Function: ellchangecompose
Section: elliptic_curves
C-Name: ellchangecompose
Prototype: GGG
Help: ellchangecompose(E,v,w): composes the transformations given
 by v=[u,r,s,t] and w=[U,R,S,T].
Doc:
 Compose the transformations given by \kbd{v=[u,r,s,t]} and \kbd{w=[U,R,S,T]}
 and return \kbd{[u*U,r+R*u\^{}2,s+S*u,t+T*u\^{}3+R*s*u\^{}2]}.
 \bprog
 ? E = ellinit([a1,a2,a3,a4,a6]);
 ? v = [u,r,s,t]; w = [U,R,S,T]; P = [x,y];
 ? vw = ellchangecompose(E,v,w)
 %3 = [U*u,R*u^2+r,S*u+s,T*u^3+R*s*u^2+t]
 ? ellchangepoint(ellchangepoint(E,P,v),w) == ellchangepoint(E,P,vw)
 %4 = 1
 @eprog\noindent Note that the elliptic curve $E$ is not needed in itself,
 it indicates the domain over which the transformation is defined. This
 is required when $E$ and the transformation are defined over a number field,
 in order to support number field elements given in column form.
