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Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability

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Algebraic and Symbolic Computation Methods in Dynamical Systems

Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 9))

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Abstract

In this work, we provide an overview of the classical symbolic techniques for solving algebraic systems of equations and show the interest of such techniques in the study of some problems in dynamical system theory, namely testing the structural stability of multidimensional systems.

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Notes

  1. 1.

    \(\text {Trunc}(P_i)\) refers to the polynomial obtained after reducing all the coefficients of \(P_i\) modulo \(\text {lc}_{x_n} (P_i)\).

  2. 2.

    Here, the term compact is used for subsets of the Euclidean space \(\mathbbm {R}^n\), which are closed and bounded regarding to the classical Euclidean topology.

  3. 3.

    An algebraic variety is said to be equidimensional if all it irreducible components have the same dimension.

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Author information

Authors and Affiliations

  1. Inria, Lille-Nord Europe, Villeneuve-d’Ascq, France

    Yacine Bouzidi

  2. Inria, Paris, France

    Fabrice Rouillier

Authors
  1. Yacine Bouzidi
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  2. Fabrice Rouillier
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Correspondence to Yacine Bouzidi .

Editor information

Editors and Affiliations

  1. Inria Paris, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne University, Paris, France

    Alban Quadrat

  2. Lehrstuhl D fuer Mathematik, RWTH Aachen University, Aachen, Germany

    Eva Zerz

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Bouzidi, Y., Rouillier, F. (2020). Symbolic Methods for Solving Algebraic Systems of Equations and Applications for Testing the Structural Stability. In: Quadrat, A., Zerz, E. (eds) Algebraic and Symbolic Computation Methods in Dynamical Systems. Advances in Delays and Dynamics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-38356-5_8

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