I understand there are two different ways to use differential forms in SageMath:
1) in the reference document "manifold.pdf"
sage: M = Manifold(4, 'M')
sage: a = M.one_form('A') or F = M.diff_form(2, 'F')
2) in the reference document "tensors.pdf"
sage: x, y, z = var('x, y, z')
sage: U = CoordinatePatch((x, y, z))
sage: F = DifferentialForms(U)
sage: form1 = DifferentialForm(F, 0, sin(x*y)); form1
Which is the best? Are they compatible? Can I mix and match from both packages? What are their pros and cons?
Thanks.
