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May 29, 2015 at 19:04 comment added David E Speyer Wow, this is almost exactly what I was trying (see my answer). I haven't read the Josza and Mitchison papers yet, but the problem I ran into is that I could only prove the inequalities on $\partial D/\partial e_k$ when the roots were real, and I couldn't show that I could move from one real rooted polynomial to another while keeping the roots real and decreasing the coefficients. Looking now to see whether or not Josza and Mitchison address this.
May 29, 2015 at 18:55 history answered Suvrit CC BY-SA 3.0