OreMorphisms: a homological algebraic package for factoring and decomposing linear functional systems. The purpose of this paper is to demonstrate the symbolic package OREMORPHISMS which is dedicated to the implementation of different algorithms and heuristic methods for the study of the factorization, reduction and decomposition problems of general linear functional systems (e.g., systems of partial differential or difference equations, differential time-delay systems). In particular, we explicitly show how to decompose a differential timedelay system (a string with an interior mass [15]) formed by 4 equations in 6 unknowns and prove that it is equivalent to a simple equation in 3 unknowns. We finally give a list of reductions of classical systems of differential time-delay equations and partial differential equations coming from control theory and mathematical physics.

References in zbMATH (referenced in 12 articles )

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  1. Cluzeau, Thomas; Koutschan, Christoph; Quadrat, Alban; Tõnso, Maris: Effective algebraic analysis approach to linear systems over Ore algebras (2020)
  2. Cluzeau, Thomas; Quadrat, Alban: Equivalences of linear functional systems (2020)
  3. Quadrat, Alban (ed.); Zerz, Eva (ed.): Algebraic and symbolic computation methods in dynamical systems. Based on articles written for the invited sessions of the 5th symposium on system structure and control, IFAC, Grenoble, France, February 4--6, 2013 and of the 21st international symposium on mathematical theory of networks and systems (MTNS 2014), Groningen, the Netherlands, July 7--11, 2014 (2020)
  4. Bachelier, Olivier; Cluzeau, Thomas; Yeganefar, Nima: On the stability and the stabilization of linear discrete repetitive processes (2019)
  5. Bachelier, Olivier; Cluzeau, Thomas; David, Ronan; Yeganefar, Nima: Structural stabilization of linear 2D discrete systems using equivalence transformations (2017)
  6. Cluzeau, Thomas; Quadrat, Alban: A new insight into Serre’s reduction problem (2015)
  7. Robertz, Daniel: Recent progress in an algebraic analysis approach to linear systems (2015)
  8. Gómez-Torrecillas, José: Basic module theory over non-commutative rings with computational aspects of operator algebras (2014)
  9. Quadrat, A.; Robertz, D.: A constructive study of the module structure of rings of partial differential operators. (2014)
  10. Robertz, Daniel: Formal algorithmic elimination for PDEs (2014)
  11. Boudellioua, M. S.; Quadrat, A.: Serre’s reduction of linear functional systems. (2010)
  12. Fabiańska, Anna; Quadrat, Alban: Applications of the Quillen-Suslin theorem to multidimensional systems theory (2007)