Computing the Singularities of Rational Surfaces

Given a rational projective parametrization $\text{cP}(\text{ttt},\text{sss},\text{vvv})$ of a rational projective surface $\text{cS}$ we present an algorithm such that, with the exception of a finite set (maybe empty) $\text{cB}$ of projective base points of $\text{cP}$, decomposes the projective parameter plane as $\projdos\setminus \cB=\cup_{k=1}^{\ell} \cSm_k$suchthatif$(\ttt_0:\sss_0:\vvv_0)\in \cSm_k$then$\cP(\ttt_0,\sss_0,\vvv_0)$isapointof$\cS$ofmultiplicity$k$.