  We present a new algorithm for computing the real radical of an ideal and,
more generally, the-radical of , which is based on convex moment optimization.
A truncated positive generic linear functional vanishing on the generators of
is computed solving a Moment Optimization Problem (MOP). We show that, for a
large enough degree of truncation, the annihilator of generates the real
radical of. We give an e ective, general stopping criterion on the degree to
detect when the prime ideals lying over the annihilator are real and compute
the real radical as the intersection of real prime ideals lying over. The
method involves several ingredients, that exploit the properties of generic
positive moment sequences. A new e cient algorithm is proposed to compute a
graded basis of the annihilator of a truncated positive linear functional. We
propose a new algorithm to check that an irreducible decomposition of an
algebraic variety is real, using a generic real projection to reduce to the
hypersurface case. There we apply the Sign Changing Criterion, e ectively
performed with an exact MOP. Finally we illustrate our approach in some
examples.
