Magma swMATH ID: 540 Software Authors: W. Bosma, A. Steel, G. Matthews, D. Fisher, J. Cannon, S. Contini, B. Smith Description: Computer algebra system (CAS). Magma is a large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatorics. It provides a mathematically rigorous environment for defining and working with structures such as groups, rings, fields, modules, algebras, schemes, curves, graphs, designs, codes and many others. Magma also supports a number of databases designed to aid computational research in those areas of mathematics which are algebraic in nature. The overview provides a summary of Magma’s main features. One of the aims whilst developing Magma is to maintain extensive documentation describing the features of the system. This handbook is available online. The documentation section should help introduce new users to the Magma language. Magma is distributed by the Computational Algebra Group at the University of Sydney. Its development has benefited enormously from contributions made by many members of the mathematical community. We encourage all users to report any bugs they find; regular patch fixes are available from the downloads section. Homepage: http://magma.maths.usyd.edu.au/magma/ Keywords: orms Related Software: GAP; SageMath; PARI/GP; SINGULAR; Maple; Code Tables; ATLAS Group Representations; Macaulay2; ecdata; LMFDB; GitHub; Mathematica; OEIS; FGb; NTL; MeatAxe; nauty; GAP Character Table Library; CTblLib; CoCoA Cited in: 3,506 Publications This software is also referenced in ORMS. Further Publications: http://magma.maths.usyd.edu.au/magma/citations/ Standard Articles 5 Publications describing the Software, including 5 Publications in zbMATH Year Magma – a tool for number theory. Zbl 1294.68153Cannon, John; Donnelly, Steve; Fieker, Claus; Watkins, Mark 2010 Appendix: the Magma language. Zbl 1151.11064Bailey, Geoff 2006 Discovering mathematics with Magma. Reducing the abstract to the concrete. Zbl 1104.11002Bosma, Wieb (ed.); Cannon, John (ed.) 2006 The Magma algebra system. I: The user language. Zbl 0898.68039Bosma, Wieb; Cannon, John; Playoust, Catherine 1997 Programming with algebraic structures: Design of the Magma language. Zbl 0964.68595Bosma, Wieb; Cannon, John; Matthews, Graham 1994 all top 5 Cited by 3,308 Authors 74 Conder, Marston Donald Edward 55 Praeger, Cheryl Elisabeth 52 O’Brien, Eamonn A. 48 Feng, Yanquan 45 Zhou, Jinxin 43 Harada, Masaaki 36 Key, Jennifer D. 35 Leemans, Dimitri 35 Spiga, Pablo 28 Crnković, Dean 28 Giudici, Michael 27 Rodrigues, Bernardo Gabriel 27 Siksek, Samir 26 Burness, Timothy C. 26 Holt, Derek F. 26 Marušič, Dragan 25 Solé, Patrick 24 Cossidente, Antonio 23 Kutnar, Klavdija 23 Nebe, Gabriele 22 Moori, Jamshid 21 Kemper, Gregor 21 Voight, John Michael 20 de Graaf, Willem Adriaan 20 Potočnik, Primož 20 Stoll, Michael 20 Švob, Andrea 19 Bartoli, Daniele 19 Leedham-Green, Charles R. 18 Ebert, Gary Lee 18 González-Jiménez, Enrique 18 Kaya, Abidin 18 Li, Caiheng 18 Pan, Jiangmin 18 Rowley, Peter J. 17 Grassl, Markus 17 Hajdu, Lajos 17 Özbudak, Ferruh 17 Roney-Dougal, Colva M. 16 Aydin, Nuh 16 Humphries, Stephen P. 16 Liebeck, Martin Walter 16 Munemasa, Akihiro 16 Schost, Éric 16 Steinwandt, Rainer 16 Xia, Binzhou 15 Cannon, John J. 15 Faugère, Jean-Charles 15 Tonchev, Vladimir D. 15 Yildiz, Bahattin 14 Carlson, Jon Frederick 14 Eick, Bettina 14 Fisher, Tom A. 14 Prakash, Om 14 Sutherland, Andrew V. 14 Tengely, Szabolcs 13 Egan, Ronan 13 Elsenhans, Andreas-Stephan 13 Flannery, Dane Laurence 13 Guralnick, Robert Michael 13 Lewis, Mark L. 13 Malnič, Aleksander 13 Marino, Giuseppe 13 Najman, Filip 13 Pavese, Francesco 13 Rouse, Jeremy A. 13 Stein, William A. 13 Wehlau, David Louis 13 Zhou, Shenglin 12 Devillers, Alice 12 Fish, Washiela 12 Fu, Fangwei 12 Gao, Jian 12 Havas, George 12 Islam, Habibul 12 Kim, Jon-Lark 12 Kovács, István 12 Lee, Yoonjin 12 Marcugini, Stefano 12 Pambianco, Fernanda 12 Shank, R. James 12 Šparl, Primož 12 Ulas, Maciej 11 Balakrishnan, Jennifer S. 11 Bennett, Michael A. 11 Bosma, Wieb 11 Castryck, Wouter 11 Dietrich, Heiko 11 Glasby, Stephen Peter 11 Jahnel, Jörg 11 Mwambene, Eric 11 Parker, Chris W. 11 Prins, Abraham Love 11 Sonnino, Angelo 11 Várilly-Alvarado, Anthony 11 Villanueva, Mercè 10 An, Jianbei 10 Araya, Makoto 10 Artebani, Michela 10 Brooksbank, Peter A. ...and 3,208 more Authors all top 5 Cited in 378 Serials 288 Journal of Algebra 158 Journal of Symbolic Computation 157 Designs, Codes and Cryptography 125 Journal of Number Theory 118 Discrete Mathematics 109 Mathematics of Computation 99 Finite Fields and their Applications 62 Journal of Algebraic Combinatorics 54 Journal of Pure and Applied Algebra 54 Transactions of the American Mathematical Society 52 Journal of Combinatorial Theory. Series A 50 European Journal of Combinatorics 48 Advances in Mathematics of Communications 46 International Journal of Number Theory 45 LMS Journal of Computation and Mathematics 45 Cryptography and Communications 43 Acta Arithmetica 42 Journal de Théorie des Nombres de Bordeaux 37 Applicable Algebra in Engineering, Communication and Computing 34 Communications in Algebra 34 Experimental Mathematics 33 Research in Number Theory 32 Advances in Mathematics 32 The Electronic Journal of Combinatorics 31 Journal of Combinatorial Theory. Series B 31 Proceedings of the American Mathematical Society 31 Graphs and Combinatorics 29 Mathematische Zeitschrift 29 Journal of Group Theory 24 Israel Journal of Mathematics 24 Archiv der Mathematik 22 Journal of Algebra and its Applications 21 Ars Mathematica Contemporanea 18 Discrete Applied Mathematics 18 Rocky Mountain Journal of Mathematics 17 International Journal of Algebra and Computation 17 Journal of Algebra, Combinatorics, Discrete Structures and Applications 15 Journal of Geometry 15 The Ramanujan Journal 15 Mathematics in Computer Science 14 Journal of Cryptology 13 Journal of the London Mathematical Society. Second Series 12 Bulletin of the London Mathematical Society 12 Compositio Mathematica 12 Monatshefte für Mathematik 12 Journal of Combinatorial Designs 12 Documenta Mathematica 12 Advances in Geometry 11 Mathematical Proceedings of the Cambridge Philosophical Society 11 Periodica Mathematica Hungarica 11 Linear Algebra and its Applications 11 Transformation Groups 11 Journal of Applied Mathematics and Computing 11 ACM Communications in Computer Algebra 11 Science China. Mathematics 11 Forum of Mathematics, Sigma 10 Bulletin of the Australian Mathematical Society 10 Applied Mathematics and Computation 10 Manuscripta Mathematica 10 Mathematische Annalen 10 Proceedings of the London Mathematical Society. Third Series 10 Turkish Journal of Mathematics 10 Journal of Integer Sequences 10 Journal of the Australian Mathematical Society 10 International Journal of Group Theory 9 Indian Journal of Pure & Applied Mathematics 9 Annales de l’Institut Fourier 9 Journal of Graph Theory 9 Theoretical Computer Science 9 Journal of Mathematical Cryptology 8 Journal für die Reine und Angewandte Mathematik 8 Discrete & Computational Geometry 8 Glasnik Matematički. Serija III 8 The Australasian Journal of Combinatorics 8 The New York Journal of Mathematics 8 Algebras and Representation Theory 8 Acta Mathematica Sinica. English Series 8 Integers 8 SIAM Journal on Applied Algebra and Geometry 7 Beiträge zur Algebra und Geometrie 7 Duke Mathematical Journal 7 Geometriae Dedicata 7 Journal of Complexity 7 IMRN. International Mathematics Research Notices 7 Journal of High Energy Physics 7 Quantum Information Processing 7 Discrete Mathematics, Algorithms and Applications 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 6 International Journal of Theoretical Physics 6 Information Processing Letters 6 Functiones et Approximatio. Commentarii Mathematici 6 Journal of the Mathematical Society of Japan 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 Proceedings of the Japan Academy. Series A 6 Bulletin of the Korean Mathematical Society 6 Revista Matemática Iberoamericana 6 Indagationes Mathematicae. New Series 6 Computational and Applied Mathematics 6 Selecta Mathematica. New Series 6 Journal of the European Mathematical Society (JEMS) ...and 278 more Serials all top 5 Cited in 52 Fields 1,213 Number theory (11-XX) 1,036 Group theory and generalizations (20-XX) 713 Information and communication theory, circuits (94-XX) 689 Combinatorics (05-XX) 685 Algebraic geometry (14-XX) 335 Computer science (68-XX) 215 Commutative algebra (13-XX) 196 Geometry (51-XX) 135 Field theory and polynomials (12-XX) 132 Associative rings and algebras (16-XX) 97 Quantum theory (81-XX) 82 Nonassociative rings and algebras (17-XX) 68 Convex and discrete geometry (52-XX) 59 Manifolds and cell complexes (57-XX) 54 Numerical analysis (65-XX) 50 Linear and multilinear algebra; matrix theory (15-XX) 41 Dynamical systems and ergodic theory (37-XX) 38 Functions of a complex variable (30-XX) 25 Order, lattices, ordered algebraic structures (06-XX) 24 Topological groups, Lie groups (22-XX) 21 Algebraic topology (55-XX) 16 Category theory; homological algebra (18-XX) 16 \(K\)-theory (19-XX) 16 Several complex variables and analytic spaces (32-XX) 14 Special functions (33-XX) 14 Biology and other natural sciences (92-XX) 13 Differential geometry (53-XX) 12 Operations research, mathematical programming (90-XX) 9 General and overarching topics; collections (00-XX) 8 Probability theory and stochastic processes (60-XX) 8 Statistics (62-XX) 6 Ordinary differential equations (34-XX) 6 Partial differential equations (35-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Functional analysis (46-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Relativity and gravitational theory (83-XX) 4 Fluid mechanics (76-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 History and biography (01-XX) 3 Mechanics of particles and systems (70-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) Citations by Year