Re: Variable-length list?

*To*: mathgroup at smc.vnet.net*Subject*: [mg83486] Re: Variable-length list?*From*: "Hoa Bui" <hoabui05 at gmail.com>*Date*: Wed, 21 Nov 2007 02:59:51 -0500 (EST)*References*: <fhu73f$71m$1@smc.vnet.net> <4742F526.5020201@gmail.com>

Hi, Thanks for your comment, but this is not quite what I wanted to do. I tried to simplify the problem, but basically if I have a vector v={v[[1]],v[[2]],..v[[n]]} and each element v[[i]] has a range in which it can vary. I want to be able to search over all the possible combinations of the v[[i]]. (Each combination will return a vector, lets call it vi, and I want to use that vi to do something else.) The problem is that the number of dimensions (n) is not a fixed number, I want it to be a variable as well. Here's an example: If n=2, then v={a,b}. Say a={a1,a2} and b={b1,b2,b3}, then the combinations are: vi={{a1,b1}, {a1,b2}, {a1,b3}, {a2,b1}, {a2,b2}, {a2,b3}} If n=3, then v={a,b,c}. Say a={a1,a2}; b={b1,b2,b3}; c={c1,c2}, then I want to get: vi={{a1,b1,c1}, {a1,b2,c1}, {a1,b3,c1}, {a2,b1,c1}, {a2,b2,c1}, {a2,b3,c1}, {a1,b1,c2}, {a1,b2,c2}, {a1,b3,c2}, {a2,b1,c2}, {a2,b2,c2}, {a2,b3,c2}} If n=4, then I'll need another list d to represent my 4th dimension. .................................... You see, it would be easy if n is a fixed number (because then I can just use Array[] with the specified dimensions {na, nb, nc,...}. But the trouble is, even the number n of dimensions is a variable. Obviously, I cannot use For[], because each For[] only solves 1 dimension so I can only have a fixed number of dimensions searched. Is this doable? Thank you, and Happy Thanksgiving! HB On 11/20/07, Szabolcs Horv=E1t <szhorvat at gmail.com> wrote: > Hoa Bui wrote: > > Hi all, > > > > I want to have either a module or a function that inputs a > > varying-length list M[[nx]], where nx is a parameter, and accesses all > > of its elements. > > > > For example: > > > > f[M_?(Function[v,VectorQ[v,IntegerQ]]]:=Module[{i,j,k}, > > .... > > ] > > > > If M={3,4} then f would do something like: > > For [i=1,i<3,i++, > > For [j=1,j<4,j++, > > Print[i*j]; > > ] > > ] > > > > If M={3,4,5} then: > > For [i=1,i<3,i++, > > For [j=1,j<4,j++, > > For [k=1,k<5,j++, > > Print[i*j*k]; > > ] > > ] > > ] > > ] > > > > > > I wonder if this is doable in Mathematica, and/or what would be a way t= o do it? > > > > Hi, > > Never use For[], and don't use Print[] for displaying the result---just > return it instead. > > f[{dd__Integer}] := Array[Times, {dd}] > > You can still Flatten[] and Print[] the result if this is necessary. > > -- > Szabolcs >