Finding the Inverse of a Transformation: Solving for u and v

[Castilla]

By some reason I can't access to Latex...

Let be (x, y) = T(u,v) = (uv, v^u)

So x = x(u,v) = uv
and y = y(u,v) = v^u.

I see that T is an injective function, but I can't find u = u(x, y). Can you help me?

Thanks.

 

[EnumaElish]

This involves a transcendental function. I'd try Mathematica see what it'd come up with, but I am not hopeful.

 

[Castilla]

Well let's drop that function, I would thank if you could provide any example of a transformation with its inverse.

 

[EnumaElish]

Suppose x=uv, y=vu^2. Then v=x/u. Substitute into y=vu^2 to get y=xu; solve for u=y/x.

 

[Castilla]

OK, so u = u(x,y) = y/x and v = v(x,y) = (x^2)/y.

Thanks, Enuma!