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SINGULAR

swMATH ID: 866
Software Authors:
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: 1,722 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 1,806 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 1,706 more Authors
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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
21 Mathematics of Computation
21 ACM Communications in Computer Algebra
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
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Cited in 56 Fields

763 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)
83 Group theory and generalizations (20-XX)
82 Associative rings and algebras (16-XX)
77 Combinatorics (05-XX)
70 Numerical analysis (65-XX)
69 Dynamical systems and ergodic theory (37-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)
42 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)

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