2 ms·
I find it interesting that the counterexample uses C as a field. C is twisted and weird. Maybe the Jacobian Conjecture still holds for reals?
by js8 3mo ago
I find it interesting that the counterexample uses C as a field. C is twisted and weird. Maybe the Jacobian Conjecture still holds for reals?
- krackers 3mo ago>C is twisted and weird. Why do you say this? I've admittedly never done a proper complex analysis course but I got the impression that that complex differentiability was a very strong condition that results in holomprhic functions behaving "nicely" in ways that real functions do not
- js8 3mo agoShould have used quotes.. I didn't mean it in any formal sense. What I am saying the nature of unit in complex plane makes it difficult to intuitively imagine invertibility and determinants.
- yorwba 3mo agoAll the coefficients and evaluation points are rational, so it's a counterexample in all fields where 2 ≠ 0 and 3 ≠ 0, doesn't matter whether that field is the complex numbers, real numbers, rational numbers or even a finite field.
- js8 3mo agoAh you're right, thanks.