On the Problem of Separating Variables in Multivariate Polynomial Ideals
<|reference_start|>On the Problem of Separating Variables in Multivariate Polynomial Ideals: 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.<|reference_end|>
@article{buchacher2024on,
    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},
    doi={10.1145/3666000.366968},
    archivePrefix={arXiv},
    eprint={2405.19223},
    primaryClass={cs.SC}
}