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; GitHub; LMFDB; SINGULAR; Maple; ATLAS Group Representations; ecdata; Macaulay2; Mathematica; OEIS; FGb; ell-adic-galois-images; CTblLib; nauty; NTL; GAP Character Table Library; MeatAxe Cited in: 4,380 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 3,972 Authors 83 Conder, Marston Donald Edward 71 Praeger, Cheryl Elisabeth 59 Zhou, Jinxin 57 Feng, Yanquan 56 O’Brien, Eamonn A. 52 Harada, Masaaki 42 Spiga, Pablo 38 Key, Jennifer D. 38 Leemans, Dimitri 37 Crnković, Dean 35 Burness, Timothy C. 35 Solé, Patrick 34 Voight, John Michael 32 Rodrigues, Bernardo Gabriel 31 Giudici, Michael 30 Siksek, Samir 28 Holt, Derek F. 28 Marušič, Dragan 28 Švob, Andrea 27 Özbudak, Ferruh 26 Kutnar, Klavdija 25 Cossidente, Antonio 25 Nebe, Gabriele 24 Aydin, Nuh 24 Stoll, Michael 23 de Graaf, Willem Adriaan 23 Fu, Fangwei 23 Kemper, Gregor 23 Moori, Jamshid 23 Potočnik, Primož 23 Prakash, Om 22 Bartoli, Daniele 22 Xia, Binzhou 21 Gao, Jian 21 Grassl, Markus 21 Kim, Jon-Lark 21 Korban, Adrian 21 Li, Caiheng 21 Zhou, Shenglin 20 Hajdu, Lajos 20 Humphries, Stephen P. 19 Devillers, Alice 19 González-Jiménez, Enrique 19 Kaya, Abidin 19 Leedham-Green, Charles R. 19 Munemasa, Akihiro 19 Pan, Jiangmin 19 Roney-Dougal, Colva M. 19 Rowley, Peter J. 19 Shi, Minjia 19 Sutherland, Andrew V. 18 Ebert, Gary Lee 18 Elsenhans, Andreas-Stephan 18 Islam, Habibul 18 Najman, Filip 18 Schost, Éric 18 Tonchev, Vladimir D. 18 Yin, Fugang 17 Guralnick, Robert Michael 17 Liebeck, Martin Walter 17 Pavese, Francesco 17 Rouse, Jeremy A. 17 Tengely, Szabolcs 16 Dougherty, Steven T. 16 Kovács, István 16 Marino, Giuseppe 16 Steinwandt, Rainer 15 Cannon, John J. 15 Castryck, Wouter 15 Eick, Bettina 15 Faugère, Jean-Charles 15 Kudo, Momonari 15 Laface, Antonio 15 Lewis, Mark L. 15 Marcugini, Stefano 15 Pambianco, Fernanda 15 Prins, Abraham Love 15 Šparl, Primož 15 Villanueva, Mercè 15 Wehlau, David Louis 15 Yildiz, Bahattin 14 Araya, Makoto 14 Carlson, Jon Frederick 14 Fisher, Tom A. 14 Flannery, Dane Laurence 14 Jahnel, Jörg 14 Lee, Yoonjin 14 Stein, William A. 13 Balakrishnan, Jennifer S. 13 Bennett, Michael A. 13 Dietrich, Heiko 13 Du, Jiali 13 Egan, Ronan 13 Fish, Washiela 13 Güneri, Cem 13 Malnič, Aleksander 13 Miezaki, Tsuyoshi 13 Rukavina, Sanja 13 Soydan, Gokhan 13 Ulas, Maciej ...and 3,872 more Authors all top 5 Cited in 403 Serials 312 Journal of Algebra 202 Designs, Codes and Cryptography 165 Journal of Symbolic Computation 151 Discrete Mathematics 145 Journal of Number Theory 131 Finite Fields and their Applications 124 Mathematics of Computation 77 Journal of Algebraic Combinatorics 77 Advances in Mathematics of Communications 63 International Journal of Number Theory 61 Journal of Combinatorial Theory. Series A 59 Journal of Pure and Applied Algebra 59 Transactions of the American Mathematical Society 57 Research in Number Theory 56 Cryptography and Communications 54 European Journal of Combinatorics 50 Journal de Théorie des Nombres de Bordeaux 49 Acta Arithmetica 49 Applicable Algebra in Engineering, Communication and Computing 48 Experimental Mathematics 45 Communications in Algebra 45 LMS Journal of Computation and Mathematics 40 Advances in Mathematics 37 Journal of Group Theory 35 Journal of Combinatorial Theory. Series B 35 Proceedings of the American Mathematical Society 35 Graphs and Combinatorics 35 The Electronic Journal of Combinatorics 34 Quantum Information Processing 33 Mathematische Zeitschrift 32 Journal of Algebra and its Applications 29 Israel Journal of Mathematics 26 Archiv der Mathematik 25 Bulletin of the London Mathematical Society 24 International Journal of Algebra and Computation 24 Ars Mathematica Contemporanea 23 Journal of Combinatorial Designs 21 Journal of the London Mathematical Society. Second Series 20 Journal of Applied Mathematics and Computing 19 Discrete Applied Mathematics 19 Rocky Mountain Journal of Mathematics 18 Journal of Algebra, Combinatorics, Discrete Structures and Applications 17 Journal of Geometry 17 The Ramanujan Journal 17 Advances in Geometry 17 Mathematics in Computer Science 17 Forum of Mathematics, Sigma 16 Journal of Graph Theory 16 Journal of Cryptology 16 ACM Communications in Computer Algebra 15 Computational and Applied Mathematics 14 Indian Journal of Pure & Applied Mathematics 14 Mathematical Proceedings of the Cambridge Philosophical Society 14 Manuscripta Mathematica 14 Proceedings of the London Mathematical Society. Third Series 13 Bulletin of the Australian Mathematical Society 13 Compositio Mathematica 13 Monatshefte für Mathematik 13 Linear Algebra and its Applications 13 Documenta Mathematica 13 Transformation Groups 13 International Journal of Group Theory 12 Applied Mathematics and Computation 12 Mathematische Annalen 12 Indagationes Mathematicae. New Series 12 Algebra & Number Theory 12 Science China. Mathematics 12 SIAM Journal on Applied Algebra and Geometry 11 Periodica Mathematica Hungarica 11 Annales de l’Institut Fourier 11 Glasnik Matematički. Serija III 11 Turkish Journal of Mathematics 11 Journal of the Australian Mathematical Society 11 Journal of Mathematical Cryptology 10 Theoretical Computer Science 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 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 9 Discrete Mathematics, Algorithms and Applications 9 European Journal of Mathematics 9 The Art of Discrete and Applied 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 Research in the Mathematical Sciences 7 Beiträge zur Algebra und Geometrie 7 ACM Transactions on Mathematical Software 7 Annali di Matematica Pura ed Applicata. Serie Quarta ...and 303 more Serials all top 5 Cited in 53 Fields 1,560 Number theory (11-XX) 1,254 Group theory and generalizations (20-XX) 954 Information and communication theory, circuits (94-XX) 883 Algebraic geometry (14-XX) 872 Combinatorics (05-XX) 366 Computer science (68-XX) 248 Commutative algebra (13-XX) 235 Geometry (51-XX) 166 Quantum theory (81-XX) 162 Field theory and polynomials (12-XX) 158 Associative rings and algebras (16-XX) 101 Nonassociative rings and algebras (17-XX) 87 Convex and discrete geometry (52-XX) 78 Manifolds and cell complexes (57-XX) 67 Linear and multilinear algebra; matrix theory (15-XX) 61 Numerical analysis (65-XX) 53 Dynamical systems and ergodic theory (37-XX) 45 Functions of a complex variable (30-XX) 32 Algebraic topology (55-XX) 29 Order, lattices, ordered algebraic structures (06-XX) 29 Topological groups, Lie groups (22-XX) 24 Several complex variables and analytic spaces (32-XX) 21 Category theory; homological algebra (18-XX) 17 Special functions (33-XX) 16 \(K\)-theory (19-XX) 16 Operations research, mathematical programming (90-XX) 16 Biology and other natural sciences (92-XX) 13 Differential geometry (53-XX) 11 Statistics (62-XX) 10 General and overarching topics; collections (00-XX) 9 Probability theory and stochastic processes (60-XX) 7 Partial differential equations (35-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Ordinary differential equations (34-XX) 6 Functional analysis (46-XX) 6 Relativity and gravitational theory (83-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Approximations and expansions (41-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 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