|Let S be
a polynomial system of equations in X1,...,Xn.
Furthermore, assume that its coefficients depend on the symbolic
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)
are rational functions, P is a
polynomial and Z is a new
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.