Re: dynamic nested loops

*To*: mathgroup at smc.vnet.net*Subject*: [mg122851] Re: dynamic nested loops*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sat, 12 Nov 2011 07:35:17 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111110956.EAA08550@smc.vnet.net>

The form is Sum[f, Evaluate[Sequence@@iterators]] n = 3; iterators = Table[{i[m], 0, n - Sum[i[k], {k, m - 1}]}, {m, n}] {{i[1], 0, 3}, {i[2], 0, 3 - i[1]}, {i[3], 0, 3 - i[1] - i[2]}} Sum[f @@ Array[i, n], Evaluate[Sequence @@ iterators]] f[0, 0, 0] + f[0, 0, 1] + f[0, 0, 2] + f[0, 0, 3] + f[0, 1, 0] + f[0, 1, 1] + f[0, 1, 2] + f[0, 2, 0] + f[0, 2, 1] + f[0, 3, 0] + f[1, 0, 0] + f[1, 0, 1] + f[1, 0, 2] + f[1, 1, 0] + f[1, 1, 1] + f[1, 2, 0] + f[2, 0, 0] + f[2, 0, 1] + f[2, 1, 0] + f[3, 0, 0] % == Total[f @@@ Select[Tuples[Range[0, n], n], Total[#] <= n &]] True Bob Hanlon On Fri, Nov 11, 2011 at 4:56 AM, Ron <ragove at verizon.net> wrote: > i need to perform nested sums such as Sum[f, {i,imin,imax},{j, jmin, jmax}, ...{}]. In each nest the new index is a function of the previous and the max values vary. Also at the beginning I do not know how long a nest I need. I can't come up with anything that works. I could construct a list {{i,imin,imax},{j, jmin, jmax}, ...{}} but "Sum" doen't know what to do with the outside braces{...}. > ANy suggestions would be much appreciated. >

**References**:**dynamic nested loops***From:*Ron <ragove@verizon.net>