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math.AG2026
Effective bounds for polynomial systems defined over the rationals
Teresa Krick
This survey paper was primarily written as as the support for a course pesented at the JNCF2025: it aims to present some material that illustrates the kind of estimates one can obt…
math.AG2025
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…