Bertini_real swMATH ID: 9933 Software Authors: Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, CharlesW. Description: 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. Homepage: http://bertinireal.com/ Keywords: numerical algebraic geometry; cell decomposition; algebraic surface; algebraic curve; homotopy continuation; deflation Related Software: Bertini; Kronecker; ISOLATE; CGAL; FGb; HomotopyContinuation; PHCpack; Magma; insulate; HOM4PS; Macaulay2; Polytop; javaPlex; Blender; SMRSOFT; alphaCertified; Sostools; Paramotopy; Matlab; CoCoA Cited in: 14 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 976: Bertini_real: numerical decomposition of real algebraic curves and surfaces. Zbl 1484.14109Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 2017 all top 5 Cited by 27 Authors 6 Hauenstein, Jonathan D. 5 Bates, Daniel J. 5 Brake, Daniel A. 4 Sommese, Andrew John 4 Wampler, Charles W. II 3 Safey El Din, Mohab 3 Schost, Éric 3 Vu, Thi Xuan 2 Brake, Dani A. 2 Hao, Wenrui 2 Labahn, George 1 Brake, Danielle A. 1 Calussi, Gabriele 1 Chen, Changbo 1 Faugère, Jean-Charles 1 Feng, Yong 1 Hauenstein, Jon D. 1 Hong, Hoon 1 Jafarloo, Iman Bahmani 1 Kalhor, Ahmad 1 Liddell, Alan C. jun. 1 Maciejewski, Anthony A. 1 Putkaradze, Vakhtang 1 Regan, Margaret H. 1 Wu, Wenyuan 1 Yap, Chee-Keng 1 Zarei, Mojtaba all top 5 Cited in 7 Serials 2 Journal of Symbolic Computation 1 Rocky Mountain Journal of Mathematics 1 ACM Transactions on Mathematical Software 1 Automatica 1 Journal of Complexity 1 Journal of Systems Science and Complexity 1 Lecture Notes in Computer Science all top 5 Cited in 9 Fields 8 Algebraic geometry (14-XX) 6 Computer science (68-XX) 5 Numerical analysis (65-XX) 4 Commutative algebra (13-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Mechanics of particles and systems (70-XX) 1 Systems theory; control (93-XX) Citations by Year