finding out if expr has the form F(y/x^a)

NB <nijso <at> hotmail.com> writes:

> 
> Dear all,
> 
> I would like to find out if an expression is of (or can be written in)
 the general form (y/x)*f(y/x^a), with 'a' a nonzero constant. 

 This version takes into account that a is required to be nonzero.

load(pdiff);

usol(g,a0):=block([f0,g0],
if a0 = 0 then return([g,false]),
if a0 = 'any then (f0:g*x/y,g0:ratsimp(y/x*f0),
return(['a = a0,'f = f0,
g =g0,is(ratsimp(g-g0) = 0)])),
f0:ratsimp(at(ratsimp(g*x/y),y = x^(a0+1))),
g0:ratsimp(y/x*at(f0,x = y/x^a0)),
['a = a0,'f = f0,g = g0,is(ratsimp(g-g0) = 0)]);

sol3(g):=block([f0,a,f],
f0:ratsimp(g*x/y),
if freeof(x,y,f0) then return(usol(g,'any)),
if diff(f0,x) = 0 or diff(f0,y) = 0 then return([g,false]),
a0:ratsimp((-1)/at(diff(f0,y)/diff(f0,x),y = t*x)/t),
if not freeof(x,y,t,a0) then return([g,false])
 else return(usol(g,a0)));

test:[0,7,1/x,y/x,y/x*h(y/x^m),1/(y-1/x),
y^3+1/x^(3/2),h(x*y)*y/x,1/x^2,1/(y-1/x^n)];

map(sol3,test);