## 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; ecdata; Macaulay2; Mathematica; LMFDB; GitHub; OEIS; FGb; NTL; MeatAxe; nauty; GAP Character Table Library; CTblLib; CoCoA Referenced in: 3,357 Publications This software is also referenced in ORMS. Further Publications: http://magma.maths.usyd.edu.au/magma/citations/
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### Referenced by 3,170 Authors

 71 Conder, Marston D. E. 54 Praeger, Cheryl Elisabeth 52 O’Brien, Eamonn A. 48 Feng, Yanquan 43 Zhou, Jinxin 42 Harada, Masaaki 35 Key, Jennifer D. 35 Spiga, Pablo 34 Leemans, Dimitri 27 Crnković, Dean 27 Giudici, Michael 27 Rodrigues, Bernardo Gabriel 26 Marušič, Dragan 25 Holt, Derek F. 25 Siksek, Samir 24 Cossidente, Antonio 24 Solé, Patrick 23 Burness, Timothy C. 23 Kutnar, Klavdija 23 Nebe, Gabriele 21 Kemper, Gregor 21 Moori, Jamshid 20 de Graaf, Willem Adriaan 20 Potočnik, Primož 20 Švob, Andrea 19 Bartoli, Daniele 19 Leedham-Green, Charles R. 19 Stoll, Michael 19 Voight, John Michael 18 Ebert, Gary Lee 18 González-Jiménez, Enrique 18 Li, Caiheng 17 Grassl, Markus 17 Hajdu, Lajos 17 Kaya, Abidin 17 Özbudak, Ferruh 17 Pan, Jiangmin 16 Humphries, Stephen P. 16 Liebeck, Martin Walter 16 Munemasa, Akihiro 16 Roney-Dougal, Colva M. 16 Schost, Éric 16 Steinwandt, Rainer 15 Aydin, Nuh 15 Cannon, John J. 15 Faugère, Jean-Charles 15 Rowley, Peter J. 15 Tonchev, Vladimir D. 15 Yildiz, Bahattin 14 Carlson, Jon Frederick 14 Eick, Bettina 14 Tengely, Szabolcs 14 Xia, Binzhou 13 Egan, Ronan 13 Fisher, Tom A. 13 Flannery, Dane Laurence 13 Guralnick, Robert Michael 13 Lewis, Mark L. 13 Malnič, Aleksander 13 Marino, Giuseppe 13 Najman, Filip 13 Prakash, Om 13 Stein, William A. 13 Zhou, Shenglin 12 Fish, Washiela 12 Fu, Fangwei 12 Gao, Jian 12 Havas, George 12 Kim, Jon-Lark 12 Kovács, István 12 Marcugini, Stefano 12 Pambianco, Fernanda 12 Pavese, Francesco 12 Rouse, Jeremy A. 12 Shank, R. James 12 Šparl, Primož 12 Sutherland, Andrew V. 12 Ulas, Maciej 12 Wehlau, David Louis 11 Devillers, Alice 11 Dietrich, Heiko 11 Elsenhans, Andreas-Stephan 11 Islam, Habibul 11 Lee, Yoonjin 11 Mwambene, Eric 11 Prins, Abraham Love 11 Sonnino, Angelo 11 Várilly-Alvarado, Anthony 11 Villanueva, Mercè 10 An, Jianbei 10 Araya, Makoto 10 Artebani, Michela 10 Balakrishnan, Jennifer S. 10 Bennett, Michael A. 10 Bosma, Wieb 10 Brooksbank, Peter A. 10 Dougherty, Steven T. 10 Kirschmer, Markus 10 Mellinger, Keith E. 10 Mignotte, Maurice ...and 3,070 more Authors
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### Referenced in 367 Serials

 281 Journal of Algebra 154 Designs, Codes and Cryptography 153 Journal of Symbolic Computation 123 Journal of Number Theory 114 Discrete Mathematics 102 Mathematics of Computation 96 Finite Fields and their Applications 62 Journal of Algebraic Combinatorics 53 Transactions of the American Mathematical Society 52 Journal of Pure and Applied Algebra 51 Journal of Combinatorial Theory. Series A 50 European Journal of Combinatorics 47 Advances in Mathematics of Communications 45 LMS Journal of Computation and Mathematics 44 International Journal of Number Theory 42 Cryptography and Communications 41 Journal de Théorie des Nombres de Bordeaux 40 Acta Arithmetica 36 Applicable Algebra in Engineering, Communication and Computing 34 Communications in Algebra 32 Experimental Mathematics 32 The Electronic Journal of Combinatorics 31 Proceedings of the American Mathematical Society 30 Graphs and Combinatorics 29 Advances in Mathematics 29 Journal of Combinatorial Theory. Series B 27 Mathematische Zeitschrift 26 Journal of Group Theory 24 Archiv der Mathematik 23 Israel Journal of Mathematics 22 Journal of Algebra and its Applications 21 Ars Mathematica Contemporanea 21 Research in Number Theory 18 Discrete Applied Mathematics 17 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 Mathematics in Computer Science 14 The Ramanujan Journal 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 Cryptology 12 Journal of Combinatorial Designs 12 Documenta Mathematica 11 Mathematical Proceedings of the Cambridge Philosophical Society 11 Periodica Mathematica Hungarica 11 Transformation Groups 11 Advances in Geometry 11 Science China. Mathematics 10 Bulletin of the Australian Mathematical Society 10 Applied Mathematics and Computation 10 Mathematische Annalen 10 Linear Algebra and its Applications 10 Journal of Integer Sequences 10 Journal of the Australian Mathematical Society 10 ACM Communications in Computer Algebra 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 Manuscripta Mathematica 9 Proceedings of the London Mathematical Society. Third Series 9 Theoretical Computer Science 9 Journal of Applied Mathematics and Computing 9 Journal of Mathematical Cryptology 9 Forum of Mathematics, Sigma 8 Journal für die Reine und Angewandte Mathematik 8 Discrete & Computational Geometry 8 Glasnik Matematički. Serija III 8 The New York Journal of Mathematics 8 Algebras and Representation Theory 8 Acta Mathematica Sinica. English Series 7 Beiträge zur Algebra und Geometrie 7 Duke Mathematical Journal 7 Geometriae Dedicata 7 IMRN. International Mathematics Research Notices 7 The Australasian Journal of Combinatorics 7 Integers 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 SIAM Journal on Applied Algebra and Geometry 6 International Journal of Theoretical Physics 6 Information Processing Letters 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 Journal of Complexity 6 Revista Matemática Iberoamericana 6 Indagationes Mathematicae. New Series 6 Selecta Mathematica. New Series 6 Journal of the European Mathematical Society (JEMS) 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Contributions to Discrete Mathematics 6 Algebra & Number Theory 6 Discrete Mathematics, Algorithms and Applications 5 IEEE Transactions on Information Theory 5 ACM Transactions on Mathematical Software ...and 267 more Serials
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### Referenced in 52 Fields

 1,139 Number theory (11-XX) 1,001 Group theory and generalizations (20-XX) 679 Information and communication theory, circuits (94-XX) 670 Combinatorics (05-XX) 641 Algebraic geometry (14-XX) 328 Computer science (68-XX) 210 Commutative algebra (13-XX) 192 Geometry (51-XX) 131 Field theory and polynomials (12-XX) 126 Associative rings and algebras (16-XX) 84 Quantum theory (81-XX) 79 Nonassociative rings and algebras (17-XX) 64 Convex and discrete geometry (52-XX) 59 Manifolds and cell complexes (57-XX) 53 Numerical analysis (65-XX) 48 Linear and multilinear algebra; matrix theory (15-XX) 38 Functions of a complex variable (30-XX) 38 Dynamical systems and ergodic theory (37-XX) 24 Order, lattices, ordered algebraic structures (06-XX) 24 Topological groups, Lie groups (22-XX) 19 Algebraic topology (55-XX) 15 Category theory; homological algebra (18-XX) 15 $$K$$-theory (19-XX) 15 Several complex variables and analytic spaces (32-XX) 14 Special functions (33-XX) 14 Biology and other natural sciences (92-XX) 11 Differential geometry (53-XX) 11 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)