## CoCoA

 swMATH ID: 143 Software Authors: CoCoa-Team; Robbiano, Lorenzo Description: CoCoA is a system for Computations in Commutative Algebra. It is able to perform simple and sophisticated operations on multivaraiate polynomials and on various data related to them (ideals, modules, matrices, rational functions). For example, it can readily compute Grobner bases, syzygies and minimal free resolution, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA and the flexibility of its use are further enhanced by the dedicated high-level programming language. For convenience, the system offers a textual interface, an Emacs mode, and a graphical user interface common to most platforms. Computer algebra system (CAS). Homepage: http://cocoa.dima.unige.it Keywords: orms; CAS; Computer algebra system Related Software: Macaulay2; SINGULAR; CoCoALib; Maple; Mathematica; Magma; Normaliz; SageMath; 4ti2; Lugares; REDUCE; Cinderella; ApCoCoA; Geometer's Sketchpad; GAP; Gfan; PHCpack; polymake; MuPAD; GEX Referenced in: 644 Publications This software is also referenced in ORMS. Further Publications: http://cocoa.dima.unige.it/research/publications.html

### Standard Articles

5 Publications describing the Software, including 4 Publications in zbMATH Year
What is new in CoCoA? Zbl 1437.13002
Abbott, John; Bigatti, Anna Maria
2014
Stanley decompositions using CoCoA. Zbl 1310.13031
Bigatti, Anna Maria; De Negri, Emanuela
2013
CoCoA: computations in commutative algebra
Abbott, John; Bigatti, Anna; Caboara, Massimo; Robbiano, Lorenzo
2007
The CoCoA 3 framework for a family of Buchberger-like algorithms. Zbl 0898.68032
Capani, Antonio; Niesi, Gianfranco
1998
Some features of $$CoCoA 3$$. Zbl 0920.68060
Capani, A.; Niesi, G.; Robbiano, L.
1996
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### Referenced by 596 Authors

 42 Robbiano, Lorenzo 35 Van Tuyl, Adam 28 Bigatti, Anna Maria 27 Conca, Aldo 19 Migliore, Juan Carlos 16 Abbott, John A. 16 Geramita, Anthony Vito 16 Guardo, Elena 16 Kreuzer, Martin 14 Catalisano, Maria Virginia 14 Greuel, Gert-Martin 14 Rossi, Maria Evelina 13 Carlini, Enrico 13 Herzog, Jürgen 13 Pistone, Giovanni 12 Gimigliano, Alessandro 12 Roanes-Lozano, Eugenio 11 Hà, Huy Tài 11 Nagel, Uwe 11 Sáenz de Cabezón Irigaray, Eduardo 10 Botana, Francisco 10 Rapallo, Fabio 10 Wynn, Henry P. 9 Cioffi, Francesca 9 Dimca, Alexandru 9 Shin, Yong Su 9 Valla, Giuseppe 8 Hibi, Takayuki 8 Laita, Luis M. 8 Riccomagno, Eva 8 Rinaldo, Giancarlo 8 Rogantin, Maria Piera 8 Sabadini, Irene 8 Sticlaru, Gabriel 8 Varbaro, Matteo 7 Caboara, Massimo 7 De Negri, Emanuela 7 Favacchio, Giuseppe 7 Francisco, Christopher A. 7 Hernando, Antonio 7 Logar, Alessandro 7 Pfister, Gerhard 7 Torrente, Maria-Laura 7 Villarreal, Rafael Heraclio 7 Zanello, Fabrizio 6 Bernardi, Alessandra 6 Bruns, Winfried 6 Constantinescu, Alexandru 6 Harbourne, Brian 6 Orecchia, Ferruccio 6 Peterson, Chris 6 Recio, Tomas 6 Römer, Tim 6 Sharifan, Leila 5 Boffi, Giandomenico 5 Guida, Margherita 5 Mirò-Roig, Rosa Maria 5 Murai, Satoshi 5 Niesi, Gianfranco 5 Pech, Pavel 5 Sommen, Franciscus 5 Thoma, Apostolos 5 Zhu, Guangjun 4 Barile, Margherita 4 Beltrametti, Mauro C. 4 Bertone, Cristina 4 Charalambous, Hara 4 Chiantini, Luca 4 Crupi, Marilena 4 Domokos, Mátyás 4 Fassino, Claudia 4 Fatabbi, Giuliana 4 Fontana, Roberto 4 Hauenstein, Jonathan D. 4 Idà, Monica 4 Jayanthan, A. V. 4 Jiang, Zhaolin 4 Laita, Laura 4 Lorenzini, Anna 4 Maruri-Aguilar, Hugo 4 Mehta, Dhagash 4 Nanduri, Ramakrishna 4 Nguyen Cong Minh 4 Palezzato, Elisa 4 Perdon, Anna-Maria 4 Puthenpurakal, Tony J. 4 Roanes-Macías, Eugenio 4 Sommese, Andrew John 4 Struppa, Daniele Carlo 4 Vladoiu, Marius 4 Xu, Li 3 Ahn, Jeaman 3 Amata, Luca 3 Bermejo, Isabel 3 Biermann, Jennifer 3 Borna, Keivan 3 Brenner, Holger 3 Buchberger, Bruno 3 Capani, Antonio 3 Cavaliere, Maria Pia ...and 496 more Authors
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### Referenced in 183 Serials

 50 Journal of Pure and Applied Algebra 50 Journal of Symbolic Computation 46 Journal of Algebra 19 Communications in Algebra 18 Journal of Algebra and its Applications 16 Proceedings of the American Mathematical Society 12 Collectanea Mathematica 11 Transactions of the American Mathematical Society 10 Mathematics and Computers in Simulation 10 Journal of Algebraic Combinatorics 9 Beiträge zur Algebra und Geometrie 7 Advances in Mathematics 7 Mathematische Zeitschrift 6 Illinois Journal of Mathematics 6 Le Matematiche 6 Linear Algebra and its Applications 5 Acta Mathematica Vietnamica 5 Annals of the Institute of Statistical Mathematics 5 Journal of Statistical Planning and Inference 5 Applicable Algebra in Engineering, Communication and Computing 5 Journal of Commutative Algebra 4 Memoirs of the American Mathematical Society 4 Michigan Mathematical Journal 4 Nagoya Mathematical Journal 4 The Electronic Journal of Combinatorics 4 Lecture Notes in Mathematics 4 Mathematics in Computer Science 4 Journal of Statistical Theory and Practice 3 Applied Mathematics and Computation 3 Archiv der Mathematik 3 Journal of Combinatorial Theory. Series A 3 Mathematische Nachrichten 3 Osaka Journal of Mathematics 3 Ricerche di Matematica 3 Advances in Applied Mathematics 3 Journal of Automated Reasoning 3 SIAM Journal on Discrete Mathematics 3 Experimental Mathematics 3 Journal of High Energy Physics 3 ACM Communications in Computer Algebra 3 Universitext 2 Mathematical Notes 2 Metrika 2 Arkiv för Matematik 2 Mathematics of Computation 2 Compositio Mathematica 2 Czechoslovak Mathematical Journal 2 Geometriae Dedicata 2 Journal of Computational and Applied Mathematics 2 Manuscripta Mathematica 2 Rendiconti del Seminario Matematico della Università di Padova 2 Topology and its Applications 2 European Journal of Combinatorics 2 Systems & Control Letters 2 Annals of Global Analysis and Geometry 2 Forum Mathematicum 2 International Journal of Algebra and Computation 2 IMRN. International Mathematics Research Notices 2 Computational Statistics and Data Analysis 2 The Australasian Journal of Combinatorics 2 Algebra Colloquium 2 Mathematical Research Letters 2 Statistica Sinica 2 Annals of Mathematics and Artificial Intelligence 2 Portugaliae Mathematica. Nova Série 2 Mathematical Reports 2 Central European Journal of Mathematics 2 Computational Biology and Chemistry 2 Statistical Methods and Applications 2 Lecture Notes in Computer Science 2 London Mathematical Society Lecture Note Series 2 Algebra & Number Theory 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Statistics and Computing 2 Undergraduate Texts in Mathematics 1 American Mathematical Monthly 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Communications on Pure and Applied Mathematics 1 Discrete Mathematics 1 International Journal of Control 1 International Journal of Mathematical Education in Science and Technology 1 Indian Journal of Pure & Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Engineering Mathematics 1 Journal of Mathematical Biology 1 Linear and Multilinear Algebra 1 Mathematical Methods in the Applied Sciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Scandinavian Journal of Statistics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Bulletin of the London Mathematical Society 1 Commentarii Mathematici Helvetici 1 Glasgow Mathematical Journal 1 Inventiones Mathematicae 1 Journal of the Korean Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Journal of Number Theory 1 Kybernetika 1 Mathematische Annalen ...and 83 more Serials
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### Referenced in 47 Fields

 454 Commutative algebra (13-XX) 220 Algebraic geometry (14-XX) 135 Computer science (68-XX) 91 Combinatorics (05-XX) 47 Statistics (62-XX) 40 Numerical analysis (65-XX) 28 Linear and multilinear algebra; matrix theory (15-XX) 20 Convex and discrete geometry (52-XX) 18 Associative rings and algebras (16-XX) 16 Several complex variables and analytic spaces (32-XX) 13 Geometry (51-XX) 12 Biology and other natural sciences (92-XX) 12 Information and communication theory, circuits (94-XX) 11 Number theory (11-XX) 11 Group theory and generalizations (20-XX) 11 Operations research, mathematical programming (90-XX) 9 General and overarching topics; collections (00-XX) 9 Functions of a complex variable (30-XX) 8 Field theory and polynomials (12-XX) 8 Probability theory and stochastic processes (60-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 7 Partial differential equations (35-XX) 6 Mathematical logic and foundations (03-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Algebraic topology (55-XX) 6 Systems theory; control (93-XX) 4 Real functions (26-XX) 4 Special functions (33-XX) 4 Ordinary differential equations (34-XX) 4 Differential geometry (53-XX) 4 Mathematics education (97-XX) 3 Approximations and expansions (41-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Quantum theory (81-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 $$K$$-theory (19-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)