  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.
