Here is a technique which I need to do over and over and over
in Maple. I am currently writing a research paper for the International Journal of Mathematics and Mathematical Sciences.
I need to get this example out as soon as possible.
Suppose I want to create a matrix where the (i,j) entry
is the polynomial x^i + (x+1)^j
whatever the entry is.. it doesn't matter.
Point is that the entry depends upon the row i and column j
How can I create and fill such a matrix?
My matrices a slightly more complicated, involving entries
such as diff(x^i + (x+1)^j,x) where it is actually easier
to write the diff operator than to perform the differentiation
by hand. But, this is not nearly as important as my query above.
I am currently writing out by hand my 8 by 9 matrix.
Oh.. and once I have my 8x9 (or 9x8.. again, I don't care
which I make rows and which I make columns), I need to compute
the 9 8x8 minors (subdeterminants). Again, I wish to avoid writing out 9 8x8 matrices separately and computing their determinants individually.