Maple: How to use maple to generate a sequence with double variables?

Question

I am working on a sequence: seq([seq([a[i,j],b[?]],i=1..3)], j=1..3)], it has in total 9 output of a such as a[1,1],a[2,1],a[3,1],a[1,2],a[2,2],a[3,2],a[1,3],a[2,3],a[3,3], yet I need to the output of b like b[1],b[2],b[3],b[4],b[5],b[6],b[7],b[8],b[9]. I have tried to put something like seq([seq([a[i,j],b[f]],i=1..3,f=1..9)] j=1..3)] but it does not work...

Could someone help me?

Greatly appreciated!

Answer 1

seq([seq([a[i,j],b[(j-1)*3+i]],
         i=1..3)],
    j=1..3);

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

or,

seq(seq([a[i,j],b[(j-1)*3+i]],
        i=1..3),
    j=1..3);  

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

[edit] Here is code to handle your followup query:

[seq([seq([a[i,j],b[(9/2-j/2)*j-i+1]],
      i=5-j..1,-1)],
 j=1..4)];

   [[[a[4, 1], b[1]], [a[3, 1], b[2]], [a[2, 1], b[3]], [a[1, 1], b[4]]],
    [[a[3, 2], b[5]], [a[2, 2], b[6]], [a[1, 2], b[7]]],
    [[a[2, 3], b[8]], [a[1, 3], b[9]]], [[a[1, 4], b[10]]]]

Alternatively,

N := 4:
[seq([seq([a[i,j],b[j*(2*N-j+1)/2-i+1]],
          i=N-j+1..1,-1)],
     j=1..N)];