Yi Zhou, Parikshit Ram, et al.
ICLR 2023
The purpose of this paper is to give a complete effective solution to the problem of computing radicals of polynomial ideals over general fields of arbitrary characteristic. We prove that Seidenberg's "Condition P" is both a necessary and sufficient property of the coefficient field in order to be able to perform this computation. Since Condition P is an expensive additional requirement on the ground field, we use derivations and ideal quotients to recover as much of the radical as possible. If we have a basis for the vector space of derivations on our ground field, then the problem of computing radicals can be reduced to computing pth roots of elements in finite dimensional algebras.
Yi Zhou, Parikshit Ram, et al.
ICLR 2023
A.R. Gourlay, G. Kaye, et al.
Proceedings of SPIE 1989
Renu Tewari, Richard P. King, et al.
IS&T/SPIE Electronic Imaging 1996
Martin C. Gutzwiller
Physica D: Nonlinear Phenomena