Computations with Parameters: A Theoretical Background

Abstract

Consider a computational algebraic problem with inputs depending on parameters. The aim of the computation is to stratify the variety of parameters so that for each stratum \( {\mathcal{W}}_{\alpha } \), for arbitrary values of the parameters from \( {\mathcal{W}}_{\alpha } \), the solution of the problem as a function of the parameters is computed by the same algebraic formulas depending only on the stratum \( {\mathcal{W}}_{\alpha } \). We suggest a model for computations with parameters which is convenient for practical purposes and prove a fundamental result for it.