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Re: Sum of Products
*To*: mathgroup at smc.vnet.net
*Subject*: [mg126743] Re: Sum of Products
*From*: Dana DeLouis <dana01 at me.com>
*Date*: Sun, 3 Jun 2012 05:02:09 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
> Total[Times @@@ Subsets[{a, b, c}, {2}]]
Hi. Just out of educational curiosity..
This appears to be a closed form if your data is a range of integers:
fx[a_Integer?Positive,b_Integer?Positive]/;a<b :=
1/24 (b-a) (b+1-a) (3 a^2+6 a b+a+(3 b-1) b-2)
// Your equation took 13.3 seconds
Total[Times@@@Subsets[Range[1234,6789],{2}]] //Timing
{13.3337, 248323259329475}
// (Bob's excellent faster solution)
SymmetricPolynomial[2, Range[1234,6789]] //Timing
{8.89592, 248323259329475}
// Closed Form:
fx[1234, 6789] //Timing
{0.000072, 248323259329475}
= = = = = = = = = = = = =
Again, only if it's an interval.
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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