Inversibility of rational mappings and structural identifiability in automatics

摘要

We investigate different methods for testing whether a rational mapping ƒ from kn to km admits a rational inverse, or whether a polynomial mapping admits a polynomial one. We give a new solution, which seems much more efficient in practice than previously known ones using "tag" variables and standard basis, and a majoration for the degree of the standard basis calculations which is valid for both methods in the case of a polynomial map which is birational. We further show that a better bound can be given for our method, under some assumption on the form of ƒ. Our method can also extend to check whether a given polynomial belongs to the subfield generated by a finite set of fractions.

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We then illustrate our algorithm, with a application to structural identifiability. The implementation has been done in the IBM computer algebra system Scratchpad II.