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Since a number of papers (e.g. this one) treating denominators in Hilbert's 17th problem point to E.G. Strauss's unpublished letter to G. Kriesel or to Chapter 5 of Delzell's Thesis, which contains an extensive history of "bad points" for real forms, it would be nice if either of these things could be readily found online. It would also be great to have access to the paper: Delzell, C. N., Unavoidable singularities when writing polynomials as sums of squares of real rational functions. Which is cited as in preparation many places...

Question: Are there any papers freely available online that treat in detail bad points for homogeneous positive semidefinite forms? If so, where are they?

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    $\begingroup$ there is no legal copy of the thesis online, because of copyright restrictions, however, you can order a copy by following this link $\endgroup$
    – Carlo Beenakker
    Commented Jun 22, 2016 at 15:13
  • $\begingroup$ I'd still like some kind of free online treatment, since I'm only looking for some basic things, like how to tell whether a given polynomial has a bad point, or whether the "specified zero" must be a real zero, etc. I asked because it's really too bad that nothing at all can be found about this online...(I hope I am wrong!) $\endgroup$
    – Jon Bannon
    Commented Jun 22, 2016 at 15:23
  • $\begingroup$ All I can find is in Example 1 in Section 2.1 of www4.ncsu.edu/~kaltofen/bibliography/09/KLYZ09.pdf $\endgroup$
    – Jon Bannon
    Commented Jun 22, 2016 at 15:26
  • $\begingroup$ Made CW on OP's request. $\endgroup$
    – Todd Trimble
    Commented Jun 22, 2016 at 15:27
  • $\begingroup$ Thanks, Todd! I'm not asking anything mathematical here, which is why I requested CW. It's a pure reference request. $\endgroup$
    – Jon Bannon
    Commented Jun 22, 2016 at 15:31

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Delzell's thesis is available here: http://www.math.ens.fr/~benoist/textes/Delzell.pdf .

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    $\begingroup$ Cool to see this. Dr. Delzell supervised some independent studies on set theory for me during my senior year at LSU, and was a key factor on convincing me to go to grad school back in 1989. $\endgroup$
    – Todd Eisworth
    Commented Feb 9, 2021 at 14:49
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    $\begingroup$ Thank you Olivier! $\endgroup$
    – Jon Bannon
    Commented Feb 9, 2021 at 15:19

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