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Gröbner systems conversion. (English) Zbl 1409.68344
Summary: In this paper, we consider the problem of converting parametric Gröbner bases. More precisely, given a (comprehensive) Gröbner system w.r.t. a given monomial ordering, we present an efficient method to convert this system into a Gröbner system w.r.t. another monomial ordering. For this purpose, we develop the parametric variant of the generic Gröbner walk algorithm due to Fukuda et al. This new algorithm takes as input a monomial ordering and a Gröbner basis w.r.t. a set of parametric constraints, and outputs a decomposition of the given space of parameters as a finite set of (parametric) cells and for each cell a Gröbner basis w.r.t. the target monomial ordering.

MSC:
68W30 Symbolic computation and algebraic computation
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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