Continued fractions come immediately to mind as an application, per http://code.jsoftware.com/wiki/Essays/Continued_Fractions Suggestions here might be suitable to remove restrictions mentioned in that essay.
Continued fractions themselves are applied in at least the ways stated in https://math.stackexchange.com/questions/585675/what-are-the-applications-of-continued-fractions I am working a bit with Diophantine equations, so they seem like a natural tool to me. Sent from Mail for Windows 10 From: Skip Cave Sent: Wednesday, August 9, 2017 1:09 PM To: programm...@jsoftware.com Subject: Re: [Jprogramming] Fractional parts Markus, Actually, yes, I looked at using extended precision, and here's what happened: v=:2%(3r19-%x:1 2 3 245 246 247 248) v _19r8 _76r13 _57r5 4655r358 9348r719 13 9424r725 fp=. * * 1|| fp v _3r8 _11r13 _2r5 1r358 1r719 0 724r725 ip=: * * <.@| ip v _2 _5 _11 13 13 13 12 So our original definitions would work with extended precision, but the fractional parts would be rational rather than decimal. Extended precision still keeps the negative signs on the fractions. I'm not so sure about Martin's approach with extended precision: mfp1 =: 1&| NB. Martin's first suggestion for fractional part mfp1 v 5r8 2r13 3r5 1r358 1r719 0 724r725 mfp2 =: 1&#: NB. Martin's second suggestion for fractional part mfp2 v 5r8 2r13 3r5 1r358 1r719 0 724r725 fp v NB. First fractional part proposal _3r8 _11r13 _2r5 1r358 1r719 0 724r725 However, mfp1 & mvfp2 have lost the sign, so combining them by adding doesn't work for the negative numbers: v _19r8 _76r13 _57r5 4655r358 9348r719 13 9424r725 ip v _2 _5 _11 13 13 13 12 mfp1 v 5r8 2r13 3r5 1r358 1r719 0 724r725 (ip v) + (mfp1 v) _11r8 _63r13 _52r5 4655r358 9348r719 13 9424r725 (ip v) + (mfp2 v) _11r8 _63r13 _52r5 4655r358 9348r719 13 9424r725 v _19r8 _76r13 _57r5 4655r358 9348r719 13 9424r725 Skip Cave Cave Consulting LLC On Wed, Aug 9, 2017 at 10:45 AM, Schmidt-Gröttrup, Markus < m.schmidt-groett...@hs-osnabrueck.de> wrote: > Skip, have you considered to use extended precision? > In your example only small fraction are used, and the methods discussed > would apply as well without precision problems. > > v=:2%(3r19-%x:1 2 3 245 246 247 248) > > I haven’t read the whole thread, so sorry if this contribution doesn’t fit. > > Markus > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
