SINGULAR

 swMATH ID: 866 Software Authors: Wolfram Decker; Gert-Martin Greuel; Gerhard Pfister; Hans Schönemann Description: SINGULAR is a Computer Algebra system (CAS) for polynomial computations in commutative algebra, algebraic geometry, and singularity theory. SINGULAR’s main computational objects are ideals and modules over a large variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields, the rationals, floats, algebraic extensions, transcendental extensions), or localizations thereof, or quotient rings with respect to an ideal. SINGULAR features fast and general implementations for computing Groebner and standard bases, including e.g. Buchberger’s algorithm and Mora’s Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy and free-resolution computations, and many more related functionalities. Based on an easy-to-use interactive shell and a C-like programming language, SINGULAR’s internal functionality is augmented and user-extendible by libraries written in the SINGULAR programming language. A general and efficient implementation of communication links allows SINGULAR to make its functionality available to other programs. Homepage: http://www.singular.uni-kl.de Reference Manual: http://www.singular.uni-kl.de/Manual/latest/index.htm Operating Systems: ix86-Linux, SunOS-5, IRIX-6, ix86-Win (runs on Windows 95/98/NT4/2000/XP/Vista), FreeBSD, MacOS X, x86_64-Linux (AMD64/Opteron/EM64T), IA64-Linux Keywords: orms; SINGULAR Related Software: Macaulay2; CoCoA; Magma; SageMath; Maple; primdec; GAP; Plural; Mathematica; Risa/Asir; FGb; Gfan; STRINGVACUA; Normaliz; PHCpack; polymake; Bertini; 4ti2; GitHub; Kan Referenced in: 1,508 Publications This software is also referenced in ORMS. Further Publications: http://www.singular.uni-kl.de/index.php/publications/singular-related-publications.html
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Referenced by 1,580 Authors

 52 Pfister, Gerhard 50 Romanovskiĭ, Valeriĭ Georgievich 41 Greuel, Gert-Martin 41 Levandovskyy, Viktor 28 Giné, Jaume 19 Decker, Wolfram 19 Schönemann, Hans 18 Hashemi, Amir 17 Böhm, Janko 17 Frühbis-Krüger, Anne 17 He, Yang-Hui Evariste 16 Dimca, Alexandru 16 Zerz, Eva 15 Sticlaru, Gabriel 13 Ferčec, Brigita 13 Lossen, Christoph 13 Seiler, Werner M. 12 Binyamin, Muhammad Ahsan 12 Bivià-Ausina, Carles 12 Falcón Ganfornina, Raúl Manuel 12 Movasati, Hossein 12 Nabeshima, Katsusuke 12 Schulze, Mathias 11 Herzog, Jürgen 11 La Scala, Roberto 11 Lee, Wanseok 11 Markwig, Thomas 11 Ren, Yue 11 Shafer, Douglas S. 11 Sottile, Frank 11 Walcher, Sebastian 10 Gray, James A. 10 Monagan, Michael B. 10 Planas-Vilanova, Francesc 10 Popescu, Dorin 10 Schenzel, Peter 10 Tajima, Shinichi 10 Valls Anglés, Cláudia 10 Villarreal, Rafael Heraclio 10 Wang, Dingkang 9 Bermejo, Isabel 9 Coutinho, S. C. 9 Dinwoodie, Ian Hepburn 9 Eder, Christian 9 Ene, Viviana 9 Gimenez, Philippe 9 Martin, Bernd 9 Peterson, Chris 8 Anderson, Lara B. 8 Brickenstein, Michael 8 Dumnicki, Marcin 8 Escudero, Juan García 8 Hauenstein, Jonathan D. 8 Heinle, Albert 8 Montes, Antonio 8 Park, Euisung 8 Stamate, Dumitru Ioan 8 Sturmfels, Bernd 8 Szemberg, Tomasz 8 Tutaj-Gasińska, Halszka 8 Wang, Mingsheng 7 Bates, Daniel J. 7 Bruns, Winfried 7 Dickenstein, Alicia M. 7 Drton, Mathias 7 Gatermann, Karin 7 Gerdt, Vladimir Petrovich 7 Keicher, Simon 7 Kemper, Gregor 7 Liu, Jinwang 7 Llibre, Jaume 7 Lu, Dong 7 Lukas, André 7 Martín-Morales, Jorge 7 Mehmood, Khawar 7 Nuño-Ballesteros, Juan José 7 Oliveira, Regilene D. S. 7 Pearce, Roman 7 Schreyer, Frank-Olaf 7 Sommese, Andrew John 7 Szpond, Justyna 7 Tuomela, Jukka 7 Zhang, Weinian 6 Braun, Volker 6 Brodmann, Markus P. 6 Chen, Xingwu 6 Elias, Juan 6 Guarino, Adolfo 6 Han, Maoan 6 Kapustka, Grzegorz 6 Khan, Junaid Alam 6 Malara, Grzegorz 6 Marais, Magdaleen S. 6 Markwig, Hannah 6 Mourrain, Bernard 6 Noro, Masayuki 6 Piipponen, Samuli 6 Röhrle, Gerhard E. 6 Sáenz de Cabezón Irigaray, Eduardo 6 Steenpaß, Andreas ...and 1,480 more Authors
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Referenced in 334 Serials

 161 Journal of Symbolic Computation 74 Journal of Algebra 48 Journal of High Energy Physics 37 Journal of Pure and Applied Algebra 23 Journal of Algebra and its Applications 19 Experimental Mathematics 17 Communications in Algebra 17 Mathematics of Computation 16 Mathematische Zeitschrift 14 Applied Mathematics and Computation 14 Proceedings of the American Mathematical Society 14 Multidimensional Systems and Signal Processing 14 Applicable Algebra in Engineering, Communication and Computing 14 Mathematics in Computer Science 13 Transactions of the American Mathematical Society 13 ACM Communications in Computer Algebra 12 Advances in Mathematics 11 Manuscripta Mathematica 11 Linear Algebra and its Applications 10 Advances in Applied Mathematics 10 Journal of Algebraic Combinatorics 10 Revista Matemática Complutense 10 Foundations of Computational Mathematics 9 Journal of Mathematical Analysis and Applications 9 Nuclear Physics. B 9 Mathematische Nachrichten 8 Communications in Mathematical Physics 8 Journal of Computational and Applied Mathematics 8 Journal of Differential Equations 8 Topology and its Applications 8 International Journal of Algebra and Computation 7 Compositio Mathematica 7 Bulletin of the Brazilian Mathematical Society. New Series 7 Journal of Physics A: Mathematical and Theoretical 6 Annales de l’Institut Fourier 6 Collectanea Mathematica 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 Studia Scientiarum Mathematicarum Hungarica 6 Discrete & Computational Geometry 6 International Journal of Mathematics 6 Bulletin des Sciences Mathématiques 6 Computer Science Journal of Moldova 6 Analele Științifice ale Universității “Ovidius” Constanța. Seria: Matematică 6 Qualitative Theory of Dynamical Systems 6 Central European Journal of Mathematics 6 Mediterranean Journal of Mathematics 6 Algorithms and Computation in Mathematics 5 Journal of Mathematical Biology 5 Rocky Mountain Journal of Mathematics 5 Archiv der Mathematik 5 Osaka Journal of Mathematics 5 Results in Mathematics 5 SIAM Journal on Discrete Mathematics 5 Journal of Algebraic Geometry 5 Advances in Geometry 5 Advances in High Energy Physics 5 Research in the Mathematical Sciences 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Annals of the Institute of Statistical Mathematics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Geometriae Dedicata 4 Journal of the London Mathematical Society. Second Series 4 Le Matematiche 4 Mathematics and Computers in Simulation 4 Michigan Mathematical Journal 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Programming and Computer Software 4 Rendiconti del Circolo Matemàtico di Palermo. Serie II 4 Semigroup Forum 4 Acta Applicandae Mathematicae 4 Bulletin of the Iranian Mathematical Society 4 Journal of Complexity 4 Designs, Codes and Cryptography 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Documenta Mathematica 4 Transformation Groups 4 Nonlinear Dynamics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of Singularities 4 Journal of Applied Analysis and Computation 3 Computers & Mathematics with Applications 3 Bulletin of Mathematical Biology 3 Beiträge zur Algebra und Geometrie 3 The Annals of Statistics 3 Annales Polonici Mathematici 3 Canadian Journal of Mathematics 3 Inventiones Mathematicae 3 Mathematische Annalen 3 Mathematica Scandinavica 3 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 3 Systems & Control Letters 3 Bulletin of the Korean Mathematical Society 3 Japan Journal of Industrial and Applied Mathematics 3 The Journal of Geometric Analysis 3 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série 3 Journal of Mathematical Sciences (New York) 3 The Electronic Journal of Combinatorics 3 Annals of Mathematics and Artificial Intelligence 3 Advances in Theoretical and Mathematical Physics ...and 234 more Serials
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Referenced in 56 Fields

 661 Algebraic geometry (14-XX) 647 Commutative algebra (13-XX) 334 Computer science (68-XX) 181 Several complex variables and analytic spaces (32-XX) 114 Ordinary differential equations (34-XX) 84 Quantum theory (81-XX) 74 Associative rings and algebras (16-XX) 73 Group theory and generalizations (20-XX) 65 Combinatorics (05-XX) 64 Dynamical systems and ergodic theory (37-XX) 64 Numerical analysis (65-XX) 57 Number theory (11-XX) 50 Information and communication theory, circuits (94-XX) 48 Linear and multilinear algebra; matrix theory (15-XX) 43 Convex and discrete geometry (52-XX) 39 Global analysis, analysis on manifolds (58-XX) 36 Biology and other natural sciences (92-XX) 36 Systems theory; control (93-XX) 35 Field theory and polynomials (12-XX) 31 Nonassociative rings and algebras (17-XX) 31 Statistics (62-XX) 27 Partial differential equations (35-XX) 24 Differential geometry (53-XX) 19 Geometry (51-XX) 18 General and overarching topics; collections (00-XX) 18 Manifolds and cell complexes (57-XX) 18 Mechanics of particles and systems (70-XX) 18 Relativity and gravitational theory (83-XX) 17 Operations research, mathematical programming (90-XX) 16 Special functions (33-XX) 15 Functions of a complex variable (30-XX) 12 Algebraic topology (55-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 Category theory; homological algebra (18-XX) 9 Real functions (26-XX) 8 Topological groups, Lie groups (22-XX) 8 Difference and functional equations (39-XX) 8 Probability theory and stochastic processes (60-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Mathematical logic and foundations (03-XX) 6 Mechanics of deformable solids (74-XX) 4 History and biography (01-XX) 4 General algebraic systems (08-XX) 4 Fluid mechanics (76-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 2 $$K$$-theory (19-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mathematics education (97-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)