First presenter Co-presenter(s)
Name :  Guillaume  Moroz * Name:   
E-mail: E-mail:  
Affiliation: Maplesoft Name:   
Department:   E-mail:    
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Country: Canada Name:   
14-04  E-mail:    
Session: 14- Algorithms for Parametric Systems and their Applications Schedule:
Thursday, 12:00
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Title of
Groebner bases and parametrization
Let S be a polynomial system of equations in X1,...,Xn. Furthermore, assume that its coefficients depend on the symbolic parameters T1,...,Ts. A natural problem in some applications is to compute a parametrization of the solutions of S.

Under some assumptions, the solutions of S can be written under the shape:

X1=Q1(T1,...,Ts,Z),  ...,  Xn=Qn(T1,...,Ts,Z) and P(T1,...,Ts,Z)=0
where Q1,...,Qn are rational functions, P is a polynomial and Z is a new symbolic variable.

We will give an overview of different methods computing such a parametrization. Then we will present a parametrization based on Groebner basis computation for a specific product order, and show the advantages of this representation on some examples.