Abstract
In this paper a polynomial map from Cn to Cm is studied in order to investigate if it is injective out of a set of measure zero. We propose a procedure, based on truncated Gröbner basis computations, which when successful, allows to reduce the problem to an easier map, and so gives a speed-up of the general algorithms using Gröbner basis techniques. Moreover, for the special case of a polynomial map from Cn to Cn where the polynomials are at most quadratic, we propose two criteria for non-injectivity based on the structure of the Jacobian matrix and requiring only basic symbolic computations.
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Audoly, S., Bellu, G., Buttu, A. et al. Procedures to investigate injectivity of polynomial maps and to compute the inverse. AAECC 2, 91–103 (1991). https://doi.org/10.1007/BF01810570
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DOI: https://doi.org/10.1007/BF01810570