Thanks for your response. I suppose relying on integer factorization is the limiting factor (pun intended). Sage does not appear to include Gap's factint, but still, factorization of large numbers can be difficult.
Sage's four_squares function also relies on Gap's TwoSquares function, so it too is limited. I noticed that the four square problem is solved without factorization at: http://www.alpertron.com.ar/FSQUARES.HTM ... and it can take very large inputs (I tried numbers greater than 2^1000). I am wondering if the TwoSquares problem can be solved without integer factorization. Cheers! Richard On Mon, Jul 26, 2010 at 4:27 AM, Stephen Linton <s...@mcs.st-andrews.ac.uk>wrote: > How large are your inputs? For me the existing algorithms seems to work > quite well for really quite large numbers, limited mainly by integer > factorisation. > One obvious question is therefore: do you have the factint GAP package > installed? It's part of the standard GAP distribution, but I don't know > about SAGE. > > You can check with the GAP command > > InstalledPackageVersion("factint"); > > which will give a version number or "fail. > > Steve Linton > > On 26 Jul 2010, at 00:51, Richard Graham wrote: > > > I use Sage for some recreational mathematics, which in turn uses Gap. I > > would like to use the TwoSquares function with inputs that are large. Is > > there perhaps another algorithm that could be used to handle large input? > > Thanks. > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
