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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
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; polymake; Normaliz; GitHub; Bertini; PHCpack; STRINGVACUA; 4ti2; homalg
Cited in: 1,672 Documents
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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Cited by 1,752 Authors

57 Pfister, Gerhard
52 Romanovskiĭ, Valeriĭ Georgievich
47 Greuel, Gert-Martin
43 Levandovskyy, Viktor
30 Giné, Jaume
21 Böhm, Janko
20 Schönemann, Hans
19 Decker, Wolfram
18 Dimca, Alexandru
18 Hashemi, Amir
18 He, Yang-Hui Evariste
17 Frühbis-Krüger, Anne
17 Sticlaru, Gabriel
16 Zerz, Eva
14 Ferčec, Brigita
14 Nabeshima, Katsusuke
13 Binyamin, Muhammad Ahsan
13 Bivià-Ausina, Carles
13 Falcón Ganfornina, Raúl Manuel
13 Lossen, Christoph
13 Movasati, Hossein
13 Seiler, Werner M.
13 Sottile, Frank
12 Eder, Christian
12 La Scala, Roberto
12 Lee, Wanseok
12 Ren, Yue
12 Schulze, Mathias
12 Sturmfels, Bernd
11 Gimenez, Philippe
11 Gray, James A.
11 Herzog, Jürgen
11 Markwig, Thomas
11 Shafer, Douglas S.
11 Szemberg, Tomasz
11 Tajima, Shinichi
11 Walcher, Sebastian
10 Bermejo, Isabel
10 Coutinho, S. C.
10 Monagan, Michael B.
10 Nuño-Ballesteros, Juan José
10 Planas-Vilanova, Francesc
10 Popescu, Dorin
10 Schenzel, Peter
10 Valls Anglés, Cláudia
10 Villarreal, Rafael Heraclio
10 Wang, Dingkang
10 Zhang, Yang
9 Dinwoodie, Ian Hepburn
9 Dumnicki, Marcin
9 Ene, Viviana
9 Escudero, Juan García
9 Markwig, Hannah
9 Martin, Bernd
9 Park, Euisung
9 Peterson, Chris
9 Szpond, Justyna
8 Anderson, Lara B.
8 Brickenstein, Michael
8 Bruns, Winfried
8 Dickenstein, Alicia M.
8 Elias, Joan
8 García-Marco, Ignacio
8 Hauenstein, Jonathan D.
8 Heinle, Albert
8 Montes, Antonio
8 Stamate, Dumitru Ioan
8 Tutaj-Gasińska, Halszka
8 Wang, Mingsheng
7 Bates, Daniel J.
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 Malara, Grzegorz
7 Martín-Morales, Jorge
7 Mehmood, Khawar
7 Oliveira, Regilene D. S.
7 Pearce, Roman
7 Schreyer, Frank-Olaf
7 Sommese, Andrew John
7 Tiwari, Sharwan Kumar
7 Tuomela, Jukka
7 Zhang, Weinian
6 Al-Ayyoub, Ibrahim
6 Barakat, Mohamed
6 Braun, Volker
6 Brodmann, Markus P.
6 Chen, Xingwu
6 Conca, Aldo
6 Cynk, Sławomir
6 Fernandes, Wilker
6 García-Río, Eduardo
6 García Sánchez, Pedro A.
6 Guarino, Adolfo
...and 1,652 more Authors
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Cited in 364 Serials

169 Journal of Symbolic Computation
80 Journal of Algebra
55 Journal of High Energy Physics
41 Journal of Pure and Applied Algebra
27 Journal of Algebra and its Applications
21 Mathematics of Computation
20 ACM Communications in Computer Algebra
19 Experimental Mathematics
18 Communications in Algebra
18 Mathematische Zeitschrift
16 Mathematics in Computer Science
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
13 Transactions of the American Mathematical Society
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 Journal of Differential Equations
8 Topology and its Applications
8 Qualitative Theory of Dynamical Systems
8 Journal of Physics A: Mathematical and Theoretical
7 Collectanea Mathematica
7 Compositio Mathematica
7 Bulletin of the Brazilian Mathematical Society. New Series
7 Research in the Mathematical Sciences
6 Rocky Mountain Journal of Mathematics
6 Annales de l’Institut Fourier
6 Proceedings of the Edinburgh Mathematical Society. Series II
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 Journal of the London Mathematical Society. Second Series
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 SIAM Journal on Applied Algebra and Geometry
4 Annals of the Institute of Statistical Mathematics
4 Annali di Matematica Pura ed Applicata. Serie Quarta
4 Geometriae Dedicata
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 Japan Journal of Industrial and Applied Mathematics
4 Designs, Codes and Cryptography
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 Documenta Mathematica
4 Transformation Groups
4 Nonlinear Dynamics
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Journal of Applied Analysis and Computation
3 Computers & Mathematics with Applications
3 Journal of Mathematical Physics
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
...and 264 more Serials
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Cited in 56 Fields

737 Algebraic geometry (14-XX)
706 Commutative algebra (13-XX)
364 Computer science (68-XX)
214 Several complex variables and analytic spaces (32-XX)
122 Ordinary differential equations (34-XX)
101 Quantum theory (81-XX)
82 Group theory and generalizations (20-XX)
79 Associative rings and algebras (16-XX)
76 Combinatorics (05-XX)
70 Numerical analysis (65-XX)
68 Dynamical systems and ergodic theory (37-XX)
67 Number theory (11-XX)
54 Information and communication theory, circuits (94-XX)
50 Convex and discrete geometry (52-XX)
48 Linear and multilinear algebra; matrix theory (15-XX)
42 Global analysis, analysis on manifolds (58-XX)
41 Field theory and polynomials (12-XX)
38 Biology and other natural sciences (92-XX)
37 Nonassociative rings and algebras (17-XX)
37 Systems theory; control (93-XX)
35 Statistics (62-XX)
28 Partial differential equations (35-XX)
26 Differential geometry (53-XX)
24 Mechanics of particles and systems (70-XX)
22 Relativity and gravitational theory (83-XX)
19 General and overarching topics; collections (00-XX)
19 Special functions (33-XX)
19 Geometry (51-XX)
19 Manifolds and cell complexes (57-XX)
18 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)
7 Mathematical logic and foundations (03-XX)
5 General algebraic systems (08-XX)
4 History and biography (01-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 Operator theory (47-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)

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