Plural swMATH ID: 719 Software Authors: Levandovskyy, Viktor; Schönemann, Hans; Motsak, Olexander; Greuel, Gert-Martin Description: Singular is a computer algebra system (CAS) developed for efficient computations with polynomials. Plural is a (kernel) extension of Singular to noncommutative polynomial rings having PBW bases and their quotients (called G-/GR-algebras, also known as solvable polynomial algebras and PBW-algebras). All fields available in Singular and all the global monomial orderings are supported for computing left, right and two-sided Gröbner bases. There are many advanced functions, available both in the kernel and via the third-party libraries in the Singular language. Homepage: http://www.singular.uni-kl.de/Manual/3-1-3/sing_455.htm Dependencies: singular Keywords: noncommutative Gröbner bases; D-modules; universal enveloping algebras; quantum groups; noncommutative homological algebra; noncommutative factorization Related Software: SINGULAR; Macaulay2; OreModules; Kan; homalg; Maple; Letterplace; Felix; olga.lib; SageMath; HolonomicFunctions; Janet; D-modules; Risa/Asir; SymbolicData; JAS; BERGMAN; Magma; REDUCE; OreMorphisms Cited in: 91 Documents Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Plural, a non-commutative extension of Singular: past, present and future. Zbl 1229.16001Levandovskyy, Viktor 2006 Plural – a computer algebra system for noncommutative polynomial algebras. Zbl 1072.68681Levandovskyy, Viktor; Schönemann, Hans 2003 all top 5 Cited by 113 Authors 31 Levandovskyy, Viktor 6 Zerz, Eva 5 Quadrat, Alban 4 Ceria, Michela 4 Heinle, Albert 4 Hoffmann, Johannes 4 Martín-Morales, Jorge 4 Mora, Teo 4 Robertz, Daniel 3 Koutschan, Christoph 3 Schindelar, Kristina 3 Schönemann, Hans 3 Seiler, Werner M. 3 Zeid, Karim Abou 2 Abłamowicz, Rafał 2 Andres, Daniel 2 Brickenstein, Michael 2 Cluzeau, Thomas 2 Damiano, Alberto 2 Eder, Christian 2 Kredel, Heinz 2 La Scala, Roberto 2 Li, Huishi 2 Metzlaff, Tobias 2 Nabeshima, Katsusuke 2 Ohara, Katsuyoshi 2 Regensburger, Georg 2 Reyes, Armando 2 Studzinski, Grischa 2 Tajima, Shinichi 2 Zhang, Yang 1 Anderson, Lara B. 1 Aschenbrenner, Matthias 1 Barakat, Mohamed 1 Bell, Jason P. 1 Benkart, Georgia M. 1 Berthomieu, Jérémy 1 Binyamin, Muhammad Ahsan 1 Braun, Volker 1 Bringmann, Kathrin 1 Buchberger, Bruno 1 Carpentier, Sylvain 1 Chrapary, Hagen 1 Cimprič, Jaka 1 Dang Tuan Hiep 1 Decker, Wolfram 1 Fajardo, William 1 Gago-Vargas, Jesús 1 García García, Juan Ignacio 1 García Miranda, Jesus 1 García Román, Manuel 1 García Román, Socorro 1 Gentili, Graziano 1 Green, Edward Lee 1 Hartillo-Hermoso, María Isabel 1 Helton, John William 1 Hossein Poor, Jamal 1 Huang, Hau-wen 1 Hubert, Evelyne 1 Iglesias, Andrés 1 Insua Hermo, Manuel Avelino 1 Kang, Seok-Jin 1 Karp, Robert L. 1 Khan, Junaid Alam 1 Khan, Muhammad Abdul Basit 1 Klep, Igor 1 Ladra González, Manuel 1 Lee, Dong-Il 1 Leykin, Anton 1 Lezama, Oswaldo 1 Lobillo, Francisco Javier 1 Ma, XiaoDong 1 McCullough, Scott A. 1 Mialebama Bouesso, Andre S. E. 1 Mikhailov, Alexander Vasil’evich 1 Mobouale Wamba, G. 1 Motsak, Oleksandr 1 Nelson, Christopher S. 1 Ovrut, Burt A. 1 Park, Euiyong 1 Park, Hyungju 1 Pereira, Mariana 1 Pfister, Gerhard 1 Popescu, Adrian 1 Pumplün, Susanne 1 Raab, Clemens G. 1 Raum, Martin 1 Ren, Yue 1 Richter, Olav K. 1 Roggero, Margherita 1 Rosenkranz, Markus 1 Sabadini, Irene 1 Safey El Din, Mohab 1 Sarmiento, Cristian 1 Schilli, Christian 1 Solberg, Øyvind 1 Soucek, Vladimir 1 Struppa, Daniele Carlo 1 Suárez, Héctor 1 Sun, Yao ...and 13 more Authors all top 5 Cited in 30 Serials 20 Journal of Symbolic Computation 5 Journal of Algebra 5 Applicable Algebra in Engineering, Communication and Computing 4 Journal of Pure and Applied Algebra 3 Mathematics in Computer Science 2 International Journal of Algebra and Computation 2 Linear Algebra and its Applications 2 Advances in Applied Clifford Algebras 2 ACM Communications in Computer Algebra 1 Communications in Algebra 1 Letters in Mathematical Physics 1 Advances in Mathematics 1 Inventiones Mathematicae 1 Le Matematiche 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Multidimensional Systems and Signal Processing 1 Computer Science Journal of Moldova 1 Revista Matemática Complutense 1 Fundamenta Informaticae 1 Journal of High Energy Physics 1 Journal of Algebra and its Applications 1 Lecture Notes in Computer Science 1 Lecture Notes in Mathematics 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Symmetry 1 Journal of Mathematics 1 Advances in Delays and Dynamics 1 Open Mathematics all top 5 Cited in 28 Fields 50 Commutative algebra (13-XX) 43 Computer science (68-XX) 41 Associative rings and algebras (16-XX) 11 Algebraic geometry (14-XX) 10 Nonassociative rings and algebras (17-XX) 8 Systems theory; control (93-XX) 6 Several complex variables and analytic spaces (32-XX) 3 Number theory (11-XX) 3 Partial differential equations (35-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Numerical analysis (65-XX) 3 Quantum theory (81-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Field theory and polynomials (12-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Functions of a complex variable (30-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 1 General algebraic systems (08-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year