Algorithmic decidability of equality in the ring of periods - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T04:22:34Z http://mathoverflow.net/feeds/question/83004 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83004/algorithmic-decidability-of-equality-in-the-ring-of-periods Algorithmic decidability of equality in the ring of periods Vladimir Reshetnikov 2011-12-08T21:22:05Z 2013-05-12T18:48:21Z <p>Suppose two elements of <a href="http://en.wikipedia.org/wiki/Ring_of_periods" rel="nofollow">the ring of periods</a> are given by their systems of polynomial inequalities with rational coefficients. Is there a known algorithm deciding their equality? Is it known if their equality is algorithmically decidable at all?</p> <p>It is quite obvious that if they are not equal, then it can be shown after finite number of steps just by evaluating them with big enough precision. The difficult part is when they are equal.</p> http://mathoverflow.net/questions/83004/algorithmic-decidability-of-equality-in-the-ring-of-periods/130430#130430 Answer by Oksana Gimmel for Algorithmic decidability of equality in the ring of periods Oksana Gimmel 2013-05-12T18:48:21Z 2013-05-12T18:48:21Z <p>There is no known algorithm for that, and it is unknown if such an algorithm exists.</p>