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math.AG2012
On the Pierce-Birkhoff Conjecture
François Lucas, Daniel Schaub, Mark Spivakovsky
This paper represents a step in our program towards the proof of the Pierce--Birkhoff conjecture. In the nineteen eighties J. Madden proved that the Pierce-Birkhoff conjecture for…
math.AG2007
On points at infinity of real spectra of polynomial rings
François Lucas, Daniel Schaub, Mark Spivakovsky
Let R be a real closed field and A=R[x_1,...,x_n]. Let sper A denote the real spectrum of A. There are two kinds of points in sper A : finite points (those for which all of |x_1|,.…