On bounds for the effective differential Nullstellensatz
Omar Le\'on S\'anchez, Alexey Ovchinnikov
TL;DR
This paper refines bounds related to the effective differential Nullstellensatz in differential algebraic geometry, making them more explicit and applicable for analyzing computational complexity and improving algorithm efficiency.
Contribution
It provides more explicit bounds for the effective differential Nullstellensatz, enhancing understanding of computational complexity and aiding in the design of better algorithms.
Findings
More explicit bounds derived from Dicksonian and antichains sequences
Improved understanding of the computational complexity involved
Potential for designing more efficient algorithms
Abstract
Understanding bounds for the effective differential Nullstellensatz is a central problem in differential algebraic geometry. Recently, several bounds have been obtained using Dicksonian and antichains sequences (with a given growth rate). In the present paper, we make these bounds more explicit and, therefore, more applicable to understanding the computational complexity of the problem, which is essential to designing more efficient algorithms.
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