2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99894This is the first part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. The main result of this part is a constructibility result for the analytic Gröbner fan of a parametric ideal in the ring of analytic differential operators. In this part, the main tool is the notion of generic reduced standard basis.10 pages. Accepted version in Proc. Japan Academy Ser. A. (part 2 is math.AG/0603381)Rings and AlgebrasCommutative Algebratext