Define a differential form recursively
I have the following code:
n=3; x = list(var('x_%d' % i) for i in (1..2*n)); U = CoordinatePatch(x); F = DifferentialForms(U); w = DifferentialForm(F,2); for j in range(2*n-1): for k in range(2*n-1): w[j,k]=j+k; w;
It's supposed to define a differential form whose (j,k)th member is j+k, but this code just returns the 0 differential form. I've tried many variations using for, while, etc., but none seem to work. I suspect it's because a differential form is stored as a dictionary, but since I'm a beginner in Sage, I have no idea what to do. Any help is appreciated.