Tate pairing computation in SAGE III
January 10th, 2008The latest version of my ellnet class is ellnet2d_lowmem.spyx. It combines all the tricks I know of:
- The use of precomputed inverses for all steps, and precomputed squares/products for each step, as described by Stange,
- computation with a local vector to avoid overhead from function calls to keep the dictionary up-to-date,
- mixed block lengths as described in the previous post,
- and compilation to pyrex.
Thus it’s the fastest implementation I currently have for finding Tate pairings in SAGE (about twice as fast as accessing Stange’s PARI script from SAGE). Attach it in the normal way; example calculations are here.