       Re: Sum of Products - Complete The Square

• To: mathgroup at smc.vnet.net
• Subject: [mg126698] Re: Sum of Products - Complete The Square
• From: "djmpark" <djmpark at comcast.net>
• Date: Thu, 31 May 2012 02:51:22 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Thanks for introducing/reminding us of SymmetricPolynomial and the
associated SymmetricReduction. SymmetricReduction is the high tech
generalization of complete the square.

3 x^2 + y^2 + 6 x y;
Total@SymmetricReduction[%, {x, y}]

2 y^2 + 3 (x + y)^2

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/index.html

From: Bob Hanlon [mailto:hanlonr357 at gmail.com]

SymmetricPolynomial, for example,

SymmetricPolynomial[2, {a, b, c}] ==
Total[Times @@@ Subsets[{a, b, c}, {2}]] // Simplify

True

SymmetricPolynomial[2, {a, b, c, d}] ==
Total[Times @@@ Subsets[{a, b, c, d}, {2}]] // Simplify

True

SymmetricPolynomial[4, {a, b, c, d, e, f}] ==
Total[Times @@@ Subsets[{a, b, c, d, e, f}, {4}]] // Simplify

True

Bob Hanlon

On Tue, May 29, 2012 at 5:48 AM, Harvey P. Dale <hpd1 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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