Re: Iterator sequences

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: Iterator sequences*From*: TODD GAYLEY <TGAYLEY at ccit.arizona.edu>*Date*: 03 Oct 1992 20:41:20 -0700 (MST)

Hans Kunzle (hkunzle at galilei.math.ualberta.ca) asks: > Is there a way in Mathematica to generate a list of > iterators dynamically? > > What I have in mind is something like > > Sum[ Product[v[i]^j[i],{i,3}],Table[{j[i],nn[[i]]},{i,3}]] > > where nn is a given list of integers. > This won't work since Table[..] is a list of lists, not > just a sequence. I tried to fool Mathematica into > accepting it by using > > Sum[ Product[v[i]^j[i],{i,3}], > ToExpression[StringDrop[StringDrop[ > ToString[Table[{j[i],nn[[i]]},{i,3}]],1],-1]] ] > > but also get just an error message A general method to capture the contents of a list without the enclosing braces (i.e., as a sequence of items separated by commas) is to Apply Sequence to it: Sequence@@{x,y,z} -------> Sequence[x,y,z] The first function that gets its hands on a Sequence object will strip off the Sequence head, effectively splicing in a series of arguments separated by commas. Thus you can use Sequence to "package" a series of arguments to a function. Your example becomes: Sum[Product[v[i]^j[i],{i,3}],Evaluate[Sequence@@Table[{j[i],nn[[i]]},{i,3}]]] The Evaluate is necessary to overcome the HoldAll attribute of Sum. --Todd ----------------------------------------------------------------- Todd Gayley Department of Ecology and Evolutionary Biology University of Arizona tgayley at ccit.arizona.edu -or- tgayley at cs.arizona.edu