  We consider the problem of bounding away from 0 the minimum value m taken by
a polynomial P of Z[X_1,...,X_k] over the standard simplex, assuming that m>0.
Recent algorithmic developments in real algebraic geometry enable us to obtain
a positive lower bound on m in terms of the dimension k, the degree d and the
bitsize of the coefficients of P. The bound is explicit, and obtained without
any extra assumption on P, in contrast with previous results reported in the
literature.
