Macaulay2 swMATH ID: 537 Software Authors: Grayson, Daniel R.; Stillman, Michael E.; Eisenbud, David; http://www.math.uiuc.edu/Macaulay2/Contributors/ Description: Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, whose creation has been funded by the National Science Foundation since 1992. Macaulay2 includes core algorithms for computing Gröbner bases and graded or multi-graded free resolutions of modules over quotient rings of graded or multi-graded polynomial rings with a monomial ordering. The core algorithms are accessible through a versatile high level interpreted user language with a powerful debugger supporting the creation of new classes of mathematical objects and the installation of methods for computing specifically with them. Macaulay2 can compute Betti numbers, Ext, cohomology of coherent sheaves on projective varieties, primary decomposition of ideals, integral closure of rings, and more. Computer algebra system (CAS). Homepage: http://www.math.uiuc.edu/Macaulay2/ Keywords: orms; Computations; Algebraic geometry; Macaulay 2; CAS; orms; CAS; Computer algebra system Related Software: SINGULAR; CoCoA; SageMath; Bertini; Magma; Maple; PHCpack; Normaliz; GitHub; Mathematica; Gfan; GAP; 4ti2; polymake; BoijSoederberg; OEIS; Risa/Asir; CoCoALib; Kan; alphaCertified Cited in: 2,084 Documents This software is also referenced in ORMS. Further Publications: http://www.math.uiuc.edu/Macaulay2/Publications/ Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Computations in algebraic geometry with Macaulay 2. Zbl 0973.00017Eisenbud, David (ed.); Grayson, Daniel R. (ed.); Stillman, Michael (ed.); Sturmfels, Bernd (ed.) 2002 Ideals, varieties and Macaulay 2. Zbl 0994.13011Sturmfels, Bernd 2002 all top 5 Cited by 1,875 Authors 57 Sturmfels, Bernd 39 Eisenbud, David 37 Mirò-Roig, Rosa Maria 36 Schreyer, Frank-Olaf 28 Villarreal, Rafael Heraclio 26 Van Tuyl, Adam 25 Migliore, Juan Carlos 24 Nagel, Uwe 24 Raicu, Claudiu 24 Stillman, Michael Eugene 23 Leykin, Anton 22 Ottaviani, Giorgio Maria 21 Seceleanu, Alexandra 20 He, Yang-Hui Evariste 18 Francisco, Christopher A. 18 Hà, Huy Tài 17 Graf von Bothmer, Hans-Christian 17 Sam, Steven V. 17 Simis, Aron 17 Staglianò, Giovanni 17 Walther, Uli 16 Erman, Daniel 16 Hauenstein, Jonathan D. 16 McCullough, Jason 15 Dipasquale, Michael R. 15 Morey, Susan E. 15 Rodriguez, Jose Israel 15 Thomas, Rekha R. 14 Abo, Hirotachi 14 Greuel, Gert-Martin 14 Harbourne, Brian 14 Mafi, Amir 14 Peterson, Chris 14 Ranestad, Kristian 14 Sáenz de Cabezón Irigaray, Eduardo 14 Sottile, Frank 14 Vasconcelos, Wolmer V. 13 Katzman, Mordechai 13 Matusevich, Laura Felicia 13 Nguyen, Dang Hop 13 Schenck, Hal 13 Smith, Gregory G. 13 Suciu, Alexander I. 13 Weyman, Jerzy M. 12 Boij, Mats 12 Chiantini, Luca 12 Conca, Aldo 12 Decker, Wolfram 12 Helmer, Martin 12 Kahle, Thomas 12 Kleppe, Jan Oddvar 12 Krone, Robert 12 Mohammadi, Fatemeh 11 Bruns, Winfried 11 Busé, Laurent 11 Crupi, Marilena 11 Denham, Graham 11 Faridi, Sara 11 Hibi, Takayuki 11 Lin, Kuei-Nuan 11 Mezzetti, Emilia 11 Oeding, Luke 11 Swanson, Irena 11 Tohǎneanu, Ştefan O. 10 Ahn, Jeaman 10 Aluffi, Paolo 10 Berkesch Zamaere, Christine 10 Böhm, Janko 10 Böhning, Christian 10 Chardin, Marc 10 Cid-Ruiz, Yairon 10 Cook, David II 10 Gross, Elizabeth 10 Kummini, Manoj 10 Kwak, Sijong 10 Lundqvist, Samuel 10 Mantero, Paolo 10 Peeva, Irena V. 10 Selvaraja, S. 10 Sullivant, Seth 9 Galetto, Federico 9 Gray, James A. 9 Grifo, Eloísa 9 Hanany, Amihay 9 Jayanthan, A. V. 9 Macchia, Antonio 9 Maclagan, Diane 9 Nicklasson, Lisa 9 Papadakis, Stavros Argyrios 9 Pfister, Gerhard 9 Possieri, Corrado 9 Römer, Tim 9 Schwede, Karl E. 9 Shen, Yihuang 9 Sidman, Jessica 9 Tornambè, Antonio 9 Varbaro, Matteo 9 Vu, Thanh 8 Angelini, Elena 8 Botbol, Nicolás ...and 1,775 more Authors all top 5 Cited in 296 Serials 188 Journal of Algebra 138 Journal of Pure and Applied Algebra 126 Journal of Symbolic Computation 60 Proceedings of the American Mathematical Society 58 The Journal of Software for Algebra and Geometry 52 Transactions of the American Mathematical Society 46 Communications in Algebra 45 Journal of High Energy Physics 42 Journal of Algebraic Combinatorics 36 Advances in Mathematics 33 Advances in Applied Mathematics 33 Journal of Commutative Algebra 30 Mathematische Zeitschrift 30 Linear Algebra and its Applications 27 Journal of Algebra and its Applications 23 Collectanea Mathematica 20 SIAM Journal on Applied Algebra and Geometry 19 Le Matematiche 19 Experimental Mathematics 18 Michigan Mathematical Journal 17 Mathematische Annalen 16 Archiv der Mathematik 16 Compositio Mathematica 16 International Journal of Algebra and Computation 16 Foundations of Computational Mathematics 14 Mathematics of Computation 14 Journal of Combinatorial Theory. 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International Mathematics Research Notices 11 The Electronic Journal of Combinatorics 10 Bulletin of Mathematical Biology 10 Illinois Journal of Mathematics 10 Algebra & Number Theory 9 Discrete Mathematics 9 Canadian Journal of Mathematics 9 Journal für die Reine und Angewandte Mathematik 9 Manuscripta Mathematica 9 Computer Aided Geometric Design 9 Journal of Algebraic Geometry 9 Journal of the European Mathematical Society (JEMS) 8 Annales de l’Institut Fourier 8 Mathematica Scandinavica 8 Nagoya Mathematical Journal 8 SIAM Journal on Matrix Analysis and Applications 8 Applicable Algebra in Engineering, Communication and Computing 8 Documenta Mathematica 8 Mathematics in Computer Science 8 ACM Communications in Computer Algebra 8 Research in the Mathematical Sciences 7 Beiträge zur Algebra und Geometrie 7 Inventiones Mathematicae 7 Proceedings of the London Mathematical Society. Third Series 7 Finite Fields and their Applications 6 Israel Journal of Mathematics 6 Nuclear Physics. 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Serie II 5 Discrete & Computational Geometry 5 Journal of the American Mathematical Society 5 Designs, Codes and Cryptography 5 Annals of Combinatorics 5 Advances in Geometry 5 Algorithms and Computation in Mathematics 5 Algebraic Combinatorics 4 Journal of Mathematical Biology 4 Rocky Mountain Journal of Mathematics 4 Journal of Geometry and Physics 4 European Journal of Combinatorics 4 Bulletin of the Korean Mathematical Society 4 Forum Mathematicum 4 International Journal of Mathematics 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Mathematical Programming. Series A. Series B 4 The Australasian Journal of Combinatorics 4 Selecta Mathematica. New Series 4 Algebras and Representation Theory 4 Revista Matemática Complutense 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 Oberwolfach Reports 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Advances in High Energy Physics 4 Kyoto Journal of Mathematics 3 Discrete Applied Mathematics 3 International Journal of Control 3 Letters in Mathematical Physics 3 Physics Letters. B 3 American Journal of Mathematics 3 The Annals of Statistics ...and 196 more Serials all top 5 Cited in 54 Fields 1,197 Commutative algebra (13-XX) 1,105 Algebraic geometry (14-XX) 310 Combinatorics (05-XX) 227 Computer science (68-XX) 132 Convex and discrete geometry (52-XX) 125 Linear and multilinear algebra; matrix theory (15-XX) 106 Numerical analysis (65-XX) 96 Associative rings and algebras (16-XX) 92 Quantum theory (81-XX) 85 Several complex variables and analytic spaces (32-XX) 76 Group theory and generalizations (20-XX) 63 Statistics (62-XX) 53 Number theory (11-XX) 49 Biology and other natural sciences (92-XX) 45 Operations research, mathematical programming (90-XX) 45 Information and communication theory, circuits (94-XX) 41 Algebraic topology (55-XX) 35 Manifolds and cell complexes (57-XX) 33 Nonassociative rings and algebras (17-XX) 29 Category theory; homological algebra (18-XX) 28 Differential geometry (53-XX) 21 Special functions (33-XX) 21 Dynamical systems and ergodic theory (37-XX) 19 Field theory and polynomials (12-XX) 19 Geometry (51-XX) 18 Systems theory; control (93-XX) 17 Approximations and expansions (41-XX) 16 Order, lattices, ordered algebraic structures (06-XX) 16 Global analysis, analysis on manifolds (58-XX) 15 General and overarching topics; collections (00-XX) 15 Partial differential equations (35-XX) 15 Probability theory and stochastic processes (60-XX) 14 Relativity and gravitational theory (83-XX) 11 Ordinary differential equations (34-XX) 8 Mechanics of particles and systems (70-XX) 6 \(K\)-theory (19-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Topological groups, Lie groups (22-XX) 5 Functions of a complex variable (30-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 History and biography (01-XX) 4 Real functions (26-XX) 4 Functional analysis (46-XX) 3 General algebraic systems (08-XX) 3 Fluid mechanics (76-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of deformable solids (74-XX) 1 Mathematical logic and foundations (03-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 Mathematics education (97-XX) Citations by Year