found one solution BUT...

Antonio_S — Sat, 21 Apr 2007 15:24:09 Z

seem to have found one way to answer this, but it only works when you put all the numbers from 3 sets into the same set as detailed below, it automatically sorts the numbers in the ascending order; > (combinat[permute])({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 3); [[0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 1, 5], [0, 1, 6], [0, 1, 7], [0, 1, 8], [0, 1, 9], [0, 2, 1], [0, 2, 3], [0, 2, 4], [0, 2, 5], [0, 2, 6], [0, 2, 7], [0, 2, 8], [0, 2, 9], [0, 3, 1], [0, 3, 2], [0, 3, 4], [0, 3, 5], [0, 3, 6], [0, 3, 7], [0, 3, 8], [0, 3, 9], [0, 4, 1], [0, 4, 2], [0, 4, 3], [0, 4, 5], [0, 4, 6], [0, 4, 7], [0, 4, 8], [0, 4, 9], [0, 5, 1], [0, 5, 2], [0, 5, 3], [0, 5, 4], [0, 5, 6], [0, 5, 7], [0, 5, 8], [0, 5, 9], [0, 6, 1], [0, 6, 2], [0, 6, 3], [0, 6, 4], [0, 6, 5], [0, 6, 7], [0, 6, 8], [0, 6, 9], [0, 7, 1], [0, 7, 2], [0, 7, 3], [0, 7, 4], [0, 7, 5], [0, 7, 6], [0, 7, 8], [0, 7, 9], [0, 8, 1], [0, 8, 2], [0, 8, 3], [0, 8, 4], [0, 8, 5], [0, 8, 6], [0, 8, 7], [0, 8, 9], [0, 9, 1], [0, 9, 2], [0, 9, 3], [0, 9, 4], [0, 9, 5], [0, 9, 6], [0, 9, 7], [0, 9, 8], [1, 0, 2], [1, 0, 3], [1, 0, 4], [1, 0, 5], [1, 0, 6], [1, 0, 7], [1, 0, 8], [1, 0, 9], [1, 2, 0], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 3, 0], [1, 3, 2], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], [1, 4, 0], [1, 4, 2], [1, 4, 3], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9], [1, 5, 0], [1, 5, 2], [1, 5, 3], [1, 5, 4], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 6, 0], [1, 6, 2], [1, 6, 3], [1, 6, 4], [1, 6, 5], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 7, 0], [1, 7, 2], [1, 7, 3], [1, 7, 4], [1, 7, 5], [1, 7, 6], [1, 7, 8], [1, 7, 9], [1, 8, 0], [1, 8, 2], [1, 8, 3], [1, 8, 4], [1, 8, 5], [1, 8, 6], [1, 8, 7], [1, 8, 9], [1, 9, 0], [1, 9, 2], [1, 9, 3], [1, 9, 4], [1, 9, 5], [1, 9, 6], [1, 9, 7], [1, 9, 8], [2, 0, 1], [2, 0, 3], [2, 0, 4], [2, 0, 5], [2, 0, 6], [2, 0, 7], [2, 0, 8], [2, 0, 9], [2, 1, 0], [2, 1, 3], [2, 1, 4], [2, 1, 5], [2, 1, 6], [2, 1, 7], [2, 1, 8], [2, 1, 9], [2, 3, 0], [2, 3, 1], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9], [2, 4, 0], [2, 4, 1], [2, 4, 3], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9], [2, 5, 0], [2, 5, 1], [2, 5, 3], [2, 5, 4], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9], [2, 6, 0], [2, 6, 1], [2, 6, 3], [2, 6, 4], [2, 6, 5], [2, 6, 7], [2, 6, 8], [2, 6, 9], [2, 7, 0], [2, 7, 1], [2, 7, 3], [2, 7, 4], [2, 7, 5], [2, 7, 6], [2, 7, 8], [2, 7, 9], [2, 8, 0], [2, 8, 1], [2, 8, 3], [2, 8, 4], [2, 8, 5], [2, 8, 6], [2, 8, 7], [2, 8, 9], [2, 9, 0], [2, 9, 1], [2, 9, 3], [2, 9, 4], [2, 9, 5], [2, 9, 6], [2, 9, 7], [2, 9, 8], [3, 0, 1], [3, 0, 2], [3, 0, 4], [3, 0, 5], [3, 0, 6], [3, 0, 7], [3, 0, 8], [3, 0, 9], [3, 1, 0], [3, 1, 2], [3, 1, 4], [3, 1, 5], [3, 1, 6], [3, 1, 7], [3, 1, 8], [3, 1, 9], [3, 2, 0], [3, 2, 1], [3, 2, 4], [3, 2, 5], [3, 2, 6], [3, 2, 7], [3, 2, 8], [3, 2, 9], [3, 4, 0], [3, 4, 1], [3, 4, 2], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 4, 9], [3, 5, 0], [3, 5, 1], [3, 5, 2], [3, 5, 4], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 5, 9], [3, 6, 0], [3, 6, 1], [3, 6, 2], [3, 6, 4], [3, 6, 5], [3, 6, 7], [3, 6, 8], [3, 6, 9], [3, 7, 0], [3, 7, 1], [3, 7, 2], [3, 7, 4], [3, 7, 5], [3, 7, 6], [3, 7, 8], [3, 7, 9], [3, 8, 0], [3, 8, 1], [3, 8, 2], [3, 8, 4], [3, 8, 5], [3, 8, 6], [3, 8, 7], [3, 8, 9], [3, 9, 0], [3, 9, 1], [3, 9, 2], [3, 9, 4], [3, 9, 5], [3, 9, 6], [3, 9, 7], [3, 9, 8], [4, 0, 1], [4, 0, 2], [4, 0, 3], [4, 0, 5], [4, 0, 6], [4, 0, 7], [4, 0, 8], [4, 0, 9], [4, 1, 0], [4, 1, 2], [4, 1, 3], [4, 1, 5], [4, 1, 6], [4, 1, 7], [4, 1, 8], [4, 1, 9], [4, 2, 0], [4, 2, 1], [4, 2, 3], [4, 2, 5], [4, 2, 6], [4, 2, 7], [4, 2, 8], [4, 2, 9], [4, 3, 0], [4, 3, 1], [4, 3, 2], [4, 3, 5], [4, 3, 6], [4, 3, 7], [4, 3, 8], [4, 3, 9], [4, 5, 0], [4, 5, 1], [4, 5, 2], [4, 5, 3], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 5, 9], [4, 6, 0], [4, 6, 1], [4, 6, 2], [4, 6, 3], [4, 6, 5], [4, 6, 7], [4, 6, 8], [4, 6, 9], [4, 7, 0], [4, 7, 1], [4, 7, 2], [4, 7, 3], [4, 7, 5], [4, 7, 6], [4, 7, 8], [4, 7, 9], [4, 8, 0], [4, 8, 1], [4, 8, 2], [4, 8, 3], [4, 8, 5], [4, 8, 6], [4, 8, 7], [4, 8, 9], [4, 9, 0], [4, 9, 1], [4, 9, 2], [4, 9, 3], [4, 9, 5], [4, 9, 6], [4, 9, 7], [4, 9, 8], [5, 0, 1], [5, 0, 2], [5, 0, 3], [5, 0, 4], [5, 0, 6], [5, 0, 7], [5, 0, 8], [5, 0, 9], [5, 1, 0], [5, 1, 2], [5, 1, 3], [5, 1, 4], [5, 1, 6], [5, 1, 7], [5, 1, 8], [5, 1, 9], [5, 2, 0], [5, 2, 1], [5, 2, 3], [5, 2, 4], [5, 2, 6], [5, 2, 7], [5, 2, 8], [5, 2, 9], [5, 3, 0], [5, 3, 1], [5, 3, 2], [5, 3, 4], [5, 3, 6], [5, 3, 7], [5, 3, 8], [5, 3, 9], [5, 4, 0], [5, 4, 1], [5, 4, 2], [5, 4, 3], [5, 4, 6], [5, 4, 7], [5, 4, 8], [5, 4, 9], [5, 6, 0], [5, 6, 1], [5, 6, 2], [5, 6, 3], [5, 6, 4], [5, 6, 7], [5, 6, 8], [5, 6, 9], [5, 7, 0], [5, 7, 1], [5, 7, 2], [5, 7, 3], [5, 7, 4], [5, 7, 6], [5, 7, 8], [5, 7, 9], [5, 8, 0], [5, 8, 1], [5, 8, 2], [5, 8, 3], [5, 8, 4], [5, 8, 6], [5, 8, 7], [5, 8, 9], [5, 9, 0], [5, 9, 1], [5, 9, 2], [5, 9, 3], [5, 9, 4], [5, 9, 6], [5, 9, 7], [5, 9, 8], [6, 0, 1], [6, 0, 2], [6, 0, 3], [6, 0, 4], [6, 0, 5], [6, 0, 7], [6, 0, 8], [6, 0, 9], [6, 1, 0], [6, 1, 2], [6, 1, 3], [6, 1, 4], [6, 1, 5], [6, 1, 7], [6, 1, 8], [6, 1, 9], [6, 2, 0], [6, 2, 1], [6, 2, 3], [6, 2, 4], [6, 2, 5], [6, 2, 7], [6, 2, 8], [6, 2, 9], [6, 3, 0], [6, 3, 1], [6, 3, 2], [6, 3, 4], [6, 3, 5], [6, 3, 7], [6, 3, 8], [6, 3, 9], [6, 4, 0], [6, 4, 1], [6, 4, 2], [6, 4, 3], [6, 4, 5], [6, 4, 7], [6, 4, 8], [6, 4, 9], [6, 5, 0], [6, 5, 1], [6, 5, 2], [6, 5, 3], [6, 5, 4], [6, 5, 7], [6, 5, 8], [6, 5, 9], [6, 7, 0], [6, 7, 1], [6, 7, 2], [6, 7, 3], [6, 7, 4], [6, 7, 5], [6, 7, 8], [6, 7, 9], [6, 8, 0], [6, 8, 1], [6, 8, 2], [6, 8, 3], [6, 8, 4], [6, 8, 5], [6, 8, 7], [6, 8, 9], [6, 9, 0], [6, 9, 1], [6, 9, 2], [6, 9, 3], [6, 9, 4], [6, 9, 5], [6, 9, 7], [6, 9, 8], [7, 0, 1], [7, 0, 2], [7, 0, 3], [7, 0, 4], [7, 0, 5], [7, 0, 6], [7, 0, 8], [7, 0, 9], [7, 1, 0], [7, 1, 2], [7, 1, 3], [7, 1, 4], [7, 1, 5], [7, 1, 6], [7, 1, 8], [7, 1, 9], [7, 2, 0], [7, 2, 1], [7, 2, 3], [7, 2, 4], [7, 2, 5], [7, 2, 6], [7, 2, 8], [7, 2, 9], [7, 3, 0], [7, 3, 1], [7, 3, 2], [7, 3, 4], [7, 3, 5], [7, 3, 6], [7, 3, 8], [7, 3, 9], [7, 4, 0], [7, 4, 1], [7, 4, 2], [7, 4, 3], [7, 4, 5], [7, 4, 6], [7, 4, 8], [7, 4, 9], [7, 5, 0], [7, 5, 1], [7, 5, 2], [7, 5, 3], [7, 5, 4], [7, 5, 6], [7, 5, 8], [7, 5, 9], [7, 6, 0], [7, 6, 1], [7, 6, 2], [7, 6, 3], [7, 6, 4], [7, 6, 5], [7, 6, 8], [7, 6, 9], [7, 8, 0], [7, 8, 1], [7, 8, 2], [7, 8, 3], [7, 8, 4], [7, 8, 5], [7, 8, 6], [7, 8, 9], [7, 9, 0], [7, 9, 1], [7, 9, 2], [7, 9, 3], [7, 9, 4], [7, 9, 5], [7, 9, 6], [7, 9, 8], [8, 0, 1], [8, 0, 2], [8, 0, 3], [8, 0, 4], [8, 0, 5], [8, 0, 6], [8, 0, 7], [8, 0, 9], [8, 1, 0], [8, 1, 2], [8, 1, 3], [8, 1, 4], [8, 1, 5], [8, 1, 6], [8, 1, 7], [8, 1, 9], [8, 2, 0], [8, 2, 1], [8, 2, 3], [8, 2, 4], [8, 2, 5], [8, 2, 6], [8, 2, 7], [8, 2, 9], [8, 3, 0], [8, 3, 1], [8, 3, 2], [8, 3, 4], [8, 3, 5], [8, 3, 6], [8, 3, 7], [8, 3, 9], [8, 4, 0], [8, 4, 1], [8, 4, 2], [8, 4, 3], [8, 4, 5], [8, 4, 6], [8, 4, 7], [8, 4, 9], [8, 5, 0], [8, 5, 1], [8, 5, 2], [8, 5, 3], [8, 5, 4], [8, 5, 6], [8, 5, 7], [8, 5, 9], [8, 6, 0], [8, 6, 1], [8, 6, 2], [8, 6, 3], [8, 6, 4], [8, 6, 5], [8, 6, 7], [8, 6, 9], [8, 7, 0], [8, 7, 1], [8, 7, 2], [8, 7, 3], [8, 7, 4], [8, 7, 5], [8, 7, 6], [8, 7, 9], [8, 9, 0], [8, 9, 1], [8, 9, 2], [8, 9, 3], [8, 9, 4], [8, 9, 5], [8, 9, 6], [8, 9, 7], [9, 0, 1], [9, 0, 2], [9, 0, 3], [9, 0, 4], [9, 0, 5], [9, 0, 6], [9, 0, 7], [9, 0, 8], [9, 1, 0], [9, 1, 2], [9, 1, 3], [9, 1, 4], [9, 1, 5], [9, 1, 6], [9, 1, 7], [9, 1, 8], [9, 2, 0], [9, 2, 1], [9, 2, 3], [9, 2, 4], [9, 2, 5], [9, 2, 6], [9, 2, 7], [9, 2, 8], [9, 3, 0], [9, 3, 1], [9, 3, 2], [9, 3, 4], [9, 3, 5], [9, 3, 6], [9, 3, 7], [9, 3, 8], [9, 4, 0], [9, 4, 1], [9, 4, 2], [9, 4, 3], [9, 4, 5], [9, 4, 6], [9, 4, 7], [9, 4, 8], [9, 5, 0], [9, 5, 1], [9, 5, 2], [9, 5, 3], [9, 5, 4], [9, 5, 6], [9, 5, 7], [9, 5, 8], [9, 6, 0], [9, 6, 1], [9, 6, 2], [9, 6, 3], [9, 6, 4], [9, 6, 5], [9, 6, 7], [9, 6, 8], [9, 7, 0], [9, 7, 1], [9, 7, 2], [9, 7, 3], [9, 7, 4], [9, 7, 5], [9, 7, 6], [9, 7, 8], [9, 8, 0], [9, 8, 1], [9, 8, 2], [9, 8, 3], [9, 8, 4], [9, 8, 5], [9, 8, 6], [9, 8, 7]] Is there any command in Maple that takes 3 sets and produces combinations in the following order: [A1,B1,C1], [A2,B1,C1], [A3,B1,C1], [A4,B1,C1], [A1,B2,C1] thanks

combinat[cartprod] or combstruct

JacquesC — Sun, 22 Apr 2007 04:37:22 Z

Here are two ways of doing it, one relatively simple, and one that scales nicely:

 > (A,B,C) := ({1,3,4,8}, {5,6,9}, {2,0,7}):
> T := combinat[cartprod]([A,B,C]):
> S := table(): 
> for i from 1 while not T[finished] do S[i] := T[nextvalue]() end do:
> res := [seq(S[j],j=1..i-1)]:

and now 'res' is a list of lists exactly as you ask above. The more complicated way is via combstruct:

 > with(combstruct):
# create a structure
> P := {Z=Prod( Union(a[1],a[3],a[4],a[8]), Union(a[5],a[6],a[9]), Union(a[2],a[0],a[7])) , seq(a[i]=Atom,i=0..9)}:
# enumerate them all
> res := allstructs([Z,P,unlabelled],size=3):
# make the results pretty
> rr := eval(res, Prod=((a,b,c)->[op(1,a),op(1,b),op(1,c)]));

  rr := [[8, 6, 0], [3, 6, 7], [1, 5, 2], [4, 6, 0], [1, 9, 2],

        [8, 9, 2], [8, 9, 0], [4, 6, 7], [8, 6, 2], [8, 5, 7],

        [3, 5, 2], [1, 9, 7], [3, 5, 0], [4, 5, 0], [1, 9, 0],

        [1, 6, 7], [1, 6, 2], [1, 6, 0], [4, 5, 2], [3, 9, 0],

        [8, 5, 2], [3, 9, 7], [1, 5, 0], [4, 9, 7], [8, 6, 7],

        [8, 9, 7], [3, 6, 0], [3, 9, 2], [4, 9, 0], [8, 5, 0],

        [3, 5, 7], [4, 5, 7], [1, 5, 7], [4, 6, 2], [4, 9, 2],

        [3, 6, 2]]

>

Many thanks!

Antonio_S — Sun, 22 Apr 2007 05:40:21 Z

Many thanks!

une methode possible

xavier — Fri, 22 Jun 2007 14:02:13 Z

bonjour, une maniere de faire est: frtotx:=proc(s);l:=[seq([s[1][i]],i=1..nops(s[1]))];for ki from 2 to nops(s) do l:=[seq(seq([op(l[i]),s[ki][j]],j=1..nops(s[ki])),i=1..nops(l))];od;return(l);end; on fait par exemple frtotx([[1,2,3],[1,2]]); [[1, 1], [1, 2], [2, 1], [2, 2], [3, 1], [3, 2]]

Using nested seq(...)'s

John Fredsted — Tue, 26 Jun 2007 21:02:00 Z

Though not being a single command, here is another way which gives a list of combinations: [seq(seq(seq([A[i],B[j],C[k]],k=1..nops(C)),j=1..nops(B)),i=1..nops(A))]; To get them nicely ordered, maybe it would be preferable to let A, B, and C themselves be lists, instead of sets.

another beginner's tip

Tim Van Dusen — Tue, 26 Jun 2007 21:21:45 Z

I'm relatively new to Maple, and it was suggested elsewhere, that maybe I should do a book, in the book section here in MaplePrimes concerning the way I learn from maple. I'm still working on that idea, but in the meantime, I'll jump in here with an idea for other new users. When I come across a bunch of good ideas like the ones here, I create a new maple worksheet with the examples, along with a link to this page at the top and a few comments about the original question and people who gave some good ideas. I then save the worksheet with an appropriate name in a folder that I use just for that sort of thing. I'm not sure if others have the same problem of forgetting things that I seem to have acquired in my latter years, but because of that, I try to record and categorize as much as I can so it's more easily obtainable when needed rather than end up becoming frustrated when I encounter a situation when I need what I read "somewhere" but can't remember what it was that I read or even where I read it.

MaplePrimes - answers and comments on Question, Combinations of numbers in sets

found one solution BUT...

combinat[cartprod] or combstruct

Many thanks!

une methode possible

Using nested seq(...)'s

another beginner's tip