Regina swMATH ID: 4862 Software Authors: B.A. Burton, R. Budney, W. Pettersson, et al. Description: Computational topology with Regina: algorithms, heuristics and implementations. Regina is a software package for studying 3-manifold triangulations and normal surfaces. It includes a graphical user interface and Python bindings, and also supports angle structures, census enumeration, combinatorial recognition of triangulations, and high-level functions such as 3-sphere recognition, unknot recognition and connected sum decomposition. par This paper brings 3-manifold topologists up-to-date with Regina as it appears today, and documents for the first time in the literature some of the key algorithms, heuristics and implementations that are central to Regina’s performance. These include the all-important simplification heuristics, key choices of data structures and algorithms to alleviate bottlenecks in normal surface enumeration, modern implementations of 3-sphere recognition and connected sum decomposition, and more. We also give some historical background for the project, including the key role played by Rubinstein in its genesis 15 years ago, and discuss current directions for future development. Homepage: https://regina-normal.github.io Keywords: 3-manifolds; algorithms; software; simplification; normal surfaces; recognition; angle structures Related Software: SnapPy; SnapPea; GitHub; SageMath; Normaliz; simpcomp; polymake; GAP; LibTW; FXrays; Library of Triangulations; Homology; Gfan; Macaulay2; Magma; ComputeTW; SCIP; gmp; Veering; bdyslopes Cited in: 49 Publications This software is also referenced in ORMS. all top 5 Cited by 57 Authors 19 Burton, Benjamin A. 9 Spreer, Jonathan 8 Tillmann, Stephan 6 Rubinstein, J. Hyam 4 Maria, Clément 2 Dunfield, Nathan M. 2 Garoufalidis, Stavros 2 Lindblom, Lee 2 Matveev, Sergeĭ Vladimirovich 2 Özlen, Melih 2 Segerman, Henry 1 Battista, Ludovico 1 Bruns, Winfried 1 Casella, Alex 1 Dadd, Blake 1 Dell, Holger 1 Downey, Rodney Graham 1 Duan, Aochen 1 Fominykh, Evgeny Anatol’evich 1 Friedl, Stefan 1 Futer, David 1 Gill, Montek 1 Goodman, Jacob Eli 1 Görner, Matthias 1 Hodgson, Craig D. 1 Huszár, Kristóf 1 Joswig, Michael 1 Kang, Ensil 1 Kawauchi, Akio 1 Khe, Alexander K. 1 Kolpakov, Alexander A. 1 Komusiewicz, Christian 1 Lewiner, Thomas 1 Lofano, Davide 1 Luo, Feng 1 Lutz, Frank Hagen 1 Martelli, Bruno 1 O’Rourke, Joseph 1 Paixão, João 1 Purcell, Jessica Shepherd 1 Reid, Alan W. 1 Rinne, Oliver 1 Riolo, Stefano 1 Sieg, Richard 1 Siejakowski, Rafał Marian 1 Söger, Christof 1 Talmon, Nimrod 1 Tayama, Ikuo 1 Taylor, Nicholas W. 1 Taylor, Samuel Joseph 1 Tóth, Csaba D. 1 Tsuruga, Mimi 1 Vesnin, Andrei Yu. 1 Wagner, Uli 1 Weller, Mathias 1 Worden, William 1 Zhang, Fan all top 5 Cited in 27 Serials 5 Proceedings of the American Mathematical Society 3 Discrete & Computational Geometry 3 Journal of Applied and Computational Topology 2 ACM Transactions on Mathematical Software 2 Transactions of the American Mathematical Society 2 Experimental Mathematics 2 Algebraic & Geometric Topology 1 General Relativity and Gravitation 1 Israel Journal of Mathematics 1 Journal of Computational Physics 1 Russian Mathematical Surveys 1 Mathematics of Computation 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Tôhoku Mathematical Journal. Second Series 1 Topology and its Applications 1 Algorithmica 1 L’Enseignement Mathématique. 2e Série 1 Journal of Knot Theory and its Ramifications 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 The New York Journal of Mathematics 1 Foundations of Computational Mathematics 1 Graduate Studies in Mathematics 1 Algorithms and Computation in Mathematics 1 Groups, Geometry, and Dynamics 1 Quantum Topology 1 Discrete Mathematics and its Applications all top 5 Cited in 18 Fields 44 Manifolds and cell complexes (57-XX) 12 Computer science (68-XX) 6 Convex and discrete geometry (52-XX) 5 Combinatorics (05-XX) 3 Algebraic geometry (14-XX) 2 Geometry (51-XX) 2 Relativity and gravitational theory (83-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year