On the Problem of Separating Variables in Multivariate Polynomial Ideals
Abstract
For a given ideal I in K[x1,...,xn,y1,...,ym] in a polynomial ring with n+m variables, we want to find all elements that can be written as f-g for some f in K[x1,...,xn] and some g in K[y1,...,ym], i.e., all elements of I that contain no term involving at the same time one of the x1,...,xn and one of the y1,...,ym. For principal ideals and for ideals of dimension zero, we give a algorithms that compute all these polynomials in a finite number of steps.
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