Computing branches and asymptotes of meromorphic functions (Q6100700)

The lowest degree curve \(\tilde{\mathcal{C}}\) approximating a given one \(\mathcal{C}\) near a given point at infinity is known as a generalized asymptote of \(\mathcal{C}\). The paper begins by recalling the formal definition of a generalized asymptote by means of Puisieux series near the points at infinity of a curve. Later the authors review previously existing algorithms to compute generalized asymptotes of plane algebraic curves, either implicitly or explicitly defined. As its main result, the paper introduces, by means of the concept of perfect curves (a curve that is its own generalized asymptote), a way to extend those tecniques to parametrically defined curves in any-dimensional spaces through limit computations. It must be also noted that the parametrization is not assumed to be rational.