  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 effective, 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 efficient 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, effectively performed with an
exact MOP. Finally we illustrate our approach in some examples.

Commutative Algebra;Algebraic Geometry;Optimization and Control