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30 papers · 1 filter
Jacobi Stability Analysis for Systems of ODEs Using Symbolic Computation
Bo Huang, Dongming Wang, Jing Yang
The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory…
Solving parameter-dependent semi-algebraic systems
Louis Gaillard, Mohab Safey El Din
We consider systems of polynomial equations and inequalities in where and $\boldsymbol{y} = (y_1,…
Faster real root decision algorithm for symmetric polynomials
George Labahn, Cordian Riener, Mohab Safey El Din +2
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the a…
Algorithm for connectivity queries on real algebraic curves
Md Nazrul Islam, Adrien Poteaux, Rémi Prébet
We consider the problem of answering connectivity queries on a real algebraic curve. The curve is given as the real trace of an algebraic curve, assumed to be in generic position,…
Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry
Damien Chablat, Rémi Prébet, Mohab Safey El Din +2
Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been st…
A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System
Christian Eder, Pierre Lairez, Rafael Mohr +1
Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-u…