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; GitHub; LMFDB; Macaulay2; ecdata; Mathematica; OEIS; FGb; NTL; nauty; GAP Character Table Library; MeatAxe; CTblLib; CHEVIE Cited in: 3,755 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 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 3,488 Authors 78 Conder, Marston Donald Edward 55 Praeger, Cheryl Elisabeth 53 O’Brien, Eamonn A. 51 Feng, Yanquan 49 Zhou, Jinxin 46 Harada, Masaaki 38 Key, Jennifer D. 35 Leemans, Dimitri 35 Spiga, Pablo 31 Solé, Patrick 30 Crnković, Dean 30 Rodrigues, Bernardo Gabriel 29 Burness, Timothy C. 28 Giudici, Michael 27 Holt, Derek F. 27 Marušič, Dragan 27 Siksek, Samir 25 Cossidente, Antonio 25 Nebe, Gabriele 24 Kutnar, Klavdija 24 Voight, John Michael 22 Moori, Jamshid 22 Švob, Andrea 21 Kemper, Gregor 21 Potočnik, Primož 21 Stoll, Michael 20 Aydin, Nuh 20 Bartoli, Daniele 20 de Graaf, Willem Adriaan 20 Özbudak, Ferruh 20 Prakash, Om 19 González-Jiménez, Enrique 19 Grassl, Markus 19 Kaya, Abidin 19 Leedham-Green, Charles R. 19 Pan, Jiangmin 18 Ebert, Gary Lee 18 Humphries, Stephen P. 18 Li, Caiheng 18 Roney-Dougal, Colva M. 18 Rowley, Peter J. 18 Xia, Binzhou 17 Gao, Jian 17 Hajdu, Lajos 17 Kim, Jon-Lark 17 Tonchev, Vladimir D. 16 Fu, Fangwei 16 Islam, Habibul 16 Liebeck, Martin Walter 16 Munemasa, Akihiro 16 Schost, Éric 16 Steinwandt, Rainer 16 Zhou, Shenglin 15 Cannon, John J. 15 Eick, Bettina 15 Elsenhans, Andreas-Stephan 15 Faugère, Jean-Charles 15 Yildiz, Bahattin 14 Carlson, Jon Frederick 14 Fisher, Tom A. 14 Guralnick, Robert Michael 14 Korban, Adrian 14 Lewis, Mark L. 14 Marcugini, Stefano 14 Marino, Giuseppe 14 Najman, Filip 14 Pambianco, Fernanda 14 Pavese, Francesco 14 Rouse, Jeremy A. 14 Sutherland, Andrew V. 14 Tengely, Szabolcs 14 Wehlau, David Louis 13 Balakrishnan, Jennifer S. 13 Dougherty, Steven T. 13 Egan, Ronan 13 Fish, Washiela 13 Flannery, Dane Laurence 13 Jahnel, Jörg 13 Malnič, Aleksander 13 Šparl, Primož 13 Stein, William A. 12 Araya, Makoto 12 Castryck, Wouter 12 Devillers, Alice 12 Havas, George 12 Kovács, István 12 Laface, Antonio 12 Lee, Yoonjin 12 Morgan, Luke 12 Mwambene, Eric 12 Shank, R. James 12 Shi, Minjia 12 Ulas, Maciej 12 Villanueva, Mercè 11 Bennett, Michael A. 11 Bosma, Wieb 11 Daniels, Harris B. 11 Dietrich, Heiko 11 Gildea, Joe 11 Glasby, Stephen Peter ...and 3,388 more Authors all top 5 Cited in 384 Serials 297 Journal of Algebra 175 Designs, Codes and Cryptography 161 Journal of Symbolic Computation 131 Discrete Mathematics 131 Journal of Number Theory 110 Mathematics of Computation 109 Finite Fields and their Applications 68 Journal of Algebraic Combinatorics 57 Advances in Mathematics of Communications 56 Transactions of the American Mathematical Society 55 Journal of Pure and Applied Algebra 52 Journal of Combinatorial Theory. Series A 52 European Journal of Combinatorics 49 International Journal of Number Theory 48 Cryptography and Communications 45 Acta Arithmetica 45 LMS Journal of Computation and Mathematics 44 Journal de Théorie des Nombres de Bordeaux 43 Applicable Algebra in Engineering, Communication and Computing 41 Experimental Mathematics 41 Research in Number Theory 37 Communications in Algebra 34 Advances in Mathematics 33 Journal of Combinatorial Theory. Series B 33 Proceedings of the American Mathematical Society 33 Graphs and Combinatorics 33 Journal of Group Theory 32 The Electronic Journal of Combinatorics 30 Mathematische Zeitschrift 25 Israel Journal of Mathematics 25 Journal of Algebra and its Applications 24 Archiv der Mathematik 23 Quantum Information Processing 21 Ars Mathematica Contemporanea 19 Discrete Applied Mathematics 19 International Journal of Algebra and Computation 18 Rocky Mountain Journal of Mathematics 18 Journal of Algebra, Combinatorics, Discrete Structures and Applications 16 Mathematics in Computer Science 15 Journal of Geometry 15 The Ramanujan Journal 14 Journal of Cryptology 14 Journal of Applied Mathematics and Computing 14 Forum of Mathematics, Sigma 13 Compositio Mathematica 13 Journal of the London Mathematical Society. Second Series 13 Documenta Mathematica 13 Advances in Geometry 12 Applied Mathematics and Computation 12 Bulletin of the London Mathematical Society 12 Monatshefte für Mathematik 12 Journal of Combinatorial Designs 12 Transformation Groups 11 Indian Journal of Pure & Applied Mathematics 11 Mathematical Proceedings of the Cambridge Philosophical Society 11 Periodica Mathematica Hungarica 11 Annales de l’Institut Fourier 11 Manuscripta Mathematica 11 Linear Algebra and its Applications 11 Journal of the Australian Mathematical Society 11 ACM Communications in Computer Algebra 11 Science China. Mathematics 11 International Journal of Group Theory 11 SIAM Journal on Applied Algebra and Geometry 10 Bulletin of the Australian Mathematical Society 10 Mathematische Annalen 10 Proceedings of the London Mathematical Society. Third Series 10 Turkish Journal of Mathematics 10 Journal of Integer Sequences 9 Journal of Graph Theory 9 Journal für die Reine und Angewandte Mathematik 9 Theoretical Computer Science 9 Revista Matemática Iberoamericana 9 Journal of High Energy Physics 9 Integers 9 Journal of Mathematical Cryptology 8 International Journal of Theoretical Physics 8 Duke Mathematical Journal 8 Geometriae Dedicata 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 Mediterranean Journal of Mathematics 8 Discrete Mathematics, Algorithms and Applications 8 The Art of Discrete and Applied Mathematics 7 Beiträge zur Algebra und Geometrie 7 Journal of Complexity 7 IMRN. International Mathematics Research Notices 7 Indagationes Mathematicae. New Series 7 Computational and Applied Mathematics 7 Selecta Mathematica. New Series 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 Research in the Mathematical Sciences 6 Information Processing Letters 6 Canadian Mathematical Bulletin 6 Functiones et Approximatio. Commentarii Mathematici 6 Journal of the Mathematical Society of Japan ...and 284 more Serials all top 5 Cited in 52 Fields 1,303 Number theory (11-XX) 1,099 Group theory and generalizations (20-XX) 798 Information and communication theory, circuits (94-XX) 750 Combinatorics (05-XX) 741 Algebraic geometry (14-XX) 347 Computer science (68-XX) 222 Commutative algebra (13-XX) 206 Geometry (51-XX) 142 Field theory and polynomials (12-XX) 142 Associative rings and algebras (16-XX) 135 Quantum theory (81-XX) 88 Nonassociative rings and algebras (17-XX) 72 Convex and discrete geometry (52-XX) 68 Manifolds and cell complexes (57-XX) 56 Numerical analysis (65-XX) 52 Linear and multilinear algebra; matrix theory (15-XX) 43 Dynamical systems and ergodic theory (37-XX) 39 Functions of a complex variable (30-XX) 26 Topological groups, Lie groups (22-XX) 24 Order, lattices, ordered algebraic structures (06-XX) 23 Algebraic topology (55-XX) 20 Several complex variables and analytic spaces (32-XX) 18 Category theory; homological algebra (18-XX) 16 Special functions (33-XX) 15 \(K\)-theory (19-XX) 14 Biology and other natural sciences (92-XX) 13 Differential geometry (53-XX) 12 Operations research, mathematical programming (90-XX) 10 General and overarching topics; collections (00-XX) 8 Probability theory and stochastic processes (60-XX) 8 Statistics (62-XX) 7 Partial differential equations (35-XX) 6 Ordinary differential equations (34-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Functional analysis (46-XX) 5 Relativity and gravitational theory (83-XX) 4 Mathematical logic and foundations (03-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 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of deformable solids (74-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