Hey guys,
I have a problem with the solve command. And since the websites are down, I cant help myself. I have a function x(y) and an intervall for y. This function or the set of points described by the function should now be transformed to another area of the plane. So now I can get a(x,y)=1/y and b(x,y)=x/(x+y-1) with just plugging in, then everything depeends from the y Invtervall. But I want to get the form b(a) and an intervall for a. So that I can see the function directly. So i thought I just put everything into the solve command and than ask for a solution for {a,b} and expected to get what I want. (Uploading the script here gives an error)
restart;
Sol := solve({a = 1/y, b = x/(x + y - 1), x = (y - 1)^2, 1 < y, y < 5/4});
Sol_ab := solve({a = 1/y, b = x/(x + y - 1), x = (y - 1)^2, 1 < y, y < 5/4}, {a, b});
#expected (or wanted) solution
#with y = 1/a and the inequalities we get 4/5 < a and a < 1 with y
#with y = we get x(a)/a and y(a) and reach b = 1/a - 1
#all together: Sol={b=1/a - 1, 4/4<a, a<1};
THe problem is, that I get an empty set which is obviously wrong. So I somehow make an error when making the variables I want concrete with adding {a,b}. What do I do wrong? Or is there a better command for what I want to achieve? In this case I can solve the problem via hand, but I have more complex tranformations and mor ecomplex functions x(y), so thats why I ask for general help with my problem.
Thank ypu in advance
Felix
