alt Hacker NewsThis is so unreasonable! As @__alpoge__ himself notes this is classic crank graveyard territory and yet the counter example is something a grad student in 1997 could have found w a ~3 day computer search. Wild!
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> and yet the counter example is something a grad student in 1997 could have found w a ~3 day computer search
Is that true? Even restricting this to f(x,y,z) and coefficients and powers to 1 ≤ x ≤ 10, there are a lot of polynomials to check, and checking requires checking the Jacobian determinant and, if it’s a non zero constant, finding two points for which the polynomial produces the same value.
Or is there a way to generate all polynomials with a non-zero Jacobian determinant, and does that speed up things? (My intuition say it wouldn’t, because I guess those with zero determinants are rare)
So IIUC no one really worked on that in „professional” or rather university world since then?
The search space for a naive brute force of three polynomials of degree <= 7 with integer coefficients <= 12 is roughly 10^500. I think it would take a little longer than that.