Re: Math Problem in Mathematica
- To: mathgroup@smc.vnet.net
- Subject: [mg10357] Re: Math Problem in Mathematica
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Date: Mon, 12 Jan 1998 04:09:54 -0500
- Organization: University of Western Australia
- 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.
>
> FindMinimum seemed like the right idea, but I don't know how to make it
> work for a function of discrete values.
A direct implementation works fine:
In[1]:= f[i_, j_, n_] = Abs[Sqrt[1 - (i/n)^2] - j/n];
In[2]:= S[n_] := Sum[Min[Table[f[i, j, n], {j, n}]], {i, 1, n}]
In[3]:= S[7]
Out[3]=
24 4 Sqrt[3] 3 Sqrt[5] 2 Sqrt[6] 2 Sqrt[10] -- - --------- -
--------- - --------- + ---------- - 7 7 7
7 7
Sqrt[13] Sqrt[33]
-------- - --------
7 7
Note that Mathematica gives you the exact answer to this problem rather
than a numerical approximation:
In[4]:= N[%]
Out[4]= 0.348436
This does not agree with the answer above. If the sum over is
restricted to 1<=i<n then you do get an answer of approximately 0.20.
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul@physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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