Let S be
a polynomial system of equations in X_{1},...,X_{n}.
Furthermore, assume that its coefficients depend on the symbolic
parameters T_{1},...,T_{s}.
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:
X_{1}=Q_{1}(T_{1},...,T_{s},Z), ..., X_{n}=Q_{n}(T_{1},...,T_{s},Z)
and P(T_{1},...,T_{s},Z)=0
where Q_{1},...,Q_{n}
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.
