*To*: mathgroup@smc.vnet.net*Subject*: [mg10397] Re: Math Problem in Mathematica*From*: Allan Hayes <hay@haystack.demon.co.uk>*Date*: Mon, 12 Jan 1998 04:10:43 -0500*References*: <694bda$kp6@smc.vnet.net>

Daniel wrote: > The problem I would like to formulate in Mathematica is: Let f[i,j] = > Abs[Sqrt[1-(i/n)^2]-j/n]. i and j run from 1 to n, and n is a fixed > integer >=1. I want to find the sum S of the minimum of f over j, for > each i for given n. > > Example: n=7. Min (i=1, j from 1 to 7)= .01 > Min (i=2, """ )= .04 > Min (i=3, ... = .05 > etc. > > and the sum S = 0.20. Daniel:Since this is discrete it can be tackled it directly f[i_,j_,n_] := Abs[Sqrt[1-(i/n)^2]-j/n] s[n_] := Sum[ Min[Table[f[i,j,n]//N,{j,1,n}]],{i,1,n}] s[20]//Timing {3.86667 Second,0.262656} Or by looking at Solve[(n^2-i^2)==j^2,j] {{j -> -Sqrt[-i^2 + n^2]}, {j -> Sqrt[-i^2 + n^2]}} and allowing for the case i = n s2[n_]:=Sum[Min[N[ f[i,#,n]]&/@({ Max[#,1],Max[#+1,1]}&[Floor[Sqrt[n^2-i^2]]])],{i,1,n}] s2[20]//Timing {0.533333 Second,0.262656} -- Allan Hayes Training and Consulting Leicester, UK hay@haystack.demon.co.uk http://www.haystack.demon.co.uk voice: +44 (0)116 271 4198 fax: +44 (0)116 271 8642