I believe I have an explanation, but I'd like to know what others think, in particular with regard to randomness.
The source is a bald assertion by Gosper in HAKMEM, which I was reading for information on continued fraction calculations. It's an interesting read. http://www.inwap.com/pdp10/hbaker/hakmem/hakmem.html Best wishes, John Roger Hui wrote: > Rationals in J are expressed in lowest terms, that is, > the numerator and denominator are relatively prime. > Consequently it can not be that both are even, > and if they were to start with then in their reduced form > they would contribute to the portion where the denom > is odd. > > The full answer to your question probably can be > worked out from this. > > > > ----- Original Message ----- > From: John Randall <[EMAIL PROTECTED]> > Date: Wednesday, May 7, 2008 9:15 > Subject: [Jchat] Denominators of random rationals > To: [email protected] > >> Random rationals do not have random denominators. >> >> NB. denominator of rational >> denom=:{: @ (2&x:) >> NB. generate some random rationals >> f=:_2 %/\ x: @: >: @ ?. @: #~ >> NB. proportion of odd denominators >> g=:(+/%#) @: (1 = 2 |denom"0) >> >> g 1e6 f 1e4 >> 0.6806 >> >> About 2/3 of the rationals have odd denominators, and only 1/3 have >> even denominators. >> >> Problem: Why? >> >> >> Best wishes, >> >> John > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
