REDUCE swMATH ID: 789 Software Authors: Anthony C. Hearn; Rayna, Gerhard; Rainer Schöpf; Thomas Sturm Description: REDUCE is an interactive system for general algebraic computations of interest to mathematicians, scientists and engineers. Computer algebra system (CAS). It has been produced by a collaborative effort involving many contributors. Its capabilities include: expansion and ordering of polynomials and rational functions; substitutions and pattern matching in a wide variety of forms; automatic and user controlled simplification of expressions; calculations with symbolic matrices; arbitrary precision integer and real arithmetic; facilities for defining new functions and extending program syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution of a variety of algebraic equations; facilities for the output of expressions in a variety of formats; facilities for generating optimized numerical programs from symbolic input; calculations with a wide variety of special functions; Dirac matrix calculations of interest to high energy physicists. Homepage: http://reduce-algebra.sourceforge.net/ Keywords: orms; computer algebra Related Software: Maple; Mathematica; MACSYMA; DIMSYM; EXCALC; AXIOM; CRACK; REDLOG; SINGULAR; LIE; GENTRAN; SPDE; CoCoA; MuPAD; Macaulay2; DERIVE; SYMMGRP; QEPCAD; CALI; Magma Cited in: 736 Documents This software is also referenced in ORMS. Further Publications: http://reduce-algebra.sourceforge.net/bibl/bib.html Standard Articles 4 Publications describing the Software, including 3 Publications in zbMATH Year REDUCE is free software as of January 2009 Hearn, Anthony C. 2009 Introduction into computer algebra using REDUCE. For mathematiciens, computer scientists and physicists. (Einführung in die Computeralgebra mit Reduce. Für Mathematiker, Informatiker und Physiker.) Zbl 0783.68005Ueberberg, Johannes 1992 Interactive REDUCE programs for calculating classical, non-classical, and approximate symmetries of differential equations. Zbl 0774.68070Nucci, M. C. 1992 Algebraic computing with REDUCE. Lecture notes from the 1st Brazilian school on computer algebra, held in Rio de Janeiro, Brazil, July 24 to August 11, 1989. Zbl 0755.68015MacCallum, Malcolm A. H.; Wright, Francis J. 1991 all top 5 Cited by 852 Authors 28 Nucci, Maria Clara 18 Meleshko, Sergey V. 14 Moitsheki, Raseelo J. 12 Leach, Peter Gavin Lawrence 10 Van Hulzen, Johan A. 9 Liska, Richard 8 Gerdt, Vladimir Petrovich 8 Hehl, Friedrich W. 8 Serdyukova, S. I. 8 Sophocleous, Christodoulos 7 Oliveri, Francesco 7 Schrüfer, Eberhard 7 Sturm, Thomas 6 Fitch, John 6 Ganzha, Victor G. 6 Hereman, Willy A. 6 MacCallum, Malcolm A. H. 6 Niki, Naoto 6 Popowicz, Ziemowit 6 Schwarz, Fritz 6 Steeb, Willi-Hans 5 Berkovich, Lev M. 5 Davenport, James Harold 5 Goldman, Victor V. 5 Gorgone, Matteo 5 Gragert, Peter K. H. 5 Hearn, Anthony C. 5 Heinle, Albert 5 Kölbig, Kurt Siegfried 5 Macías, Alfredo 5 Neun, Winfried 5 Ojika, Takeo 5 Rouff, Marc 5 Zharkov, A. Yu. 4 Alfeld, Peter 4 Baekler, Peter 4 Banerjee, J. Ranjan 4 Broadhurst, David John 4 Calmet, Jacques 4 Carminati, John 4 Chekanov, N. A. 4 Elishakoff, Isaac 4 Gatermann, Karin 4 Ibragimov, Nail Hairullovich 4 Ito, Masaaki 4 Koepf, Wolfram A. 4 Kreimer, Dirk 4 Kryukov, A. P. 4 Levandovskyy, Viktor 4 Lloyd, Noel Glynne 4 Makinde, Oluwole Daniel 4 Özer, Mehmet Naci 4 Pearson, Jane Margaret 4 Prince, Geoff E. 4 Rostovtsev, Vitaly A. 4 Seiler, Werner M. 4 Socorro, José 4 Vinitsky, Sergue I. 4 Vitolo, Raffaele F. 4 Vorozhtsov, Evgenii V. 3 Barbot, Jean-Pierre 3 Bayram, Mustafa 3 Broadbridge, Philip 3 Buchberger, Bruno 3 Caviness, Bob F. 3 Cliffe, K. Andrew 3 Cordeiro, Gauss Moutinho 3 Cox, David A. 3 Das, Ashok K. 3 dos Santos, Renato P. 3 Edneral, Victor F. 3 Edwards, Maureen P. 3 Frutos-Alfaro, Francisco 3 Gawthrop, Peter J. 3 Gräbe, Hans-Gert 3 Gubbiotti, Giorgio 3 Hartley, David H. 3 Hietarinta, Jarmo 3 Kendall, Wilfrid S. 3 Kersten, Paul H. M. 3 Konishi, Sadanori 3 Lämmerzahl, Claus 3 Little, John Brittain 3 McCrea, J. Dermott 3 Möller, Hans Michael 3 Nakagawa, Shigekazu 3 Neta, Beny 3 Norman, Arthur C. 3 O’Connor, J. E. R. 3 O’Shea, Donal B. 3 Roanes-Lozano, Eugenio 3 Roberts, Anthony John 3 Sasaki, Tateaki 3 Scheen, Christian 3 Shapeev, Vasiliĭ Pavlovich 3 Skea, James E. F. 3 Taşcan, Filiz 3 Tavener, Simon J. 3 Uwano, Yoshio 3 Vulcanov, Dumitru N. ...and 752 more Authors all top 5 Cited in 203 Serials 55 Journal of Symbolic Computation 40 Computer Physics Communications 19 Journal of Computational Physics 17 Programming and Computer Software 15 Journal of Mathematical Physics 14 Applied Mathematics and Computation 14 Mathematics and Computers in Simulation 13 Journal of Mathematical Analysis and Applications 11 Journal of Nonlinear Mathematical Physics 10 Classical and Quantum Gravity 10 General Relativity and Gravitation 10 Physics Letters. A 10 SIGSAM Bulletin 9 Computer Methods in Applied Mechanics and Engineering 9 Journal of Physics A: Mathematical and General 7 Computers & Mathematics with Applications 7 Journal of Computational and Applied Mathematics 7 Mathematical and Computer Modelling 6 Physics Letters. 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Zeitschrift für angewandte Mathematik und Physik 2 Differential Equations 2 Journal of Econometrics 2 Quaestiones Mathematicae 2 Theoretical Computer Science 2 Transactions of the American Mathematical Society 2 Journal of Automated Reasoning 2 Applied Mathematics Letters 2 IMPACT of Computing in Science and Engineering 2 Numerical Algorithms 2 Computational Mathematics and Mathematical Physics 2 Annals of Physics 2 Communications in Statistics. Simulation and Computation 2 Celestial Mechanics and Dynamical Astronomy 2 SIAM Journal on Scientific Computing 2 Electronic Journal of Differential Equations (EJDE) 2 Fundamental’naya i Prikladnaya Matematika 2 Doklady Mathematics 2 BIT. Nordisk Tidskrift for Informationsbehandling 2 Lecture Notes in Computer Science 2 Lecture Notes in Mathematics 2 Mathematics and its Applications (Dordrecht) 2 Advances in Mathematical Physics 1 International Journal of Modern Physics A 1 Advances in Applied Probability 1 Applicable Analysis 1 Astronomische Nachrichten 1 Astrophysics and Space Science 1 Astronomicheskiĭ Zhurnal 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Computers and Fluids 1 Communications in Mathematical Physics 1 Earth, Moon, and Planets 1 Geophysical and Astrophysical Fluid Dynamics 1 IMA Journal of Applied Mathematics 1 IMA Journal of Numerical Analysis 1 Ingenieur-Archiv 1 International Journal of Non-Linear Mechanics 1 International Journal for Numerical Methods in Fluids 1 International Journal of Theoretical Physics 1 Journal of Applied Mathematics and Mechanics 1 Journal of the Australian Mathematical Society, Series B 1 Journal of Engineering Mathematics ...and 103 more Serials all top 5 Cited in 57 Fields 301 Computer science (68-XX) 162 Numerical analysis (65-XX) 129 Partial differential equations (35-XX) 107 Ordinary differential equations (34-XX) 63 Fluid mechanics (76-XX) 54 Quantum theory (81-XX) 54 Relativity and gravitational theory (83-XX) 50 Mechanics of particles and systems (70-XX) 46 Dynamical systems and ergodic theory (37-XX) 42 Differential geometry (53-XX) 34 Commutative algebra (13-XX) 34 Global analysis, analysis on manifolds (58-XX) 34 Mechanics of deformable solids (74-XX) 26 Systems theory; control (93-XX) 22 Field theory and polynomials (12-XX) 22 Statistics (62-XX) 17 Nonassociative rings and algebras (17-XX) 16 Biology and other natural sciences (92-XX) 15 Approximations and expansions (41-XX) 14 Special functions (33-XX) 14 Classical thermodynamics, heat transfer (80-XX) 13 Algebraic geometry (14-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Topological groups, Lie groups (22-XX) 10 Mathematical logic and foundations (03-XX) 10 Probability theory and stochastic processes (60-XX) 9 Number theory (11-XX) 9 Functions of a complex variable (30-XX) 8 General and overarching topics; collections (00-XX) 7 Associative rings and algebras (16-XX) 7 Optics, electromagnetic theory (78-XX) 5 Group theory and generalizations (20-XX) 5 Operator theory (47-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Mathematics education (97-XX) 4 Combinatorics (05-XX) 4 Difference and functional equations (39-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geometry (51-XX) 4 Geophysics (86-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Astronomy and astrophysics (85-XX) 3 Operations research, mathematical programming (90-XX) 2 Potential theory (31-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Manifolds and cell complexes (57-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Abstract harmonic analysis (43-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) Citations by Year