Reduction of Power Series in a Polydisc with Respect to a Gröbner Basis

Volume 53 / 2005

Justyna Szpond Bulletin Polish Acad. Sci. Math. 53 (2005), 137-145 MSC: 13P10, 32C07. DOI: 10.4064/ba53-2-3


We deal with a reduction of power series convergent in a polydisc with respect to a Gröbner basis of a polynomial ideal. The results are applied to proving that a Nash function whose graph is algebraic in a “large enough” polydisc, must be a polynomial. Moreover, we give an effective method for finding this polydisc.


  • Justyna SzpondInstitute of Mathematics
    Pedagogical University
    Podchor/a/zych 2
    30-084 Krak/ow, Poland

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