Hello all, I've spent the last week starting on my project of computing all totally real fields of bounded root discriminant. I've got code now in Magma, Pari, and SAGE, and most unfortunately, the Magma code is fastest!
The things that are slowing down SAGE right now is: (1) The interface to Pari lacks the nfdisc() and nfisisom() commands, or something like them. Right now, I don't even see how to compare if two number fields are isomorphic in SAGE?! These could be patched without too much effort and minimal overhead (a la Martin's instructions), right? (2) Real root finding predominates the computation. I was hoping that numpy would do this the fastest--but now it seems to be giving erratic results (see http://trac.sagemath.org/sage_trac/ticket/583). It may turn out that most optimized thing would be for me to write a Newton- Raphson iteration in cython, but this could quickly turn into a large recreate-the-wheel kind of project. [Essentially, one uses the fact that the derivative of a totally real polynomial is also totally real, and then inductively one finds bounds on the coefficients. Then we're just using Rolle's theorem (!), and we need to find the root in an interval given by the adjacent roots of the derivatives.] Any suggestions or guidance that any of you have would be most appreciated. Thanks, John Voight Assistant Professor of Mathematics University of Vermont [EMAIL PROTECTED] [EMAIL PROTECTED] http://www.cems.uvm.edu/~voight/ --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
