For a given ideal I in K[x_1,...,x_n,y_1,...,y_m] 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[x_1,...,x_n] and some g in K[y_1,...,y_m], i.e., all elements of I that contain no term involving at the same time one of the x_1,...,x_n and one of the y_1,...,y_m. For principal ideals and for ideals of dimension zero, we give a algorithms that compute all these polynomials in a finite number of steps.

翻译：对于多项式环K[x_1,...,x_n,y_1,...,y_m]中给定的理想I（包含n+m个变量），我们希望找出所有可表示为f-g形式的元素，其中f∈K[x_1,...,x_n]，g∈K[y_1,...,y_m]。换言之，即找出理想I中所有不包含同时涉及x_1,...,x_n与y_1,...,y_m中任意变量的项的多项式。针对主理想及零维理想情形，我们提出了可在有限步骤内计算所有此类多项式的算法。