Implicitization of differential rational parametric equations

  • Authors:

  • Xiao-Shan Gao

  • Affiliations:

  • Key Lab of Mathematics Mechanization, Institute of System Science, AMSS, Academia Sinica, Beijing 100080, China

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2003

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Abstract

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