A Landen-Type Method for Computation of Weierstrass Functions

Landen's method is widely known in the context of elliptic integrals and Jacobi elliptic functions. Its essence consists in calculating an elliptic function or integral through the values of the same function with other modular parameters corresponding to doubling one of the periods. Iterating this procedure results in an efficient computational method, particularly since the modular parameters experience quadratic convergence. The report will be devoted to a similar method for computation of Weierstrass functions. It will also be shown how to efficiently calculate the Abel map of a genus 1 curve (in other words, elliptic integral in Weierstrass form) and periods of the elliptic curve, given only the Weierstrass invariants.
(This is a joint work with K.Malkov)