hikmot swMATH ID: 34524 Software Authors: Hoffman, Neil; Ichihara, Kazuhiro; Kashiwagi, Masahide; Masai, Hidetoshi; Oishi, Shin’ichi; Takayasu, Akitoshi Description: HIKMOT is a python module that can be used for verified computations for hyperbolic 3-manifolds. This is based on the procedure in the following paper: Verified computations for hyperbolic 3-manifolds. For a given cusped 3-manifold M admitting an ideal triangulation, we describe a method to rigorously prove that either M or a filling of M admits a complete hyperbolic structure via verified computer calculations. Central to our method are an implementation of interval arithmetic and Krawczyk’s Test. These techniques represent an improvement over existing algorithms as they are faster, while accounting for error accumulation in a more direct and user friendly way. Homepage: http://www.oishi.info.waseda.ac.jp/~takayasu/hikmot/ Dependencies: Python Related Software: SnapPy; SnapPea; GitHub; Regina; Magma; GAP; bfh_python; Veering; Macaulay2; Coq Interval; cheeky; Coq; Twister; Snap; Boost C++ Libraries; KnotInfo Cited in: 13 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Verified computations for hyperbolic 3-manifolds. Zbl 1337.57044Hoffman, Neil; Ichihara, Kazuhiro; Kashiwagi, Masahide; Masai, Hidetoshi; Oishi, Shin’ichi; Takayasu, Akitoshi 2016 all top 5 Cited by 25 Authors 2 Akbulut, Selman 2 Dunfield, Nathan M. 2 Ichihara, Kazuhiro 2 Masai, Hidetoshi 2 Ruberman, Daniel 1 Auckly, David R. 1 Brock, Jeffrey F. 1 Casella, Alex 1 Haraway, Robert C. III 1 Hoffman, Neil R. 1 Jong, In Dae 1 Kashiwagi, Masahide 1 Katerba, Charles 1 Kim, Hee Jung 1 Lin, Francesco 1 Lipnowski, Michael 1 Melvin, Paul M. 1 Oishi, Shin’ichi 1 Paoluzzi, Luisa 1 Sakuma, Makoto 1 Takayasu, Akitoshi 1 Tanaka, Toshifumi 1 Tillmann, Stephan 1 Worden, William 1 Yildiz, Eylem Zeliha all top 5 Cited in 9 Serials 2 Osaka Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Experimental Mathematics 1 Commentarii Mathematici Helvetici 1 Inventiones Mathematicae 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Topology and its Applications 1 Journal of the American Mathematical Society 1 Journal of Gökova Geometry Topology GGT Cited in 4 Fields 13 Manifolds and cell complexes (57-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) Citations by Year