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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Reduction of power series in a polydisc with respect to a Gröbner basis

Szpond J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 2

137-145

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.

On factorization of polynomials with holomorphic coefficients

Frontczak M., Skibiński A., Spodzieja S.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 1

39-54

In the paper some equivalent conditions to pointwise reducibility of polynomials with holomorphic coefficients (in an arbitrary connected set) are given.