Help with indexing in MuPAD

Hi,

I am looking for some help to do the following in MuPAD :

AA := sum(sum(q[i][j],i=1..2),j=1..2)

This gives me AA = q11 + q12 + q21 + q22. Now I want to specify that q12 = q21. How would I do that? I tried to use the 'Assume' command in MuPAD, but haven't made much progress.

Also, What is the difference between writing 'q_1' and 'q[1]' in MuPAD. I guess the first one refers to a subscript while the second one acts like an index. Is this right?

Thanks,

yogesh

Answer 1

[Walter Roberson]

q_1 is a full symbol name that happens to be displayed as if there is a subscript, but there is no relationship between (say) q_1 and q_2 .

q[1] uses the indexing method of the datatype that "q" is.

Your code will not give

AA = q11 + q12 + q21 + q22

it will give

AA = q[1][1] + q[1][2] + q[2][1] + q[2][2]

Unless, that is, that q[1][1] happens to have been given a value that the symbol q11 (and so on.) Which is possible if you defined q as a Matrix but did not initialize it.

Did you try

assume(q[1][2] = q[2][1])

Also, when you defined q, did you try giving it parameters for special properties such as Symmetric ?

[yogesh]

Thanks for your reply. I tried the following :

assume (q[1][2] = q[2][1])
aa := sum(sum(q[i][j],i=1..2),j=1..2)

which gives

q[1][1] + q[1][2] + q[2][1] + q[2][2]

I also tried

aa := sum(sum(q[i][j],i=1..2),j=1..2) assuming (q[1][2] = q[2][1])

But the result is same as before. To be more clear, what I want to do is to specify certain symmetry conditions for terms in the series involving 3 or 4 summation indexes. The total number of terms comes to around 80, so it's not easy to specify the symmetry conditions manually (which don't seem to work as seen above).

What would you suggest? Thanks for the help.

-yogesh