Bertini_real

Algorithm 976 Bertini_real: software for one- and two-dimensional real algebraic sets. Bertini_real is a command line program for numerically decomposing the real portion of a one- or two-dimensional complex irreducible algebraic set in any reasonable number of variables. Using numerical homotopy continuation to solve a series of polynomial systems via regeneration from a witness set, a set of real vertices is computed, along with connection information and associated homotopy functions. The challenge of embedded singular curves is overcome using isosingular deflation. This decomposition captures the topological information and can be used for further computation and refinement.


References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Solving determinantal systems using homotopy techniques (2021)
  2. Labahn, George; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan: Homotopy techniques for solving sparse column support determinantal polynomial systems (2021)
  3. Chen, Changbo; Wu, Wenyuan; Feng, Yong: Visualizing planar and space implicit real algebraic curves with singularities (2020)
  4. Jafarloo, Iman Bahmani; Calussi, Gabriele: Weak Hadamard star configurations and apolarity (2020)
  5. Brake, Danielle A.; Hauenstein, Jonathan D.; Regan, Margaret H.: polyTop: software for computing topology of smooth real surfaces (2018)
  6. Zarei, Mojtaba; Kalhor, Ahmad; Brake, Dani: Arc length based maximal Lyapunov functions and domains of attraction estimation for polynomial nonlinear systems (2018)
  7. Bates, Daniel J.; Brake, Dani A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W.: Homotopies for connected components of algebraic sets with application to computing critical sets (2017)
  8. Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W.: Algorithm 976: Bertini(_-)real: numerical decomposition of real algebraic curves and surfaces (2017)
  9. Brake, Daniel A.; Bates, Daniel J.; Putkaradze, Vakhtang; Maciejewski, Anthony A.: Workspace multiplicity and fault tolerance of cooperating robots (2016)
  10. Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C.: Validating the completeness of the real solution set of a system of polynomial equations (2016)
  11. Bates, Daniel J.; Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W.: On computing a cell decomposition of a real surface containing infinitely many singularities (2014)
  12. Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W.: Bertini_real: software for one- and two-dimensional real algebraic sets (2014)
  13. Hong, Hoon (ed.); Yap, Chee (ed.): Mathematical software -- ICMS 2014. 4th international congress, Seoul, South Korea, August 5--9, 2014. Proceedings (2014)