パラメータ付きのイデアル操作の計算について

Abstract

This article introduces computations of ideals with parameters. Many ideal operations with parameters can be computed using comprehensive Gröbner systems. Let K[A, X] be the polynomial ring over a field 𝘒, where A= {a₁, ..., aₘ} is a set of parameters and X = {x₁, ..., xₙ} is a set of ordinary valuables. For a value α∈Kᵐ, we denote by φα the homomorphism from K[A, X]→K[X] by φα(f(A, X)) = f (α, X). For a given parametric ideal operation F and input ideals I₁, ..., Iₗ of K[A, X], we compute a system of pairs (Sᵢ, Gᵢ) such that φα(Gᵢ) is a basis of F(φα(I₁), ..., φα(Iₗ)) for all α∈ Sᵢ and ∪Sᵢ = Kᵐ.