Oeding, Luke; Ottaviani, Giorgio; Sommese, Andrew J.: Homotopy techniques for tensor decomposition and perfect identifiability (2019)
  18. Kosta, Dimitra; Kubjas, Kaie: Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry (2019)
  19. Ren, Yue; Martini, Johannes W. R.; Torres, Jacinta: Decoupled molecules with binding polynomials of bidegree ((n,2)) (2019)
  20. Sertöz, Emre Can: Computing periods of hypersurfaces (2019)

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