The main goal was to put together a p-adic heights calculator for hyperelliptic curves. Before we have extensions of p-adics, we could:
 * Write a tiny integrals calculator for Weierstrass residue discs.
 * Expand a rational function with poles only in Weierstrass residue discs as a power series.
 * Implement Besser's techniques for calculating with local indices.

After that, we could:
 * Implement full Coleman integration between points defined over extension fields. (Beware: this requires a semilinear version of the fundamental linear system.)

Longer term projects could include:
 * Develop a version of Harvey's algorithm for computing Coleman integrals.
 * Come up with a good framework for doing iterated Coleman integrals (for use in the nonabelian Chabauty method).