Max,
> To the best of my knowledge, no, factorization is required to solve this. > The two squares problem is considerably harder than the four squares > problem. > Factorization is required. Ok, thanks! Richard On Thu, Jul 29, 2010 at 4:00 AM, Max Horn <m...@quendi.de> wrote: > Dear Richard, dear Forum, > > Am 29.07.2010 um 06:15 schrieb Richard Graham: > > > Dear Dmitrii, > > > > Thanks for the tip on enhancing my Sage install. > > > > However, all the factoring power my little laptop can produce won't > factor > > an RSA challenge number in any reasonable time, but the four squares > > algorithm at: > > > > http://www.alpertron.com.ar/FSQUARES.HTM > > > > ... can produce the sums of squares in less than a few seconds. > > Of course. Two get a sum of three or four squares, you don't need to > factor. The site you refer to mentions that explicitly. > > So, if you just want to write a number as sum of four squares (where 0^2 is > allowed as a summand), then you do not have to use TwoSquares, but rather > should use an algorithm for that. > > Darin Alpern even kindly provides the source code for what he does on his > website, as well as alink to a page which explains how the four squares > applet works: <http://www.alpertron.com.ar/4SQUARES.HTM>, scroll to the > bottom for the factorization free approach. > > > > > > My real question is about the TwoSquares algorithm. Is there a better (or > > perhaps extended/augmented) TwoSquares algorithm that Gap could use that > > would extend its range of usefulness? > > To the best of my knowledge, no, factorization is required to solve this. > The two squares problem is considerably harder than the four squares > problem. > > > Cheers, > Max > > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
