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