⇤ ← Revision 1 as of 20070930 13:36:34
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Put together a padic heights calculator for hyperelliptic curves.  The main goal was to put together a padic heights calculator for hyperelliptic curves. Before we have extensions of padics, 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. 
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Develop a version of Harvey's algorithm for computing Coleman integrals.  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.) 
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Come up with a good framework for doing iterated Coleman integrals (for use in the nonabelian Chabauty method).  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). 
The main goal was to put together a padic heights calculator for hyperelliptic curves. Before we have extensions of padics, 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).