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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; SageMath; Magma; Maple; GAP; primdec; Plural; Mathematica; Gfan; FGb; Risa/Asir; polymake; Normaliz; Bertini; PHCpack; STRINGVACUA; GitHub; 4ti2; homalg
Cited in: 1,636 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 1,711 Authors

56 Pfister, Gerhard
51 Romanovskiĭ, Valeriĭ Georgievich
46 Greuel, Gert-Martin
42 Levandovskyy, Viktor
29 Giné, Jaume
21 Böhm, Janko
20 Schönemann, Hans
19 Decker, Wolfram
18 Dimca, Alexandru
18 Hashemi, Amir
17 Frühbis-Krüger, Anne
17 He, Yang-Hui Evariste
17 Sticlaru, Gabriel
16 Zerz, Eva
14 Nabeshima, Katsusuke
13 Binyamin, Muhammad Ahsan
13 Bivià-Ausina, Carles
13 Falcón Ganfornina, Raúl Manuel
13 Ferčec, Brigita
13 Lossen, Christoph
13 Seiler, Werner M.
12 La Scala, Roberto
12 Lee, Wanseok
12 Movasati, Hossein
12 Ren, Yue
12 Schulze, Mathias
12 Sottile, Frank
12 Sturmfels, Bernd
11 Eder, Christian
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 Coutinho, S. C.
10 Monagan, Michael B.
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 Bermejo, Isabel
9 Dinwoodie, Ian Hepburn
9 Dumnicki, Marcin
9 Ene, Viviana
9 Escudero, Juan García
9 Markwig, Hannah
9 Martin, Bernd
9 Nuño-Ballesteros, Juan José
9 Park, Euisung
9 Peterson, Chris
9 Szpond, Justyna
8 Anderson, Lara B.
8 Brickenstein, Michael
8 Bruns, Winfried
8 Dickenstein, Alicia M.
8 Hauenstein, Jonathan D.
8 Montes, Antonio
8 Stamate, Dumitru Ioan
8 Tutaj-Gasińska, Halszka
8 Wang, Mingsheng
7 Bates, Daniel J.
7 Drton, Mathias
7 Elias, Joan
7 García-Marco, Ignacio
7 Gatermann, Karin
7 Gerdt, Vladimir Petrovich
7 Heinle, Albert
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 Barakat, Mohamed
6 Braun, Volker
6 Brodmann, Markus P.
6 Chen, Xingwu
6 Conca, Aldo
6 Cynk, Sławomir
6 Fernandes, Wilker
6 García Sánchez, Pedro A.
6 Guarino, Adolfo
6 Hampton, Marshall
6 Han, Maoan
...and 1,611 more Authors
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Cited in 357 Serials

168 Journal of Symbolic Computation
80 Journal of Algebra
54 Journal of High Energy Physics
39 Journal of Pure and Applied Algebra
27 Journal of Algebra and its Applications
21 Mathematics of Computation
19 Experimental Mathematics
18 Communications in Algebra
18 Mathematische Zeitschrift
16 Mathematics in Computer Science
15 Applicable Algebra in Engineering, Communication and Computing
15 ACM Communications in Computer Algebra
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
11 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 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 Journal of Physics A: Mathematical and Theoretical
7 Computer Physics Communications
7 Collectanea Mathematica
7 Compositio Mathematica
7 Qualitative Theory of Dynamical Systems
7 Bulletin of the Brazilian Mathematical Society. New Series
6 Rocky Mountain Journal of Mathematics
6 Annales de l’Institut Fourier
6 Proceedings of the Edinburgh Mathematical Society. Series II
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 Research in the Mathematical Sciences
5 Journal of Mathematical Biology
5 Archiv der Mathematik
5 Journal of the London Mathematical Society. Second Series
5 Osaka Journal of Mathematics
5 Results in Mathematics
5 SIAM Journal on Discrete Mathematics
5 Advances in Geometry
5 Advances in High Energy Physics
5 Journal of Singularities
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 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 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
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
4 SIAM Journal on Applied Algebra and Geometry
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
3 The Journal of Geometric Analysis
...and 257 more Serials
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Cited in 56 Fields

724 Algebraic geometry (14-XX)
694 Commutative algebra (13-XX)
355 Computer science (68-XX)
209 Several complex variables and analytic spaces (32-XX)
119 Ordinary differential equations (34-XX)
96 Quantum theory (81-XX)
83 Group theory and generalizations (20-XX)
79 Associative rings and algebras (16-XX)
73 Combinatorics (05-XX)
70 Numerical analysis (65-XX)
66 Dynamical systems and ergodic theory (37-XX)
62 Number theory (11-XX)
54 Information and communication theory, circuits (94-XX)
50 Convex and discrete geometry (52-XX)
49 Linear and multilinear algebra; matrix theory (15-XX)
42 Global analysis, analysis on manifolds (58-XX)
39 Field theory and polynomials (12-XX)
37 Nonassociative rings and algebras (17-XX)
37 Systems theory; control (93-XX)
36 Biology and other natural sciences (92-XX)
35 Statistics (62-XX)
28 Partial differential equations (35-XX)
26 Differential geometry (53-XX)
23 Mechanics of particles and systems (70-XX)
20 Relativity and gravitational theory (83-XX)
19 General and overarching topics; collections (00-XX)
19 Geometry (51-XX)
18 Special functions (33-XX)
18 Manifolds and cell complexes (57-XX)
17 Operations research, mathematical programming (90-XX)
16 Functions of a complex variable (30-XX)
14 Category theory; homological algebra (18-XX)
14 Algebraic topology (55-XX)
12 Order, lattices, ordered algebraic structures (06-XX)
10 Topological groups, Lie groups (22-XX)
10 Real functions (26-XX)
8 Difference and functional equations (39-XX)
8 Probability theory and stochastic processes (60-XX)
8 Statistical mechanics, structure of matter (82-XX)
8 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
7 Mechanics of deformable solids (74-XX)
6 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 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)

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