We have a working prototype using native machine precission, but we still have to make a lot of tests to adjust the constant for initial estimations. We would like to also write a version that could work with multiple precission, and maybe a fallback method that increases the precission if needed, but that is still a long way ahead.
Our problem is that we are two people working on that, on different countries, and with other lines of research keeping us busy, so we advance quite slowly. Our library does something very simple: gets a polynomial f(x,y) (given as a list of complex interval coefficients) in two variables, and one aproximate root of f(0,y) (with some condition on the aproximation, namely that the newton interval method can prove that there is a unique root in some neighborhood). Then returns a piecewise linear curve in [0,1]xC (given by a list of pairs (t_i,y_i) with 0<=t_i<=1 and y_i a complex numb er) with the following (granted) property: there is a tubular neighborhood of the piecewise linear curve such that, at every t, there is only one root of the polynomial f(t,y) inside it. The result is granted to be correct, but the method needs that we don't encounter any singularity in the way. Otherwise, it will never end. This is not intended to give a fast method to compute a root of a polynomial, but to follow the track of a given root when we deform the coefficients. El lunes, 17 de marzo de 2014 17:32:38 UTC+1, Volker Braun escribió: > > On Monday, March 17, 2014 6:05:58 AM UTC-4, mmarco wrote: >> >> I am working, together with a colleague, on a library to compute provable >> homotopy continuation, using interval arithmetic. We need to write >> something new because (AFAIK): >> a) the available software does not provide provable results i.e. in some >> critical cases they are not granted to give correct results. >> b) we need not only the solutions after the homotopy process, but the >> whole path run by them (we want to compute braid monodromy). >> > > Sounds great! Whats your current status on that? I completely agree with > the sentiment that homotopy continuation is a good tool but to really get > the most out of it you need to be able to control the inner workings. So > just an external program to call isn't good enough. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
