Problem when solving example with differential forms

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davidge
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Hi was reading about differential forms, when I tried to solve the example
EPOnpJe.png
given in this pdf https://www.rose-hulman.edu/~bryan/lottamath/difform.pdf. According to it, the answer is that on the image above. But when I tried to solve this same example by following the expression for ##w## given in this pdf http://www.bose.res.in/~amitabha/diffgeom/chap13.pdf, namely that a p-form ##w## can be written as $$\frac{1}{p!}w_{\mu_1 ... \mu_p}dx^{\mu_1} \wedge \ ... \ \wedge dx^{\mu_p}$$ and that ##w##, in this case, applied to two vectors ##v_{(1)}## and ##v_{(2)}## is ##w_{i j}v_{(1)}^i v_{(2)}^j##, the answer that I'm getting diverges from that given in the other pdf. What is wrong?
 

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I noticed that the only problem is that in one pdf they introduce a factor ##1 / p!## while in the other they don't. My answer is off by a factor of ##1/2## in this case. So what is the correct?

I guess if one were going to consider only the anti-symmetric part of ##A(u)B(v)## then a factor of ##1/2## would be needed. But if one were considering ##A(u)B(v) - A(v)B(u)## it is not clear whether a factor of ##1/2## is needed. (##A, B## are one-forms and ##v, u## are vectors)
 
haushofer said:
You ask us what's wrong with your calculation we do not get to see?
After this thread, I noticed that I have forgotten to summing over all components and that was the cause of not getting the right result.
Thanks
 
Look, if you want people to invest time to help you, you shouldn't expect them to have paranormal abilities.

I've read a couple of your questions now and they seem highly confused, giving me the impression that you're studying stuff without the right background.