SINGULAR swMATH ID: 866 Software Authors: Decker, Wolfram; Greuel, Gert-Martin; Pfister, Gerhard; Schönemann, Hans 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 Source Code: https://github.com/Singular/Singular 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; SageMath; Magma; Maple; GAP; primdec; Plural; Mathematica; Gfan; FGb; Risa/Asir; GitHub; polymake; Normaliz; Bertini; PHCpack; STRINGVACUA; 4ti2; homalg Cited in: 1,723 Documents This software is also referenced in ORMS. Further Publications: http://www.singular.uni-kl.de/index.php/publications/singular-related-publications.html Standard Articles 4 Publications describing the Software, including 4 Publications in zbMATH Year SINGULAR: a computer algebra system for polynomial computations. Zbl 1344.13002Greuel, G. M.; Pfister, G.; Schönemann, H. 2008 A Singular introduction to commutative algebra. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann. 2nd extended ed. Zbl 1133.13001Greuel, Gert-Martin; Pfister, Gerhard 2007 A Singular introduction to commutative algebra. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann. Zbl 1023.13001Greuel, Gert-Martin; Pfister, Gerhard 2002 SINGULAR: A computer algebra system for singularity theory, algebraic geometry and commutative algebra. Zbl 0902.14040Greuel, G.-M.; Pfister, G.; Schönemann, H. 1997 all top 5 Cited by 1,808 Authors 58 Pfister, Gerhard 53 Romanovskiĭ, Valeriĭ Georgievich 48 Greuel, Gert-Martin 43 Levandovskyy, Viktor 30 Giné, Jaume 21 Böhm, Janko 20 Frühbis-Krüger, Anne 20 Schönemann, Hans 19 Decker, Wolfram 19 Hashemi, Amir 18 Dimca, Alexandru 18 He, Yang-Hui Evariste 17 Sticlaru, Gabriel 16 Zerz, Eva 15 Binyamin, Muhammad Ahsan 14 Ferčec, Brigita 14 Lee, Wanseok 14 Nabeshima, Katsusuke 14 Seiler, Werner M. 13 Bivià-Ausina, Carles 13 Falcón Ganfornina, Raúl Manuel 13 La Scala, Roberto 13 Lossen, Christoph 13 Movasati, Hossein 13 Sottile, Frank 12 Eder, Christian 12 Ren, Yue 12 Schulze, Mathias 12 Sturmfels, Bernd 12 Szemberg, Tomasz 11 Gimenez, Philippe 11 Gray, James A. 11 Herzog, Jürgen 11 Markwig, Thomas 11 Nuño-Ballesteros, Juan José 11 Shafer, Douglas S. 11 Tajima, Shinichi 11 Walcher, Sebastian 11 Wang, Dingkang 10 Bermejo, Isabel 10 Coutinho, S. C. 10 Monagan, Michael B. 10 Planas-Vilanova, Francesc 10 Popescu, Dorin 10 Schenzel, Peter 10 Szpond, Justyna 10 Valls Anglés, Cláudia 10 Villarreal, Rafael Heraclio 10 Zhang, Yang 9 Dinwoodie, Ian Hepburn 9 Dumnicki, Marcin 9 Elias, Joan 9 Ene, Viviana 9 Escudero, Juan García 9 Markwig, Hannah 9 Martin, Bernd 9 Park, Euisung 9 Peterson, Chris 8 Anderson, Lara B. 8 Brickenstein, Michael 8 Bruns, Winfried 8 Dickenstein, Alicia M. 8 García-Marco, Ignacio 8 Hauenstein, Jonathan D. 8 Heinle, Albert 8 Lu, Dong 8 Mehmood, Khawar 8 Montes, Antonio 8 Stamate, Dumitru Ioan 8 Tiwari, Sharwan Kumar 8 Tutaj-Gasińska, Halszka 8 Wang, Mingsheng 7 Bates, Daniel J. 7 Drton, Mathias 7 García-Río, Eduardo 7 Gatermann, Karin 7 Gerdt, Vladimir Petrovich 7 Keicher, Simon 7 Kemper, Gregor 7 Liu, Jinwang 7 Llibre, Jaume 7 Lukas, André 7 Malara, Grzegorz 7 Martín-Morales, Jorge 7 Nasrollah Nejad, Abbas 7 Oliveira, Regilene D. S. 7 Pearce, Roman 7 Pokora, Piotr 7 Schreyer, Frank-Olaf 7 Sommese, Andrew John 7 Tuomela, Jukka 7 Vázquez-Lorenzo, Ramón 7 Zhang, Weinian 6 Al-Ayyoub, Ibrahim 6 Allman, Elizabeth S. 6 Barakat, Mohamed 6 Braun, Volker 6 Brodmann, Markus P. 6 Chen, Xingwu 6 Conca, Aldo ...and 1,708 more Authors all top 5 Cited in 370 Serials 170 Journal of Symbolic Computation 83 Journal of Algebra 57 Journal of High Energy Physics 42 Journal of Pure and Applied Algebra 28 Journal of Algebra and its Applications 22 ACM Communications in Computer Algebra 21 Mathematics of Computation 20 Communications in Algebra 19 Experimental Mathematics 18 Mathematische Zeitschrift 16 Mathematics in Computer Science 15 Transactions of the American Mathematical Society 15 Applicable Algebra in Engineering, Communication and Computing 14 Applied Mathematics and Computation 14 Proceedings of the American Mathematical Society 14 Multidimensional Systems and Signal Processing 12 Advances in Mathematics 12 Manuscripta Mathematica 11 International Journal of Algebra and Computation 11 Linear Algebra and its Applications 11 Journal of Algebraic Combinatorics 11 Revista Matemática Complutense 11 Foundations of Computational Mathematics 10 Advances in Applied Mathematics 9 Computer Physics Communications 9 Journal of Mathematical Analysis and Applications 9 Nuclear Physics. B 9 Journal of Computational and Applied Mathematics 9 Mathematische Nachrichten 9 Discrete & Computational Geometry 9 Mediterranean Journal of Mathematics 8 Communications in Mathematical Physics 8 Collectanea Mathematica 8 Journal of Differential Equations 8 Topology and its Applications 8 Qualitative Theory of Dynamical Systems 8 Journal of Physics A: Mathematical and Theoretical 7 Rocky Mountain Journal of Mathematics 7 Compositio Mathematica 7 Proceedings of the Edinburgh Mathematical Society. Series II 7 Bulletin of the Brazilian Mathematical Society. New Series 7 Research in the Mathematical Sciences 6 Annales de l’Institut Fourier 6 Results in Mathematics 6 Studia Scientiarum Mathematicarum Hungarica 6 International Journal of Mathematics 6 Journal of Algebraic Geometry 6 Bulletin des Sciences Mathématiques 6 Computer Science Journal of Moldova 6 Analele Științifice ale Universității “Ovidius” Constanța. Seria: Matematică 6 Central European Journal of Mathematics 6 Algorithms and Computation in Mathematics 6 Journal of Commutative Algebra 6 Journal of Singularities 5 Journal of Mathematical Biology 5 Mathematical Proceedings of the Cambridge Philosophical Society 5 Archiv der Mathematik 5 Geometriae Dedicata 5 Journal of the London Mathematical Society. Second Series 5 Michigan Mathematical Journal 5 Osaka Journal of Mathematics 5 SIAM Journal on Discrete Mathematics 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Advances in Geometry 5 Advances in High Energy Physics 5 East Asian Mathematical Journal 5 Journal of Applied Analysis and Computation 5 SIAM Journal on Applied Algebra and Geometry 4 Bulletin of Mathematical Biology 4 Annals of the Institute of Statistical Mathematics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Le Matematiche 4 Mathematics and Computers in Simulation 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 Japan Journal of Industrial and Applied Mathematics 4 Designs, Codes and Cryptography 4 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 The Electronic Journal of Combinatorics 4 Annals of Mathematics and Artificial Intelligence 4 Boletín de la Sociedad Matemática Mexicana. Third Series 4 Documenta Mathematica 4 Transformation Groups 4 Nonlinear Dynamics 4 Journal of Systems Science and Complexity 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Computers & Mathematics with Applications 3 Journal of Mathematical Physics 3 Letters in Mathematical Physics 3 Beiträge zur Algebra und Geometrie 3 The Annals of Statistics 3 Annales Polonici Mathematici 3 Canadian Journal of Mathematics 3 Inventiones Mathematicae ...and 270 more Serials all top 5 Cited in 56 Fields 765 Algebraic geometry (14-XX) 730 Commutative algebra (13-XX) 375 Computer science (68-XX) 221 Several complex variables and analytic spaces (32-XX) 123 Ordinary differential equations (34-XX) 103 Quantum theory (81-XX) 84 Group theory and generalizations (20-XX) 82 Associative rings and algebras (16-XX) 77 Combinatorics (05-XX) 70 Dynamical systems and ergodic theory (37-XX) 70 Numerical analysis (65-XX) 68 Number theory (11-XX) 56 Information and communication theory, circuits (94-XX) 50 Convex and discrete geometry (52-XX) 49 Linear and multilinear algebra; matrix theory (15-XX) 44 Global analysis, analysis on manifolds (58-XX) 43 Field theory and polynomials (12-XX) 40 Biology and other natural sciences (92-XX) 37 Nonassociative rings and algebras (17-XX) 37 Systems theory; control (93-XX) 36 Statistics (62-XX) 28 Partial differential equations (35-XX) 27 Differential geometry (53-XX) 24 Mechanics of particles and systems (70-XX) 21 Geometry (51-XX) 21 Manifolds and cell complexes (57-XX) 21 Relativity and gravitational theory (83-XX) 20 General and overarching topics; collections (00-XX) 20 Special functions (33-XX) 19 Operations research, mathematical programming (90-XX) 16 Functions of a complex variable (30-XX) 15 Algebraic topology (55-XX) 14 Category theory; homological algebra (18-XX) 12 Order, lattices, ordered algebraic structures (06-XX) 11 Real functions (26-XX) 10 Topological groups, Lie groups (22-XX) 8 Difference and functional equations (39-XX) 8 Probability theory and stochastic processes (60-XX) 8 Mechanics of deformable solids (74-XX) 8 Statistical mechanics, structure of matter (82-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Mathematical logic and foundations (03-XX) 5 General algebraic systems (08-XX) 4 History and biography (01-XX) 4 Operator theory (47-XX) 4 Fluid mechanics (76-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 \(K\)-theory (19-XX) 3 Approximations and expansions (41-XX) 3 Functional analysis (46-XX) 3 Mathematics education (97-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) Citations by Year