In 1990 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results for the improved projection was subsequently noticed. In this report we study a more limited but rigorous concept of Lazard's valuation: namely, we study Lazard's valuation of a multivariate polynomial at a point. We prove some basic properties of the limited Lazard valuation and identify some relationships between valuation-invariance and order-invariance.
Cite
@article{arxiv.1501.06563,
title = {On Lazard's Valuation and CAD Construction},
author = {Scott McCallum and Hoon Hong},
journal= {arXiv preprint arXiv:1501.06563},
year = {2015}
}