More dumb carelessness on my part — sorry. I mean a rational mapping f: D —> D carrying D to D - J (where D = {{x,y) in R^2 | x^2+y^2 < 1} and J = {(x,0) in R^2 | 0 <= x < 1}) of the form f(x,y) = (P_1(x,y)/Q_1(x,y), P_2(x,y)/Q_2(x,y)). Arrgh. —Dan
On Oct 17, 2015, at 4:35 PM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 17/10/2015 22:25, Dan Asimov wrote:
Puzzle: -------
Let D in R^2 denote the open unit disk {(x,y) | x^2 + y^2 < 1}
Let J denote the interval [0,1) x {0} in R^2. ... f(x,y) = P(x,y) / Q(x,y)
Just to clarify: do you mean
f(x,y) = (g(x,y),h(x,y))
where
g(x,y) = P(x,y) / Q(x,y) h(x,y) = R(x,y) / S(x,y)
with P,Q,R,S being polynomials? (Rather than, e.g., anything explicitly to do with complex numbers.)