Macaulay2 swMATH ID: 537 Software Authors: Grayson, Daniel R.; Stillman, Michael E.; Eisenbud, David 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; GitHub; PHCpack; Maple; Normaliz; Mathematica; polymake; GAP; 4ti2; Gfan; HomotopyContinuation; BoijSoederberg; OEIS; Book3264Examples; alphaCertified; Risa/Asir Cited in: 2,372 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 Ideals, varieties and Macaulay 2. Zbl 0994.13011Sturmfels, Bernd 2002 Computations in algebraic geometry with Macaulay 2. Zbl 0973.00017Eisenbud, David (ed.); Grayson, Daniel R. (ed.); Stillman, Michael (ed.); Sturmfels, Bernd (ed.) 2002 all top 5 Cited by 2,145 Authors 74 Sturmfels, Bernd 40 Eisenbud, David 39 Mirò-Roig, Rosa Maria 38 Schreyer, Frank-Olaf 30 Van Tuyl, Adam 29 Villarreal, Rafael Heraclio 26 Raicu, Claudiu 26 Stillman, Michael Eugene 25 Leykin, Anton 25 Migliore, Juan Carlos 25 Nagel, Uwe 25 Ottaviani, Giorgio Maria 23 He, Yang-Hui Evariste 21 Seceleanu, Alexandra 19 Staglianò, Giovanni 18 Francisco, Christopher A. 18 Graf von Bothmer, Hans-Christian 18 Hà, Huy Tài 18 McCullough, Jason 18 Morey, Susan E. 18 Rodriguez, Jose Israel 18 Simis, Aron 18 Sottile, Frank 18 Thomas, Rekha R. 17 Crupi, Marilena 17 Erman, Daniel 17 Hauenstein, Jonathan D. 17 Sam, Steven V. 17 Walther, Uli 16 Dipasquale, Michael R. 16 Mohammadi, Fatemeh 16 Ranestad, Kristian 16 Sáenz de Cabezón Irigaray, Eduardo 16 Schenck, Hal 15 Nguyen, Dang Hop 15 Vasconcelos, Wolmer V. 15 Weyman, Jerzy M. 14 Abo, Hirotachi 14 Cid-Ruiz, Yairon 14 Conca, Aldo 14 Faridi, Sara 14 Greuel, Gert-Martin 14 Harbourne, Brian 14 Helmer, Martin 14 Lin, Kuei-Nuan 14 Mafi, Amir 14 Peterson, Chris 14 Smith, Gregory G. 13 Chiantini, Luca 13 Ficarra, Antonino 13 Katzman, Mordechai 13 Krone, Robert 13 Matusevich, Laura Felicia 13 Oeding, Luke 13 Suciu, Alexander I. 12 Boij, Mats 12 Decker, Wolfram 12 Denham, Graham 12 Duff, Timothy 12 Galetto, Federico 12 Kahle, Thomas 12 Kleppe, Jan Oddvar 12 Kwak, Sijong 12 Lundqvist, Samuel 12 Mantero, Paolo 12 Peeva, Irena V. 12 Swanson, Irena 11 Böhning, Christian 11 Bruns, Winfried 11 Busé, Laurent 11 Gross, Elizabeth 11 Hibi, Takayuki 11 Kummini, Manoj 11 Mezzetti, Emilia 11 Nicklasson, Lisa 11 Schwede, Karl E. 11 Shen, Yihuang 11 Wynn, Henry P. 10 Ahn, Jeaman 10 Aluffi, Paolo 10 Berkesch Zamaere, Christine 10 Böhm, Janko 10 Chardin, Marc 10 Cook, David II 10 Jayanthan, A. V. 10 Montaño, Jonathan 10 Römer, Tim 10 Sammartano, Alessio 10 Selvaraja, S. 10 Sullivant, Seth 9 Amata, Luca 9 Angelini, Elena 9 Breiding, Paul 9 Chen, Justin 9 El Khoury, Sabine 9 Faenzi, Daniele 9 Gray, James A. 9 Grifo, Eloísa 9 Hanany, Amihay 9 Hoşten, Serkan ...and 2,045 more Authors all top 5 Cited in 330 Serials 204 Journal of Algebra 149 Journal of Pure and Applied Algebra 138 Journal of Symbolic Computation 73 The Journal of Software for Algebra and Geometry 66 Proceedings of the American Mathematical Society 57 Communications in Algebra 55 Transactions of the American Mathematical Society 52 Journal of High Energy Physics 48 Journal of Algebraic Combinatorics 39 Journal of Commutative Algebra 38 Advances in Mathematics 36 Advances in Applied Mathematics 33 Mathematische Zeitschrift 33 Journal of Algebra and its Applications 31 Linear Algebra and its Applications 26 Collectanea Mathematica 23 SIAM Journal on Applied Algebra and Geometry 22 Foundations of Computational Mathematics 21 Michigan Mathematical Journal 20 International Journal of Algebra and Computation 19 Le Matematiche 19 Mathematische Annalen 19 Experimental Mathematics 16 Archiv der Mathematik 16 Compositio Mathematica 15 Mathematics of Computation 15 Acta Mathematica Vietnamica 14 Journal of Combinatorial Theory. 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Series B 4 The Australasian Journal of Combinatorics 4 Revista Matemática Complutense 4 Communications in Contemporary Mathematics 4 SIAM Journal on Applied Dynamical Systems ...and 230 more Serials all top 5 Cited in 53 Fields 1,357 Commutative algebra (13-XX) 1,248 Algebraic geometry (14-XX) 371 Combinatorics (05-XX) 255 Computer science (68-XX) 148 Convex and discrete geometry (52-XX) 138 Linear and multilinear algebra; matrix theory (15-XX) 117 Numerical analysis (65-XX) 111 Quantum theory (81-XX) 107 Associative rings and algebras (16-XX) 99 Several complex variables and analytic spaces (32-XX) 92 Group theory and generalizations (20-XX) 77 Statistics (62-XX) 62 Number theory (11-XX) 59 Biology and other natural sciences (92-XX) 56 Operations research, mathematical programming (90-XX) 52 Information and communication theory, circuits (94-XX) 45 Algebraic topology (55-XX) 40 Nonassociative rings and algebras (17-XX) 37 Manifolds and cell complexes (57-XX) 32 Category theory; homological algebra (18-XX) 32 Differential geometry (53-XX) 25 Special functions (33-XX) 24 Dynamical systems and ergodic theory (37-XX) 22 Field theory and polynomials (12-XX) 22 Geometry (51-XX) 21 Systems theory; control (93-XX) 20 Approximations and expansions (41-XX) 19 Partial differential equations (35-XX) 19 Probability theory and stochastic processes (60-XX) 18 Order, lattices, ordered algebraic structures (06-XX) 18 Global analysis, analysis on manifolds (58-XX) 17 General and overarching topics; collections (00-XX) 17 Relativity and gravitational theory (83-XX) 12 Ordinary differential equations (34-XX) 8 Mechanics of particles and systems (70-XX) 7 \(K\)-theory (19-XX) 7 Topological groups, Lie groups (22-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Statistical mechanics, structure of matter (82-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Functions of a complex variable (30-XX) 4 History and biography (01-XX) 4 Real functions (26-XX) 4 Functional analysis (46-XX) 3 General algebraic systems (08-XX) 3 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Operator theory (47-XX) 1 Mathematics education (97-XX) Citations by Year