Picking out columns from a matrix using MAGMA How do I form a new matrix from a given one by picking out some of its columns, using MAGMA?

You can actually do this really easily in Magma using the ColumnSubmatrix command, no looping necessary.  You can use this in a few ways.
For example if you have a matrix $A$ and you want $B$ to be made up a selection of columns:
1st, 2nd, $\ldots$, 5th columns: 
B := ColumnSubmatrix(A, 5);

3rd, 4th, $\ldots$, 7th columns: 
B := ColumnSubmatrix(A, 3, 4);

(since 7=3+4) OR 
ColumnSubmatrixRange(A, 3, 7);

2nd, 5th, 8th columns: This is trickier.  Magma doesn't let you do this cleanly.  But you can select rows 2, 5, and 8 of a matrix individually. You can obviously replace [2,5,8] with any arbitrary sequence.
Transpose(Matrix(Transpose(A)[[2,5,8]]));

