@Kitonum 2. So what is the reason that one side is a straight line? And what do you mean by "it is easy to verify that it is not straight" ??
Do you mean the not straight line is given by r=1, so
plot([exp(t), exp(-t), t = 0 .. 1])
So is that map bugged?
3. No I really mean that in
x€[0,1] and y€[0,1], so
However how do you proceed if you cannot solve for r and t ?
Is there some build in stuff or do you need to use RootOf?
4. Is there something like
seq([x, t, t = 0 .. 1], x = 0.1e-1 .. 1, 0.5e-1)
does not have the other endpoint at 1, because the intervals do not match up to 1.