Function: ellformallog
Section: elliptic_curves
C-Name: ellformallog
Prototype: GDPDn
Help:ellformallog(E, {n = seriesprecision}, {v = 'x}): E elliptic curve,
 returns n terms of the elliptic logarithm as a series of t =-x/y.
Doc: The formal elliptic logarithm is a series $L$ in $t K[[t]]$
 such that $d L = \omega = dx / (2y + a_1x + a_3)$, the canonical invariant
 differential attached to the model $E$. It gives an isomorphism
 from the formal group of $E$ to the additive formal group.
 \bprog
 ? E = ellinit([-1,1/4]); L = ellformallog(E, 9, 't)
 %1 = t - 2/5*t^5 + 3/28*t^7 + 2/3*t^9 + O(t^10)
 ? [f,g] = ellformaldifferential(E,8,'t);
 ? L' - f
 %3 = O(t^8)
 @eprog
