TDDS swMATH ID: 31513 Software Authors: Vladimir P. Gerdt, Markus Lange-Hegermann, Daniel Robertz Description: The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs. We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a finite set of differentially triangular and algebraically simple subsystems whose subsets of equations are involutive. Usually the decomposed system is substantially easier to investigate and solve both analytically and numerically. The distinctive property of a Thomas decomposition is disjointness of the solution sets of the output subsystems. Thereby, a solution of a well-posed initial problem belongs to one and only one output subsystem. The Thomas decomposition is fully algorithmic. It allows to perform important elements of algebraic analysis of an input differential system such as: verifying consistency, i.e., the existence of solutions; detecting the arbitrariness in the general analytic solution; given an additional equation, checking whether this equation is satisfied by all common solutions of the input system; eliminating a part of dependent variables from the system if such elimination is possible; revealing hidden constraints on dependent variables, etc. Examples illustrating the use of the package are given. Homepage: https://arxiv.org/abs/1801.09942 Dependencies: Maple Related Software: DifferentialThomas; Janet; RegularChains; LDA; AlgebraicThomas; GUARDIAN; REDLOG; QEPCAD; control.lib; Maple; DLMF; gfun; Kan; NLControl; OreAlgebraicAnalysis; OreMorphisms; DIFFALG; HolonomicFunctions; OreModules; RAGlib Cited in: 8 Publications all top 5 Cited by 18 Authors 3 Robertz, Daniel 2 Lange-Hegermann, Markus 2 Seiler, Werner M. 2 Seiß, Matthias 1 Banderier, Cyril 1 Cano, José Maria 1 Chen, Yufu 1 Falkensteiner, Sebastian 1 Gerdt, Vladimir Petrovich 1 Lyakhov, Dmitry A. 1 Marchal, Philippe 1 Michels, Dominik Ludewig 1 Quadrat, Alban 1 Sendra, Juan Rafael 1 Sturm, Thomas 1 Wallner, Michael 1 Zerz, Eva 1 Zhang, Xiaojing all top 5 Cited in 6 Serials 2 Journal of Symbolic Computation 1 The Annals of Probability 1 Advances in Applied Mathematics 1 Journal of Systems Science and Complexity 1 Mathematics in Computer Science 1 Advances in Delays and Dynamics all top 5 Cited in 14 Fields 5 Computer science (68-XX) 4 Ordinary differential equations (34-XX) 3 Commutative algebra (13-XX) 2 Field theory and polynomials (12-XX) 2 Partial differential equations (35-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year