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