References

 


  • [AB69] Auslander, Maurice and Bridger, Mark, Stable module theory. Memoirs of the American Mathematical Society, No. 94, (1969).

  • [BRa] Mohamed Barakat and Daniel Robertz, homalg - A meta-package for homological algebra. (https://arxiv.org/abs/math/0701146).

  • [BR06c] Mohamed Barakat and Daniel Robertz, Computing invariants of multidimensional linear systems on an abstract homological level. Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto (Japan), 2006, pp. 542-559.

  • [BR06d] Mohamed Barakat and Daniel Robertz, homalg: First steps to an abstract package for homological algebra. Proceedings of the X meeting on computational algebra and its applications (EACA 2006), Sevilla (Spain), 2006, pp. 29-32.

  • [BCG03] Y. A. Blinkov, C. F. Cid, V. P. Gerdt, W. Plesken, and D. Robertz, The MAPLE Package Janet: I. Polynomial Systems. II. Linear Partial Differential Equations. Proc. 6th Int. Workshop on Computer Algebra in Scientific Computing, Passau, 2003.

  • [Buc65] B. Buchberger, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Univ. Innsbruck, Austria, 1965.

  • [CQR05] F. Chyzak, A. Quadrat, and D. Robertz, Effective algorithms for parametrizing linear control systems over Ore algebras. Applicable Algebra in Engineering, Communication and Computing, 16 (2005), pp. 319-376.

  • [CQR07] F. Chyzak, A. Quadrat, and D. Robertz, OreModules: A Symbolic Package for the Study of Multidimensional Linear Systems. In: Applications of Time-Delay Systems. Chiasson, J. and Loiseau, J.-J. (Eds.), LNCIS 352, Springer, 2007, pp. 233-264.

  • [CS98] F. Chyzak and B. Salvy, Non-commutative elimination in Ore algebras proves multivariate identities. J. Symbolic Computation, 26 (1998), pp. 187-227.

  • [Cou95] S. C. Coutinho A Primer of Algebraic D-modules. London Mathematical Society Student Texts 33, Cambridge University Press, 1995.

  • [DPR99] F. Dubois, N. Petit, and P. Rouchon, Motion Planning and Nonlinear Simulations for a Tank Containing a Fluid. Proc. of the 5th European Control Conf. 1999, Karlsruhe.

  • [Fab06] Anna Fabianska, QuillenSuslin: A Maple package to compute a free basis of a projective module over the polynomial ring.

  • [FQ07] Anna Fabianska and Alban Quadrat, Applications of the Quillen-Suslin theorem to multidimensional systems theory. In: H. Park et G. Regensburger (eds.), Gröbner Bases in Control Theory and Signal Processing, Radon Series on Computational and Applied Mathematics 3, de Gruyter, 2007, 23-106.

  • [GAP06] The GAP Group, GAP - Groups, Algorithms, and Programming. (Version 4.4, 2006). (https://www.gap-system.org).

  • [Ger05] V. P. Gerdt, Involutive Algorithms for Computing Gröbner Bases. In: S. Cojocaru, G. Pfister, and V. Ufnarovski (eds.), Computational Commutative and Non-Commutative Algebraic Geometry, NATO Science Series, IOS Press, 2005, pp. 199-225.

  • [GB98a] V. P. Gerdt and Y. A. Blinkov, Involutive bases of polynomial ideals. Mathematics and Computers in Simulation, 45 (1998), pp. 519-541.

  • [GB98b] V. P. Gerdt and Y. A. Blinkov, Minimal involutive bases. Mathematics and Computers in Simulation, 45 (1998), pp. 543-560.

  • [GM03] Sergei I. Gelfand and Yuri I. Manin, Methods of homological algebra. Second ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.

  • [GPS05] G. M. Greuel, G. Pfister, and H. Schönemann, Singular 3.0, A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern, 2005, (https://www.singular.uni-kl.de).

  • [HS97] P. J. Hilton and U. Stammbach, A course in homological algebra. Second ed., Graduate Texts in Mathematics, vol. 4, Springer-Verlag, New York, 1997.

  • [Kai80] T. Kailath, Linear Systems. Prentice-Hall, 1980.

  • [LM89] H. Blaine Lawson, Jr. and Marie-Louise Michelsohn, Spin geometry. Princeton Mathematical Series, vol. 38, Princeton University Press, Princeton, NJ, 1989.

  • [LS03] Viktor Levandovskyy and Hans Schönemann, PLURAL - a computer algebra system for noncommutative polynomial algebras. Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation (New York), ACM, 2003, pp. 176-183 (electronic).

  • [MR01] J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings. Revised ed., Graduate Studies in Mathematics, vol. 30, American Mathematical Society, Providence, RI, 2001, With the cooperation of L. W. Small.

  • [Mou95] H. Mounier, Propriétés structurelles des systèmes linéaires à retards: aspects théoriques et pratiques. PhD Thesis, University of Orsay, France, 1995.

  • [PR02] N. Petit and P. Rouchon, Dynamics and Solutions to Some Control Problems for Water-Tank Systems. IEEE Trans. Autom. Contr., 47 (2002), no. 4, pp. 594-609.

  • [PR05] W. Plesken and D. Robertz, Janet's approach to presentations and resolutions for polynomials and linear pdes. Archiv der Mathematik, 84(1) (2005), pp. 22-37.

  • [PQ03] J.-F. Pommaret and A. Quadrat, A functorial approach to the behaviour of multidimensional control systems. Int. J. Appl. Math. Comput. Sci. 13(1) (2003), pp. 7-13 (Multidimensional systems $n{\rm D}$ and iterative learning control (Czocha Castle, 2000)).

  • [QR07] A. Quadrat and D. Robertz, Computation of bases of free modules over the Weyl algebras. Journal of Symbolic Computation, 42:11-12 (2007), 1113-1141.

  • [Rob06] Daniel Robertz, JanetOre: A Maple package to compute a Janet basis for modules over Ore algebras.

  • [Rot79] J. J. Rotman, An Introduction to Homological Algebra. Academic Press, 1979.