Recursive algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg97835] Recursive algorithm*From*: athanase <aeoost at gmail.com>*Date*: Mon, 23 Mar 2009 04:03:36 -0500 (EST)

hello all, i am having headaches trying to produce this recursive algorithm in mathematica: the algorithm devides a reduced fraction r where r > 1 into n steps in the form (k+1)/k 1) try the largest step (k+1)/k (say s) that will fit in r; 2) find out how to divide r/s into n-1 steps; 3) try the next biggest step, etc; 4) until the first step is small enough that n of them are smaller than r, then you are done. so for r=8 and n=3 the result is (2/1,2/1,2/1) and for r=7/5, n=2 the result is (4/3,21/20),(6/5,7/6) i have found this algorithm written in another system but attempt to translate it fails for n>2 below is the code; sincere thanks for considering this problem, athanase spsubdiv := proc(r:rational,n:integer) local i,j,l,s; if n=1 then if numer(r)=denom(r)+1 then [r] else ( NULL ) fi; else s := NULL; for i from floor(1/(r-1))+1 while (1+1/i)^n >= r do l := [spsubdiv( r/(1+1/i), n-1 )]; for j to nops(l) do if op(1,op(j,l)) <= (1+1/i) then s := s, [(1+1/i),op(op(j,l))]; fi od; od; s; fi; end:

**Follow-Ups**:**Re: Recursive algorithm***From:*Daniel Lichtblau <danl@wolfram.com>