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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 analgorithm 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 arein practice computationaly easy to obtain from any triangulation for $M^3$. Theconjecture that each closed oriented 3-manifold is induced by a solvable gemhas been verified in an exhaustible way for manifolds induced by gems with fewvertices. Our algorithm produces framed link presentations for well known3-manifolds which hitherto did not one explicitly known. A consequence of thiswork is that the 3-manifold invariants which are presently only computed fromsurgery presentations (like the Witten-Reshetkhin-Turaev invariant) becomecomputable also from triangulations. This seems to be a new and useful result.Our exposition is partitioned into 3 articles. This first article provides ourmotivation, some history on presentation of 3-manifolds and recall facts aboutgems which we need.

Framed link presentations of 3-manifolds by an $O(n^2)$ algorithm, I: gems and their duals