The Derivative of a Constructible Function is Constructible
Logic
2026-04-28 v3 Algebraic Geometry
Complex Variables
Abstract
The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subanalytic functions. A function on a globally subanalytic set is called constructible if it is a finite sum of finite products of globally subanalytic functions and the logarithm of positive globally subanalytic functions. We show that the class of constructible functions is stable under taking derivatives.
Cite
@article{arxiv.2508.02517,
title = {The Derivative of a Constructible Function is Constructible},
author = {Tobias Kaiser},
journal= {arXiv preprint arXiv:2508.02517},
year = {2026}
}
Comments
To appear in Canadian Mathematical Bulletin