Year: 2025
Type: preprint
Abstract: The computational complexity of polynomial ideals and Gröbner bases has been studied since the 1980s. In recent years, the related notions of polynomial subalgebras and SAGBI bases have gained more and more attention in computational algebra, with a view towards effective algorithms. We investigate the computational complexity of the subalgebra membership problem and degree bounds. In particular, we show completeness for the complexity class EXPSPACE and prove PSPACE-completeness for homogeneous algebras. We highlight parallels and differences compared to the settings of ideals, and also look at important classes of polynomials such as monomial algebras.
Source: arXiv (Cornell University)
Author: Kayser, Leonie
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407369375