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math.AG2026
A note on o-minimal tropicalizations
Lorenzo Baldi, Máté L. Telek
In this note, we provide several equivalent descriptions of the tropicalization of definable sets in a polynomially bounded o-minimal expansion of a real closed field. We show that…
math.AG2024
An Effective Positivstellensatz over the Rational Numbers for Finite Semialgebraic Sets
Lorenzo Baldi, Teresa Krick, Bernard Mourrain
We study the problem of representing multivariate polynomials with rational coefficients, which are nonnegative and strictly positive on finite semialgebraic sets, using rational s…
math.AG2023★ 15 cited
Degree bounds for Putinar's Positivstellensatz on the hypercube
Lorenzo Baldi, Lucas Slot
The Positivstellensätze of Putinar and Schmüdgen show that any polynomial positive on a compact semialgebraic set can be represented using sums of squares. Recently, there has…