Computing Constraint Sets for Differential Fields
Commutative Algebra
2014-04-15 v2 Classical Analysis and ODEs
Logic
Abstract
Kronecker's Theorem and Rabin's Theorem are fundamental results about computable fields F and the decidability of the set of irreducible polynomials over F. We adapt these theorems to the setting of differential fields K, with constrained pairs of differential polynomials over K assuming the role of the irreducible polynomials. We prove that two of the three basic aspects of Kronecker's Theorem remain true here, and that the reducibility in one direction (but not the other) from Rabin's Theorem also continues to hold.
Cite
@article{arxiv.1208.1152,
title = {Computing Constraint Sets for Differential Fields},
author = {Russell Miller and Alexey Ovchinnikov and Dmitry Trushin},
journal= {arXiv preprint arXiv:1208.1152},
year = {2014}
}
Comments
42 pages