User lilach leibovich - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T14:46:34Z http://mathoverflow.net/feeds/user/27047 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109192/efficient-algorithm-for-computing-the-integral-closure-of-a-computable-domain Efficient algorithm for computing the integral closure of a computable domain Lilach Leibovich 2012-10-08T23:42:30Z 2012-10-12T22:52:50Z <p>what is known? even talking about efficiency relatively to the complexity of the computation of the domain itself?</p> http://mathoverflow.net/questions/109005/decidability-of-the-generated-order Decidability of the generated order Lilach Leibovich 2012-10-06T15:18:07Z 2012-10-06T16:48:18Z <p>is the question whether a polynomial is non-negative on some semi-algebraic set (equivalently, is it in the cone denerated by some polynomials in the field of rational functions) known to be decidable?</p> http://mathoverflow.net/questions/108951/applications-of-the-ax-kochen-ershov-ake-princicple/109004#109004 Answer by Lilach Leibovich for Applications of the Ax Kochen Ershov (AKE) princicple Lilach Leibovich 2012-10-06T15:11:34Z 2012-10-06T15:11:34Z <p>AKE prinicpal alows us to deduce conclusions about the theory of the valuaed field from the theories of the residue field and value group. Via this you prove, for example, that such and such theories are model complete, which supplies you with the tool of transfer argument (as in the model theoretic proof for hilbert's Nullstellensatz). </p> <p>As for your side question, if I have understood correctly, the answer is that the residue fiels is algebraically closed and the value group is divisible.</p> http://mathoverflow.net/questions/109192/efficient-algorithm-for-computing-the-integral-closure-of-a-computable-domain Comment by Lilach Leibovich Lilach Leibovich 2012-10-13T12:45:18Z 2012-10-13T12:45:18Z @Igor: See if I care... @Gerhard: 10x, but how did you get the impression that I am looking for such? anyhow, you may fix my keyboard, if we are already talking ;-) http://mathoverflow.net/questions/109192/efficient-algorithm-for-computing-the-integral-closure-of-a-computable-domain Comment by Lilach Leibovich Lilach Leibovich 2012-10-12T22:31:10Z 2012-10-12T22:31:10Z I believe you should ask for help in communicating with people. Maybe a colleague could assist? http://mathoverflow.net/questions/109005/decidability-of-the-generated-order/109013#109013 Comment by Lilach Leibovich Lilach Leibovich 2012-10-06T17:01:58Z 2012-10-06T17:01:58Z hmm, yes, I forgot to mention (actually, any field which is dense in its real closure). Are there known relativley efficient algorithmm to it (i.e is it atleast primitive recursive), maybe using SOS stuff?