I'm not complaining about Wikipedia here, just noting for the thread: it's a vector of polynomials. It has a nonsingular Jacobian. Provided with it are 3 distinct points it sends to the same point; it can't be invertible.
What Wikipedia says about this doesn't matter, does it?
Wikipedia does have a rule allowing "routine calculations"
https://en.wikipedia.org/wiki/Wikipedia:No_original_research...
Of course given the magnitude of the statement a bit of care is warranted, but the rules do allow it.