I know Carl Witty spent a lot of time doing work on real root isolation--perhaps you could take a look at his Algebraic Reals code (sage/rings/algebraic_real.py)
Algebraic number theory is something that a lot of us want to focus on improving in the very near term. - Robert On Sep 3, 2007, at 10:43 AM, John Voight wrote: > > 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/ -~----------~----~----~----~------~----~------~--~---
