Magma swMATH ID: 540 Software Authors: Bosma, W.; Steel, A.; Matthews, G.; Fisher, D.; Cannon, J.; Contini, S.; Smith, B. 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; Code Tables; PARI/GP; SINGULAR; Maple; GitHub; LMFDB; ATLAS Group Representations; Macaulay2; ecdata; Mathematica; OEIS; FGb; CTblLib; ell-adic-galois-images; nauty; NTL; GAP Character Table Library; MeatAxe Cited in: 4,195 Documents 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 Discovering mathematics with Magma. Reducing the abstract to the concrete. Zbl 1104.11002Bosma, Wieb (ed.); Cannon, John (ed.) 2006 Appendix: the Magma language. Zbl 1151.11064Bailey, Geoff 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 3,827 Authors 81 Conder, Marston Donald Edward 66 Praeger, Cheryl Elisabeth 59 Zhou, Jinxin 56 Feng, Yanquan 55 O’Brien, Eamonn A. 50 Harada, Masaaki 41 Spiga, Pablo 38 Key, Jennifer D. 36 Crnković, Dean 35 Leemans, Dimitri 34 Burness, Timothy C. 34 Solé, Patrick 32 Rodrigues, Bernardo Gabriel 31 Giudici, Michael 30 Voight, John Michael 29 Siksek, Samir 28 Holt, Derek F. 28 Švob, Andrea 27 Marušič, Dragan 26 Özbudak, Ferruh 25 Cossidente, Antonio 25 Nebe, Gabriele 24 Aydin, Nuh 24 Kutnar, Klavdija 23 Stoll, Michael 22 Bartoli, Daniele 22 de Graaf, Willem Adriaan 22 Kemper, Gregor 22 Moori, Jamshid 22 Potočnik, Primož 22 Prakash, Om 21 Fu, Fangwei 21 Gao, Jian 21 Grassl, Markus 21 Korban, Adrian 21 Xia, Binzhou 20 Kim, Jon-Lark 19 González-Jiménez, Enrique 19 Hajdu, Lajos 19 Humphries, Stephen P. 19 Kaya, Abidin 19 Leedham-Green, Charles R. 19 Li, Caiheng 19 Pan, Jiangmin 19 Roney-Dougal, Colva M. 19 Zhou, Shenglin 18 Devillers, Alice 18 Ebert, Gary Lee 18 Elsenhans, Andreas-Stephan 18 Islam, Habibul 18 Munemasa, Akihiro 18 Rowley, Peter J. 18 Shi, Minjia 18 Sutherland, Andrew V. 18 Tonchev, Vladimir D. 17 Guralnick, Robert Michael 17 Liebeck, Martin Walter 17 Najman, Filip 17 Pavese, Francesco 17 Schost, Éric 17 Yin, Fugang 16 Dougherty, Steven T. 16 Marino, Giuseppe 16 Steinwandt, Rainer 15 Cannon, John J. 15 Castryck, Wouter 15 Eick, Bettina 15 Faugère, Jean-Charles 15 Laface, Antonio 15 Marcugini, Stefano 15 Pambianco, Fernanda 15 Rouse, Jeremy A. 15 Tengely, Szabolcs 15 Villanueva, Mercè 15 Wehlau, David Louis 15 Yildiz, Bahattin 14 Carlson, Jon Frederick 14 Fisher, Tom A. 14 Flannery, Dane Laurence 14 Jahnel, Jörg 14 Kovács, István 14 Kudo, Momonari 14 Lewis, Mark L. 14 Šparl, Primož 13 Araya, Makoto 13 Balakrishnan, Jennifer S. 13 Egan, Ronan 13 Fish, Washiela 13 Güneri, Cem 13 Lee, Yoonjin 13 Malnič, Aleksander 13 Prins, Abraham Love 13 Soydan, Gokhan 13 Stein, William A. 13 Ulas, Maciej 12 Bennett, Michael A. 12 Dietrich, Heiko 12 Gildea, Joe 12 Glasby, Stephen Peter 12 Havas, George ...and 3,727 more Authors all top 5 Cited in 396 Serials 306 Journal of Algebra 196 Designs, Codes and Cryptography 165 Journal of Symbolic Computation 147 Discrete Mathematics 138 Journal of Number Theory 122 Finite Fields and their Applications 121 Mathematics of Computation 73 Journal of Algebraic Combinatorics 71 Advances in Mathematics of Communications 59 Journal of Combinatorial Theory. Series A 59 Journal of Pure and Applied Algebra 57 International Journal of Number Theory 56 Transactions of the American Mathematical Society 55 Cryptography and Communications 53 European Journal of Combinatorics 51 Research in Number Theory 48 Acta Arithmetica 47 Applicable Algebra in Engineering, Communication and Computing 47 Journal de Théorie des Nombres de Bordeaux 46 Experimental Mathematics 45 LMS Journal of Computation and Mathematics 43 Communications in Algebra 37 Advances in Mathematics 35 Graphs and Combinatorics 35 The Electronic Journal of Combinatorics 35 Journal of Group Theory 34 Journal of Combinatorial Theory. Series B 34 Proceedings of the American Mathematical Society 33 Mathematische Zeitschrift 33 Quantum Information Processing 32 Journal of Algebra and its Applications 29 Israel Journal of Mathematics 26 Archiv der Mathematik 25 Bulletin of the London Mathematical Society 24 Ars Mathematica Contemporanea 22 Journal of Combinatorial Designs 20 International Journal of Algebra and Computation 20 Journal of Applied Mathematics and Computing 19 Discrete Applied Mathematics 19 Rocky Mountain Journal of Mathematics 18 Journal of the London Mathematical Society. Second Series 18 Journal of Algebra, Combinatorics, Discrete Structures and Applications 17 Journal of Geometry 17 Mathematics in Computer Science 16 Journal of Cryptology 16 The Ramanujan Journal 16 Advances in Geometry 16 Forum of Mathematics, Sigma 14 Indian Journal of Pure & Applied Mathematics 14 Journal of Graph Theory 14 Computational and Applied Mathematics 14 ACM Communications in Computer Algebra 13 Bulletin of the Australian Mathematical Society 13 Compositio Mathematica 13 Monatshefte für Mathematik 13 Documenta Mathematica 13 Transformation Groups 12 Mathematical Proceedings of the Cambridge Philosophical Society 12 Applied Mathematics and Computation 12 Manuscripta Mathematica 12 Proceedings of the London Mathematical Society. Third Series 12 Indagationes Mathematicae. New Series 12 Science China. Mathematics 12 International Journal of Group Theory 11 Periodica Mathematica Hungarica 11 Annales de l’Institut Fourier 11 Mathematische Annalen 11 Glasnik Matematički. Serija III 11 Linear Algebra and its Applications 11 Turkish Journal of Mathematics 11 Journal of the Australian Mathematical Society 11 Journal of Mathematical Cryptology 11 SIAM Journal on Applied Algebra and Geometry 10 Expositiones Mathematicae 10 Journal of Integer Sequences 10 Integers 10 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 9 International Journal of Theoretical Physics 9 Geometriae Dedicata 9 Journal für die Reine und Angewandte Mathematik 9 Theoretical Computer Science 9 Revista Matemática Iberoamericana 9 The Australasian Journal of Combinatorics 9 Selecta Mathematica. New Series 9 Journal of High Energy Physics 9 Mediterranean Journal of Mathematics 8 Duke Mathematical Journal 8 Journal of the Mathematical Society of Japan 8 Discrete & Computational Geometry 8 The New York Journal of Mathematics 8 Algebras and Representation Theory 8 Acta Mathematica Sinica. English Series 8 Discrete Mathematics, Algorithms and Applications 8 Research in the Mathematical Sciences 8 European Journal of Mathematics 8 The Art of Discrete and Applied Mathematics 7 Beiträge zur Algebra und Geometrie 7 Nagoya Mathematical Journal 7 Journal of Complexity 7 IMRN. International Mathematics Research Notices ...and 296 more Serials all top 5 Cited in 53 Fields 1,483 Number theory (11-XX) 1,205 Group theory and generalizations (20-XX) 914 Information and communication theory, circuits (94-XX) 844 Combinatorics (05-XX) 842 Algebraic geometry (14-XX) 363 Computer science (68-XX) 237 Commutative algebra (13-XX) 228 Geometry (51-XX) 159 Quantum theory (81-XX) 156 Field theory and polynomials (12-XX) 153 Associative rings and algebras (16-XX) 97 Nonassociative rings and algebras (17-XX) 82 Convex and discrete geometry (52-XX) 73 Manifolds and cell complexes (57-XX) 62 Linear and multilinear algebra; matrix theory (15-XX) 59 Numerical analysis (65-XX) 49 Dynamical systems and ergodic theory (37-XX) 44 Functions of a complex variable (30-XX) 27 Order, lattices, ordered algebraic structures (06-XX) 27 Topological groups, Lie groups (22-XX) 26 Algebraic topology (55-XX) 23 Several complex variables and analytic spaces (32-XX) 20 Category theory; homological algebra (18-XX) 16 \(K\)-theory (19-XX) 16 Special functions (33-XX) 15 Operations research, mathematical programming (90-XX) 15 Biology and other natural sciences (92-XX) 12 Differential geometry (53-XX) 10 General and overarching topics; collections (00-XX) 10 Statistics (62-XX) 9 Probability theory and stochastic processes (60-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Partial differential equations (35-XX) 6 Ordinary differential equations (34-XX) 6 Relativity and gravitational theory (83-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Functional analysis (46-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) 4 Mathematics education (97-XX) 3 History and biography (01-XX) 3 Mathematical logic and foundations (03-XX) 3 Approximations and expansions (41-XX) 3 Mechanics of particles and systems (70-XX) 2 Measure and integration (28-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of deformable solids (74-XX) 1 General algebraic systems (08-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