Janet swMATH ID: 7776 Software Authors: Blinkov Y, Cid C, Gerdt V, Plesken W, Robertz D Description: The Maple package Janet implements the involutive basis technique of V. P. Gerdt and Y. A. Blinkov for computing Janet bases and Janet-like Gröbner bases for linear systems of partial differential equations. It works with left modules over differential algebras defined over differential fields of characteristic zero which exist in Maple. Janet also provides a number of tools for dealing with differential expressions and differential operators. A generic linearization for a non-linear system of partial differential equations can be computed. Some procedures translate differential expressions into jet notation and vice versa. For the Weyl algebra representing ordinary differential operators in characteristic zero whose coefficients are rational functions, an elementary divisor algorithm [Rehm 2001/2002], [Cohn 1985] is implemented to compute the Jacobson normal form of a matrix with entries in this Weyl algebra. Among the orderings for differential monomials which are available in Janet are the degree reverse lexicographical one, the pure lexicographical one, block orderings and their extensions to the case of more than one dependent variable which correspond to ”term over position” and ”position over term” orderings in the polynomial case. Four involutive criteria are implemented to avoid unnecessary reductions during involutive basis computations. Homepage: http://wwwb.math.rwth-aachen.de/Janet/janet.html Dependencies: Maple Related Software: SINGULAR; Maple; OreModules; DifferentialThomas; Macaulay2; Plural; Magma; RegularChains; Ginv; OreMorphisms; DIFFALG; QuillenSuslin; homalg; SADE; GeM; AlgebraicThomas; CRACK; JanetOre; TDDS; control.lib Cited in: 37 Publications all top 5 Cited by 43 Authors 12 Robertz, Daniel 9 Gerdt, Vladimir Petrovich 6 Plesken, Wilhelm 4 Lange-Hegermann, Markus 3 Blinkov, Yuri A. 3 Huang, S.-L. Tracy 3 Lisle, Ian G. 3 Lyakhov, Dmitry A. 3 Michels, Dominik Ludewig 3 Quadrat, Alban 2 Bächler, Thomas 2 Barakat, Mohamed 2 Blinkov, Yuriĭ Anatol’evich 2 Fabiańska, Anna 2 Khavkine, Igor 2 Levandovskyy, Viktor 2 Schindelar, Kristina 1 Aksteiner, Steffen 1 Al-Omari, Shadi 1 Andersson, Lars Åke 1 Azad, Hassan 1 Bäckdahl, Thomas 1 Blinkova, A. Yu. 1 Brakhage, Karl-Heinz 1 Casati, Matteo 1 Cluzeau, Thomas 1 Hashemi, Amir 1 Hossain, Zahid 1 Ivanov, Sergeĭ V. 1 Jambor, Sebastian 1 La Scala, Roberto 1 M.-Alizadeh, Benyamin 1 Mogilevich, Lev I. 1 Mozzhilkin, Vladimir V. 1 Niemeyer, Alice C. 1 Reid, Greg J. 1 Riedel-Kruse, Ingmar H. 1 Strzelczyk, Ansgar 1 Weber, Andreas Günter 1 Whiting, Bernard F. 1 Zaman, Fiazud Din 1 Zerz, Eva 1 Zhang, Xiaojing all top 5 Cited in 18 Serials 8 Journal of Symbolic Computation 3 Journal of Algebra 2 Communications in Mathematical Physics 2 Programming and Computer Software 2 Journal of Algebra and its Applications 1 Classical and Quantum Gravity 1 Journal of Engineering Mathematics 1 Mathematics of Computation 1 Archiv der Mathematik 1 Multidimensional Systems and Signal Processing 1 Experimental Mathematics 1 Journal of Mathematical Sciences (New York) 1 Lecture Notes in Mathematics 1 Mathematics in Computer Science 1 Symmetry 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 1 Mathematics 1 Advances in Delays and Dynamics all top 5 Cited in 25 Fields 17 Commutative algebra (13-XX) 15 Computer science (68-XX) 12 Partial differential equations (35-XX) 5 Field theory and polynomials (12-XX) 4 Numerical analysis (65-XX) 4 Systems theory; control (93-XX) 3 Group theory and generalizations (20-XX) 3 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 2 Associative rings and algebras (16-XX) 2 Nonassociative rings and algebras (17-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Special functions (33-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year