setting components of differential form
Hi, I don't understand how to set the components of a two-form.
M = Manifold(3, 'M', start_index=1)
U = M.open_subset('U')
X.<x,y,z> = M.chart()
basisframe = X.frame()
a = M.diff_form(2, name='a')
I just want to set a = dx wedge z^2 dy. I don't understand the format of examples in the main differential forms page on http://doc.sagemath.org. for example, this is one way they set one:
a = M.diff_form(2, name='a')
a[eU,0,1] = x*y^2 + 2*x
followed by an add_comp_by_continuation and I am not sure why or how that even works. I appreciate your help.
I was able to get a 1-form built on E3 with setting the components like
E.<x,y,z> = EuclideanSpace()
a = E.diff_form(1, name='a')
a[1]=1
a[2]= z^2
so I would have thought I could make a 2-form and set it a similar way but I am unsure what to do.. I'm also wondering how to access the basis forms for calculations. I couldn't see how to do a wedge product of my 1-form with dx, for example. I built it by setting the first component of a 1-form to 1 but is there an easier way?