## 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; Mathematica; GAP; GitHub; Gfan; polymake; 4ti2; BoijSoederberg; CoCoALib; OEIS; Risa/Asir; D-modules; Kan Referenced in: 1,932 Publications This software is also referenced in ORMS. Further Publications: http://www.math.uiuc.edu/Macaulay2/Publications/
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### Referenced by 1,733 Authors

 55 Sturmfels, Bernd 37 Eisenbud, David 35 Schreyer, Frank-Olaf 34 Mirò-Roig, Rosa Maria 27 Villarreal, Rafael Heraclio 25 Migliore, Juan Carlos 25 Van Tuyl, Adam 24 Nagel, Uwe 23 Leykin, Anton 23 Raicu, Claudiu 23 Stillman, Michael Eugene 22 Ottaviani, Giorgio Maria 20 He, Yang-Hui Evariste 18 Francisco, Christopher A. 17 Graf von Bothmer, Hans-Christian 17 Seceleanu, Alexandra 16 Hà, Huy Tài 16 McCullough, Jason 16 Sam, Steven V. 16 Simis, Aron 16 Staglianò, Giovanni 16 Walther, Uli 15 Thomas, Rekha R. 14 Abo, Hirotachi 14 Dipasquale, Michael R. 14 Erman, Daniel 14 Greuel, Gert-Martin 14 Hauenstein, Jonathan D. 14 Morey, Susan E. 14 Peterson, Chris 14 Ranestad, Kristian 14 Vasconcelos, Wolmer V. 13 Harbourne, Brian 13 Katzman, Mordechai 13 Matusevich, Laura Felicia 13 Rodriguez, Jose Israel 13 Sáenz de Cabezón Irigaray, Eduardo 13 Sottile, Frank 13 Suciu, Alexander I. 13 Weyman, Jerzy M. 12 Boij, Mats 12 Decker, Wolfram 12 Krone, Robert 12 Nguyen, Dang Hop 12 Schenck, Hal 12 Smith, Gregory G. 11 Chiantini, Luca 11 Conca, Aldo 11 Denham, Graham 11 Helmer, Martin 11 Kahle, Thomas 11 Kleppe, Jan Oddvar 11 Mafi, Amir 11 Oeding, Luke 11 Swanson, Irena 10 Ahn, Jeaman 10 Berkesch Zamaere, Christine 10 Böhm, Janko 10 Böhning, Christian 10 Bruns, Winfried 10 Busé, Laurent 10 Chardin, Marc 10 Cook, David II 10 Gross, Elizabeth 10 Lin, Kuei-Nuan 10 Lundqvist, Samuel 10 Mohammadi, Fatemeh 10 Peeva, Irena V. 10 Sullivant, Seth 10 Tohǎneanu, Ştefan O. 9 Aluffi, Paolo 9 Crupi, Marilena 9 Faridi, Sara 9 Galetto, Federico 9 Gray, James A. 9 Kummini, Manoj 9 Kwak, Sijong 9 Maclagan, Diane 9 Mantero, Paolo 9 Mezzetti, Emilia 9 Pfister, Gerhard 9 Römer, Tim 9 Sidman, Jessica 9 Vu, Thanh 8 Brambilla, Maria Chiara 8 Chen, Justin 8 Cid-Ruiz, Yairon 8 González Sarabia, Manuel 8 Grifo, Eloísa 8 Guardo, Elena 8 Hanany, Amihay 8 Hibi, Takayuki 8 Hoşten, Serkan 8 Jayanthan, A. V. 8 Laubenbacher, Reinhard C. 8 Oneto, Alessandro 8 Papadakis, Stavros Argyrios 8 Parrilo, Pablo A. 8 Popescu, Sorin 8 Possieri, Corrado ...and 1,633 more Authors
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### Referenced in 284 Serials

 176 Journal of Algebra 134 Journal of Pure and Applied Algebra 119 Journal of Symbolic Computation 58 Proceedings of the American Mathematical Society 55 The Journal of Software for Algebra and Geometry 49 Transactions of the American Mathematical Society 41 Communications in Algebra 39 Journal of Algebraic Combinatorics 37 Journal of High Energy Physics 35 Advances in Mathematics 30 Linear Algebra and its Applications 30 Journal of Commutative Algebra 29 Mathematische Zeitschrift 28 Advances in Applied Mathematics 26 Journal of Algebra and its Applications 21 Collectanea Mathematica 19 Experimental Mathematics 18 Le Matematiche 18 Michigan Mathematical Journal 16 Compositio Mathematica 16 Mathematische Annalen 16 Foundations of Computational Mathematics 15 Archiv der Mathematik 15 SIAM Journal on Applied Algebra and Geometry 14 Journal of Combinatorial Theory. Series A 14 International Journal of Algebra and Computation 12 Acta Mathematica Vietnamica 11 Mathematics of Computation 11 Annali di Matematica Pura ed Applicata. Serie Quarta 11 IMRN. International Mathematics Research Notices 10 Communications in Mathematical Physics 10 Algebra & Number Theory 9 Bulletin of Mathematical Biology 9 Canadian Journal of Mathematics 9 Illinois Journal of Mathematics 9 Computer Aided Geometric Design 9 Journal of Algebraic Geometry 9 Journal of the European Mathematical Society (JEMS) 8 Discrete Mathematics 8 Annales de l’Institut Fourier 8 Journal für die Reine und Angewandte Mathematik 8 Manuscripta Mathematica 8 Mathematica Scandinavica 8 SIAM Journal on Matrix Analysis and Applications 8 The Electronic Journal of Combinatorics 8 Documenta Mathematica 8 Mathematics in Computer Science 8 Research in the Mathematical Sciences 7 Beiträge zur Algebra und Geometrie 7 Inventiones Mathematicae 7 Nagoya Mathematical Journal 7 Proceedings of the London Mathematical Society. Third Series 7 Finite Fields and their Applications 6 Nuclear Physics. B 6 Geometriae Dedicata 6 Journal of the London Mathematical Society. Second Series 6 Applicable Algebra in Engineering, Communication and Computing 6 Mathematical Research Letters 6 Pure and Applied Mathematics Quarterly 6 Lecture Notes in Mathematics 6 European Journal of Mathematics 5 Israel Journal of Mathematics 5 Annals of the Institute of Statistical Mathematics 5 Duke Mathematical Journal 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Journal of the American Mathematical Society 5 Designs, Codes and Cryptography 5 Annals of Combinatorics 5 Advances in Geometry 5 Mediterranean Journal of Mathematics 5 Algorithms and Computation in Mathematics 4 Rocky Mountain Journal of Mathematics 4 Memoirs of the American Mathematical Society 4 European Journal of Combinatorics 4 Discrete & Computational Geometry 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 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Advances in High Energy Physics 4 ACM Communications in Computer Algebra 4 Algebraic Combinatorics 3 International Journal of Control 3 Journal of Mathematical Biology 3 Letters in Mathematical Physics 3 Physics Letters. B 3 Journal of Geometry and Physics 3 American Journal of Mathematics 3 The Annals of Statistics 3 Osaka Journal of Mathematics 3 Bulletin of the Korean Mathematical Society 3 SIAM Journal on Discrete Mathematics 3 SIAM Journal on Optimization 3 Advances in Computational Mathematics 3 Revista Matemática Complutense ...and 184 more Serials
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### Referenced in 54 Fields

 1,106 Commutative algebra (13-XX) 1,035 Algebraic geometry (14-XX) 278 Combinatorics (05-XX) 215 Computer science (68-XX) 123 Convex and discrete geometry (52-XX) 120 Linear and multilinear algebra; matrix theory (15-XX) 100 Numerical analysis (65-XX) 91 Associative rings and algebras (16-XX) 81 Quantum theory (81-XX) 80 Several complex variables and analytic spaces (32-XX) 72 Group theory and generalizations (20-XX) 55 Statistics (62-XX) 48 Number theory (11-XX) 46 Biology and other natural sciences (92-XX) 42 Operations research, mathematical programming (90-XX) 42 Information and communication theory, circuits (94-XX) 40 Algebraic topology (55-XX) 35 Manifolds and cell complexes (57-XX) 32 Nonassociative rings and algebras (17-XX) 29 Category theory; homological algebra (18-XX) 24 Differential geometry (53-XX) 21 Dynamical systems and ergodic theory (37-XX) 18 Special functions (33-XX) 18 Geometry (51-XX) 17 Systems theory; control (93-XX) 16 Field theory and polynomials (12-XX) 15 Order, lattices, ordered algebraic structures (06-XX) 15 Approximations and expansions (41-XX) 15 Relativity and gravitational theory (83-XX) 14 General and overarching topics; collections (00-XX) 14 Probability theory and stochastic processes (60-XX) 13 Partial differential equations (35-XX) 13 Global analysis, analysis on manifolds (58-XX) 10 Ordinary differential equations (34-XX) 7 Mechanics of particles and systems (70-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 $$K$$-theory (19-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 Real functions (26-XX) 4 Functional analysis (46-XX) 3 History and biography (01-XX) 3 General algebraic systems (08-XX) 3 Fluid mechanics (76-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-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 Mechanics of deformable solids (74-XX) 1 Mathematics education (97-XX)