beginning reeked of... maybe not ai, but bad writing
but the further into the text, the better the prose
by the end it was great
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good to know that conjecture has been false for real numbers for a while now
but the further into the text, the better the prose
by the end it was great
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good to know that conjecture has been false for real numbers for a while now
I guess the answer is that a polynomial map whose Jacobian determinant is constant non-zero over the reals may not also be constant non-zero over all the complex numbers.
counterexample for reals moved point=0 outside reals, but kept point=point inside
you can see the "jacobian is sum of squares" being mentioned - that is sufficient to say there's no negative values in the reals, but doesn't work for the whole complex field
for complex numbers you have to have jacobian be a constant, or you'll get the zero somewhere
Still, overall a very nice piece of pedagogy. If you didn't grok determinants before, this will probably help.