English

On the Problem of Separating Variables in Multivariate Polynomial Ideals

Symbolic Computation 2024-05-30 v1

Abstract

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.

Cite

@article{arxiv.2405.19223,
  title  = {On the Problem of Separating Variables in Multivariate Polynomial Ideals},
  author = {Manfred Buchacher and Manuel Kauers},
  journal= {arXiv preprint arXiv:2405.19223},
  year   = {2024}
}
R2 v1 2026-06-28T16:45:49.888Z