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Regina

swMATH ID: 4862
Software Authors: Burton, B. A.; Budney, R.; Pettersson, W.; 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; Normaliz; SageMath; simpcomp; GAP; polymake; LibTW; lrs; FXrays; MathOverflow; Dionysus; CHomP; PHAT; Library of Triangulations; Homology; Gfan; Macaulay2; Magma
Cited in: 62 Documents
This software is also referenced in ORMS.
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Cited by 89 Authors

19 Burton, Benjamin A.
9 Spreer, Jonathan
8 Tillmann, Stephan
6 Rubinstein, J. Hyam
4 Maria, Clément
3 Dunfield, Nathan M.
3 Lindblom, Lee
3 Martelli, Bruno
2 Garoufalidis, Stavros
2 Huszár, Kristóf
2 Kegel, Marc
2 Matveev, Sergeĭ Vladimirovich
2 Özlen, Melih
2 Rinne, Oliver
2 Segerman, Henry
1 Anderson, Chris K.
1 Ayaz, Fethi
1 Baker, Kenneth L.
1 Barkeshli, Maissam
1 Battista, Ludovico
1 Bruns, Winfried
1 Bulmash, Daniel
1 Cartin, Daniel
1 Casali, Maria Rita
1 Casella, Alex
1 Cristofori, Paola
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 Gabai, David
1 Gill, Montek Singh
1 Goodman, Jacob Eli
1 Görner, Matthias
1 Hodgson, Craig D.
1 Ichihara, Kazuhiro
1 Italiano, Giovanni
1 Joswig, Michael
1 Kang, Ensil
1 Kawauchi, Akio
1 Khe, Alexander K.
1 Kobayashi, Ryohei
1 Koda, Yuya
1 Kolpakov, Alexander A.
1 Komusiewicz, Christian
1 Le, Khanh
1 Lewiner, Thomas
1 Lofano, Davide
1 Luo, Feng
1 Lutz, Frank Hagen
1 Meyerhoff, Robert
1 Migliorini, Matteo
1 Mohnke, Klaus
1 Naoe, Hironobu
1 Nishimura, Yuya
1 Obeidin, Malik
1 Onaran, Sinem Çelik
1 O’Rourke, Joseph
1 Paixão, João
1 Purcell, Jessica Shepherd
1 Reid, Alan W.
1 Riolo, Stefano
1 Rudd, Cameron Gates
1 Sangston, Geoffrey
1 Sieg, Richard
1 Siejakowski, Rafał Marian
1 Söger, Christof
1 Talmon, Nimrod
1 Tani, Sei’ichi
1 Tata, Srivatsa
1 Tayama, Ikuo
1 Taylor, Nicholas W.
1 Taylor, Samuel Joseph
1 Thurston, Nathaniel
1 Tóth, Csaba D.
1 Tripp, Samuel
1 Tsang, Chi Cheuk
1 Tsuruga, Mimi
1 Vesnin, Andrei Yu.
1 Wagner, Uli
1 Weller, Mathias
1 Wood, Adam
1 Worden, William
1 Wright, Ana
1 Yarmola, Andrew
1 Zhang, Fan
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Cited in 32 Serials

5 Proceedings of the American Mathematical Society
4 Discrete & Computational Geometry
3 Experimental Mathematics
3 Journal of Applied and Computational Topology
2 Journal of Computational Physics
2 ACM Transactions on Mathematical Software
2 Inventiones Mathematicae
2 Transactions of the American Mathematical Society
2 Journal of Knot Theory and its Ramifications
2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
2 The New York Journal of Mathematics
2 Algebraic & Geometric Topology
1 Communications in Mathematical Physics
1 General Relativity and Gravitation
1 Israel Journal of Mathematics
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal of Mathematical Physics
1 Russian Mathematical Surveys
1 Mathematics of Computation
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 Revista Matemática Complutense
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
1 CGT. Computing in Geometry and Topology
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Cited in 25 Fields

55 Manifolds and cell complexes (57-XX)
13 Computer science (68-XX)
6 Convex and discrete geometry (52-XX)
5 Combinatorics (05-XX)
3 Algebraic geometry (14-XX)
3 Geometry (51-XX)
3 Relativity and gravitational theory (83-XX)
3 Operations research, mathematical programming (90-XX)
2 Number theory (11-XX)
2 Group theory and generalizations (20-XX)
2 Dynamical systems and ergodic theory (37-XX)
2 Differential geometry (53-XX)
2 General topology (54-XX)
2 Numerical analysis (65-XX)
1 History and biography (01-XX)
1 Commutative algebra (13-XX)
1 Topological groups, Lie groups (22-XX)
1 Functions of a complex variable (30-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Partial differential equations (35-XX)
1 Algebraic topology (55-XX)
1 Mechanics of particles and systems (70-XX)
1 Quantum theory (81-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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