We study the triangular representation of zero-dimensional varieties defined over the rational field and prove polynomial bounds in terms of intrinsic quantities for the height (resp. degree) of the coefficients of such triangular sets, whereas previous bounds were exponential.Expand

We show that computing suitable sections of the polar varieties associated to generic projections of V gives at least one point in each connected component of V ∩ <b>R</b><sup>.Expand

We present an algorithm based on the birthday paradox, which is a low-memory parallel counterpart to the algorithm of Matsuo, Chao and Tsujii, but the memory requirement drops from several GB to almost nothing.Expand