Details:
Title  Properness defects of projection and minimal discriminant variety  Author(s)  Guillaume Moroz  Type  Article in Journal  Abstract  The problem of describing the solutions of a polynomial system appears in many different fields such as robotic, control theory, etc. When the system depends on parameters, its minimal discriminant variety is the set of parameter values around which the roots of the system cannot be expressed as a continuous function of the parameters. In particular, an important component of the minimal discriminant variety is the set of properness defects. This article presents a method efficient in practice and in theory to compute the nonproperness set of a projection mapping, by reducing the problem to a problem of variable elimination. We also present a reduction of the computation of the minimal discriminant variety to the computation of the nonproperness set of a projection mapping. This result allows us to deduce a bound on the degree and the time computation of the minimal discriminant variety of a parametric system under some assumptions.  Keywords  Parametric polynomial system, Discriminant variety, Elimination, Deterministic complexity  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111000848 
Language  English  Journal  Journal of Symbolic Computation  Volume  46  Number  10  Pages  1139  1157  Year  2011  Edition  0  Translation 
No  Refereed 
No 
