Comments on: Something you should know about: Quantifier Elimination (Part II) http://cstheory.blogoverflow.com/2012/02/something-you-should-know-about-quantifier-elimination-part-ii/ The Theoretical Computer Science Stack Exchange Blog Fri, 18 Mar 2016 21:21:18 +0000 hourly 1 https://wordpress.org/?v=4.5.6 By: Masahiro Sakai http://cstheory.blogoverflow.com/2012/02/something-you-should-know-about-quantifier-elimination-part-ii/#comment-4408 Sun, 10 Feb 2013 15:33:59 +0000 http://cstheory.blogoverflow.com/?p=1102#comment-4408 Thank you very much for a great article. I understand the concept of real quantifier elimination with your article.

But when I tried to implement the algorithm, I noticed that your definition of zmod does not work well. For example, let p = ax^2 + bx + c and q = 2ax+b, and if it guesses a≠0, then (p zmod q) = (ax^2 + bx + c) zmod (2ax+b) = 2a(ax^2 + bx + c) – ax(2ax+b) = abx + 2ac, i.e. the degree of (p zmod q) does not decrease. And it prevents the hierarchy of collections of polynomials from converging. The MR(p,q) defined by Michaux and Ozturk does not have the problem.

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