Since EDS are the rank 1 case of elliptic nets, Stange’s approach to the rank 2 case can be specialised to them: we are only concerned with terms of the form (x,0), so only the bottom row of a block need be calculated. Such sequences are considered when pairing a point with itself.
Thus I’ve simplified the ellnet class to give another eds class. I’ve changed the internals so that this class can be initialized and interacted with in the same way as my previous eds class based on Shipsey’s algorithm. (You retrieve the n term from a rank 1 net X using X[n] rather than the X[(n,0)] required for a general elliptic net, for instance.) There will probably be a few discrepencies to be ironed out, but I’ve thrown in the ward_point methods necessary for height calculation, and hope to have the two versions interchangeable in due course.
This requires only 1 initial inversion, and continues to use the step-by-step precomputation speedups given by Stange. It doesn’t support the larger jumps possible with Shipsey’s algorithm, although my existing code doesn’t exploit these as fully as it could anyway. Final doublings are still performed with smaller blocks, so for height estimation purposes it’s probably wise to choose a power of two for the term used.
The next post illustrates pairing computation with rank 1 nets.
