Tutorial on Differential Forms: I would expect A1 ^ A2 + A2 ^ A1 = 0

Question

Hi, I am just beginning. Looking at the tutorial I am confused by the answer cadabra gives: A1 ^ A2 + A2 ^ A1 = 2 A1 ^ A2. I would have expected 0 as result.

Answer 1

In the tutorial, A1 is a one-form (degree=1) and A2 is a two-form (degree=2). For those, the wedge product is symmetric. You are probably thinking of the wedge product of two one-forms.

Comments

you are right, for a k-form u and a l-form v the rule is $u\wedge v & =(-1)^{kl}v\wedge u$