This 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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evenhash 12 hours ago | parent | next [-]

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.

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Someone a day ago | parent | prev | next [-]

> 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)

	▲	rao-v 15 hours ago \| parent [-]
		I mean you’d probably just generate random low descriptive length f(x,y,z), check for a const determinant then poke for invertibility. Be fun to ask Fable to write a search program to find more counter examples using only early grad theory to guide the search.

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misiek08 a day ago | parent | prev [-]

So IIUC no one really worked on that in „professional” or rather university world since then?