Undergrad Problem when solving example with differential forms

[davidge]

Hi was reading about differential forms, when I tried to solve the example

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?

 

[davidge]

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]

You ask us what's wrong with your calculation we do not get to see?

 

[davidge]

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

 

[haushofer]

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.