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 111 articles , 1 standard article )

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  1. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  2. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  3. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
  4. Hauenstein, Jonathan D.; Levandovskyy, Viktor: Certifying solutions to square systems of polynomial-exponential equations (2017)
  5. Hein, Nickolas; Sottile, Frank: A lifted square formulation for certifiable Schubert calculus (2017)
  6. Imbach, Rémi; Moroz, Guillaume; Pouget, Marc: A certified numerical algorithm for the topology of resultant and discriminant curves (2017)
  7. Martín del Campo, Abraham; Rodriguez, Jose Israel: Critical points via monodromy and local methods (2017)
  8. Oeding, Luke: The quadrifocal variety (2017)
  9. Sturmfels, Bernd: The Hurwitz form of a projective variety (2017)
  10. Bates, Daniel J.; Hauenstein, Jonathan D.; Niemerg, Matthew E.; Sottile, Frank: Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials (2016)
  11. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew: BertiniLab: a MATLAB interface for solving systems of polynomial equations (2016)
  12. Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell Jr., Alan C.: Decomposing solution sets of polynomial systems using derivatives (2016)
  13. Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.: Numerical local irreducible decomposition (2016)
  14. Chen, Liping; Han, Lixing; Zhou, Liangmin: Computing tensor eigenvalues via homotopy methods (2016)
  15. Daleo, Noah S.; Hauenstein, Jonathan D.: Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme (2016)
  16. Daleo, Noah S.; Hauenstein, Jonathan D.; Oeding, Luke: Computations and equations for Segre-Grassmann hypersurfaces (2016)
  17. De Loera, Jesús A.; Petrović, Sonja; Stasi, Despina: Random sampling in computational algebra: Helly numbers and violator spaces (2016)
  18. Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R.: The Euclidean distance degree of an algebraic variety (2016)
  19. Gross, Elizabeth; Harrington, Heather A.; Rosen, Zvi; Sturmfels, Bernd: Algebraic systems biology: a case study for the Wnt pathway (2016)
  20. Hauenstein, Jonathan D.; Hein, Nickolas; Sottile, Frank: A primal-dual formulation for certifiable computations in Schubert calculus (2016)

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