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Re: Sum of Products

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126678] Re: Sum of Products
  • From: Dana DeLouis <dana01 at me.com>
  • Date: Wed, 30 May 2012 04:12:49 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

>  Is there any other, shorter, built-in Mathematica object . .
>  Total[Times @@@ Subsets[{a, b, c}, {2}]]

Hi.  This wasn't shorter, but appears faster with a large list.
It will be interesting to see other various ideas:

v=Range[1000];

{tim1,ans1} = Total[Times@@@Subsets[v,{2}]]//Timing

{0.407345,125083208250}

{tim2,ans2} = Sum[v[[j]] *Total@ v[[j+1;;-1]],{j,Length[v]-1}]//Timing

{0.007906,125083208250}


Not likely, but if your list of numbers were actually 1 to n:

(1/24)*(3*n + 2)*(n^3 - n) /. n -> 1000
125083208250

That came from the suggested closed form here:

Table[Total[Times@@@Subsets[Range[j],{2}]],{j,15}] //ToString //WolframAlpha

<< output >>

= = = = = = = = = =
HTH  :>)
Dana DeLouis
Mac & Math 8
= = = = = = = = = =


On May 29, 5:51 am, "Harvey P. Dale" <h... at nyu.edu> wrote:
>         If I have a list and want to sum the products of each possible
> grouping of two elements in the list, this program will do that:
> 
>                 Total[Times @@@ Subsets[{a, b, c}, {2}]]
> 
> Is there any other, shorter, built-in Mathematica object that will
> produce the same result?
> 
>         Thanks.
> 
>         Harvey





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