The Spectre of Math

May 28, 2013

Computation update

Filed under: Hacking,Mathematics — jlebl @ 4:45 pm

On the scale of length of computations I’ve done, this probably counts as the longest so far.  If you look down a bit in the blog you’ll find the details.  I can now report that there is no degree 21 polynomial p(x,y) with positive coefficients, with exactly 12 monomials (the least it can have), such that p(x,y) = 1 whenever x+y=1, and such that xy is one of the monomials.  Now the conjecture is that there is only one such beast (up to switching variables), dropping the condition about xy, and the computation is well on its way to prove that.  That one monomial is a bit special since it appears in these sharp polynomials for a bunch of smaller degrees.  Anyway, a few more months and we’ll have the answer.

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