References

 


  • Y. A. Blinkov, C. F. Cid, V. P. Gerdt, W. Plesken, D. Robertz,
    The MAPLE Package "Janet": I. Polynomial Systems,
    In the Proccedings of Computer Algebra in Scientific Computing CASC 2003
    edited by V. G. Ganzha, E.W. Mayr, E.V. Vorozhtsov, 31-40.
    Also available with the package from http://http://wwwb.math.rwth-aachen.de/Janet.

  • D. Cox, j. Little, D. O'Shea,
    Using Algebraic Geometry,
    Springer, 1998.

  • A. Fabiańska, A. Quadrat,
    Flat Multidimensional linear systems with constant coefficients are equivalent to controllable 1-D systems,
    In the Proceedings of Mathematical Theory of Networks and Systems (MTNS),
    Kyoto (Japan), 24-28/07/06.

  • A. Fabiańska, A. Quadrat,
    Applications of the Quillen-Suslin theorem to the multidimensional systems theory,
    INRIA Report 6126 (2007), published in Gröbner Bases in Control Theory and Signal Processing ,
    H. Park et G. Regensburger (Eds.), Radon Series on Computation and Applied Mathematics 3, de Gruyter publisher, pp. 23-106.
    Available as .pdf

  • N. Fitchas, A. Galigo,
    Nullstellensatz effectif et conjecture de Serre (Théorème de Quillen-Suslin) pour le calcul formel,
    Math. Nachr., 149 (1990), 231-253.

  • J. Gago-Vargas,
    Constructions in R[x_1,... x_n]: applications to K-theory,
    Journal of Pure and Applied Algebra, 171 (2002), 185-196.

  • K. Gałkowski,
    State-space realizations of linear 2-D systems with extensions to the general nD case,
    Lecture Notes in Control and Information Sciences, Springer 2001

  • H. Kwakernaak, R. Sivan,
    Linear Optimal Control Systems,
    Wiley-Interscience, 1972.

  • R. C. Laubenbacher, C.J. Woodburn,
    A new algorithm for the Quillen-Suslin Theorem,
    Contributions to Algebra and Geometry, 41 (2000), 23-31.

  • T.Y. Lam,
    Serre's Conjecture,
    Lecture Notes in Mathematics 635, Springer Verlag, 1978.

  • T.Y. Lam,
    Serre's Problem on projective Modules,
    Springer Monograph in Mathematics, Springer Verlag, 2006.

  • Z. Lin, N. K. Bose,
    A generalisation of Serre's Conjecture and related issues,
    Linear Algebra and Its Applications, 338 (2001), 125-138.

  • A. Logar, B. Sturmfels,
    Algorithms for the Quillen-Suslin Theorem,
    Journal of Algebra, 145 (1992), 231-239.

  • H. Logemann,
    On the transfer matrix of a neutral system: characterizations of exponential stability in input-output terms,
    Systems and Control Letters, 9 (1987), 393-400.

  • H. Lombardi, I. Yengui,
    Suslin's algorithms for reduction of unimodular rows,
    Journal of Symbolic Computation, 39 (2005), 707-717.

  • A. Morou, I. Yengui,
    An algorithm for unimodular completion over Laurent polynomial rings,
    private communication, (preprint, 2007).

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

  • H. Park, C. J. Woodburn,
    An algorithmic proof of Suslin's stability theorem for Polynomial rings,
    Journal of Algebra, 178 (1995), 277-298.

  • H. Park,
    A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems,
    PhD Thesis, University of Berkeley, USA, 1995.

  • H. Park,
    Symbolic computation and signal processing,
    Journal of Symbolic Computation, 37 (2004), 209-226.

  • H. Park,
    Generalizations and variations of Quillen-Suslin theorem and their applications,
    workshop Gröbner Bases in Control Theory and Signal Processing,
    Special semester on Gröbner Bases and related methods 2006, University of Linz (Austria), 19/05/06.

  • J. F. Pommaret,
    Solving Bose conjecture on linear multidimensional systems,
    In the Proceedings of European Control Conference (ECC), Porto (Portugal), 04-07/09/01.

  • A. Quadrat, D.Robertz,
    Constructive computation of bases of free modules over the Weyl algebras,
    INRIA Report 5786 (2005), available at http://www-sop.inria.fr/apics/personnel/Alban.Quadrat/index.html.

  • D. Quillen,
    Projective modules over polynomial rings,
    Invent. Math., 36 (1976), 167-171.

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

  • A. A. Suslin,
    Projective modules over polynomial rings are free,
    Dokl. Akad. Nauk. S.S.S.R. 229 (176),(Soviet Math. Dokl., 17, 1160-1164).

  • L. N. Vaserstein, A. A. Suslin,
    Serre's Problem on projective modules over polynomial rings and algebraic K-theory,
    Math. USSR Izviestija, 10 (1976), no. 5, 937-1001.

  • I. Yengui,
    Suslin's lemma for elimination,
    preprint 2006, private communication.

  • D. C. Youla, P. F. Pickel,
    The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices,
    Trans, Circuits and Systems, 31 (1984), 513-517.

  • M. Wang, D. Feng
    On Lin-Bose problem,
    LinearAlgebra and its Applications, 390 (2004), 279-285.

  • M. Wang, C. P. Kwong
    On multivariate polynomial matrix factorizations problems,
    Math. Control Signals Systems, 17 (2005), 297-311.