Function: ellmul
Section: elliptic_curves
C-Name: ellmul
Prototype: GGG
Help: ellmul(E,z,n): n times the point z on elliptic curve E (n in Z).
Doc:
 computes $[n]z$, where $z$ is a point on the elliptic curve $E$. The
 exponent $n$ is in $\Z$, or may be a complex quadratic integer if the curve $E$
 has complex multiplication by $n$ (if not, an error message is issued).
 \bprog
 ? Ei = ellinit([1,0]); z = [0,0];
 ? ellmul(Ei, z, 10)
 %2 = [0]     \\ unsurprising: z has order 2
 ? ellmul(Ei, z, I)
 %3 = [0, 0]  \\ Ei has complex multiplication by Z[i]
 ? ellmul(Ei, z, quadgen(-4))
 %4 = [0, 0]  \\ an alternative syntax for the same query
 ? Ej  = ellinit([0,1]); z = [-1,0];
 ? ellmul(Ej, z, I)
   ***   at top-level: ellmul(Ej,z,I)
   ***                 ^--------------
   *** ellmul: not a complex multiplication in ellmul.
 ? ellmul(Ej, z, 1+quadgen(-3))
 %6 = [1 - w, 0]
 @eprog
 The simple-minded algorithm for the CM case assumes that we are in
 characteristic $0$, and that the quadratic order to which $n$ belongs has
 small discriminant.
