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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)

Referencing Publications by Year