Implicitization of differential rational parametric equations.
The problem of implicitization for algebraic varieties takes care of finding algorithms to get the ideal of an unirational algebraic variety from a system of parametric equations. This classical problem has been much studied in recent years with the method of Gröbner bases. Here the analogous problem is studied for differential varieties. The definitions of implicit prime ideal of a set of differential rational parametric equations and of characteristic set are given. The following problems are studied and partially solved: to find a characteristic set, to prove the independence of the parameters, to give a reparametrization if the parameters are dependent, to compute the inversion map of a set of differential rational parametric equations.
differential rational parametric equations
unirational differential algebraic varieties
scientific article; zbMATH DE number 2056565
scientific article