Implicitization of differential rational parametric equations

In this paper, we propose algorithms for the following problems in the implicitization of a set of differential rational parametric equations <f>P</f>. (1) To find a characteristic set for the implicit prime ideal of <f>P</f>. (2) To find a canonical representation for the image of <f>P</f>. (3) To decide whether the parameters of <f>P</f> are independent, and if not, to re-parameterize <f>P</f> so that the new parametric equations have independent parameters. (4) To compute the inversion maps of <f>P</f>, and as a consequence, to decide whether <f>P</f> is proper. If the implicit variety is of dimension one and <f>P</f> is not proper, to find a proper re-parameterization for <f>P</f>. [Copyright &y& Elsevier]