  Given an special type of triangulation $T$ for an oriented closed 3-manifold
$M^3$ we produce a framed link in $S^3$ which induces the same $M^3$ by an
algorithm of complexity $O(n^2)$ where $n$ is the number of tetrahedra in $T$ .
The special class is formed by the duals of the {\em solvable gems}. These are
in practice computationaly easy to obtain from any triangulation for $M^3$. The
conjecture that each closed oriented 3-manifold is induced by a solvable gem
has been verified in an exhaustible way for manifolds induced by gems with few
vertices. Our algorithm produces framed link presentations for well known
3-manifolds which hitherto did not one explicitly known. A consequence of this
work is that the 3-manifold invariants which are presently only computed from
surgery presentations (like the Witten-Reshetkhin-Turaev invariant) become
computable also from triangulations. This seems to be a new and useful result.
Our exposition is partitioned into 3 articles. This first article provides our
motivation, some history on presentation of 3-manifolds and recall facts about
gems which we need.
