@inproceedings{46618a75d4a84316a7d13840b53ccdd7,
title = "Inversibility of rational mappings and structural identifiability in automatics",
abstract = "We investigate different methods for testing whether a rational mapping f 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 f. Our method can also extend to check whether a given polynomial belongs to the subfield generated by a finite set of fractions. We then illustrate our algorithm, with a application to structural identifiability. The implementation has been done in the IBM computer algebra system Scratchpad II.",
author = "Fran{\c c}ois Ollivier",
note = "Publisher Copyright: {\textcopyright} 1989 ACM.; 1989 ACM-SIGSAM International Symposium on Symbolic and Algebraic Computation, ISSAC 1989 ; Conference date: 17-07-1989 Through 19-07-1989",
year = "1989",
month = jul,
day = "17",
doi = "10.1145/74540.74547",
language = "English",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
publisher = "Association for Computing Machinery",
pages = "43--54",
editor = "Gonnet, \{G. H.\}",
booktitle = "Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, ISSAC 1989",
}