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I have objects that look like, for example:

F2 = 2 d[x] ^ d[y] + 3 d[x] ^ d[z]

where ^ is Wedge (and not exponentiation). The variables inside of d[...] are not known beforehand and the number of terms is also not known; I would like to extract the coefficients that lie in front of these terms (here 2 and 3). The real objects that I have to work with are enormous, so I would like to do this as efficiently as possible, so I try to extract what differentials I have like this:

Cases[ Level[F2, 1] , _ d[a_] ^ d[b_] -> d[a] ^ d[b] ]

This returns: { d[x] ^ d[y], d[x] ^ d[z] }. So, now I can use Coefficient and all is well.

However, if I have an object like this:

F2 = 2 d[x] ^ d[y] + 3 e[1] ^ e[2]

I would like to be returned the list: { d[x] ^ d[y], e[1] ^ e[2] }; so, I try:

Cases[ Level[F2, 1] , _ d1_[a_] ^ d2_[b_] -> d1[a] ^ d2[b] ]

But this does not work. It returns an empty list. Why? And is there a way to make this work?

Edit

So, contrary to my claim, this does actually work as intended, except that an expression like:

F2 = d[x] ^ d[y]

returns an empty list. I naively expected the code I wrote above to handle an implicit coefficient as well as explicit ones. I needed to modify my code to:

Cases[ Level[F2, 1] , _ d1_[a_] ^ d2_[b_] | d1_[a_] ^ d2_[b_] -> d1[a] ^ d2[b] ]

Thanks for the help! I'll probably delete the question in due course...

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    $\begingroup$ Your example works on my machine. Try to either remove any definitions you have for d1, d2, a and b, or use :> instead of ->. $\endgroup$ – Marius Ladegård Meyer Mar 2 '16 at 19:53
  • $\begingroup$ It works for me, too. $\endgroup$ – march Mar 2 '16 at 19:54
  • $\begingroup$ Hang on. Let me see if I'm being dumb... $\endgroup$ – Zorawar Mar 2 '16 at 19:58
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    $\begingroup$ Still works here :p $\endgroup$ – Marius Ladegård Meyer Mar 2 '16 at 20:25
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    $\begingroup$ Did you, by any chance, use exponentiation in your last line of code (in Cases)? Because if I use exponentiation I do get an empty list, while using Wedge returns the desired terms. $\endgroup$ – Berg Mar 2 '16 at 21:13
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Is it not much easier and faster to simply use the following?

List@@F2/._Wedge->1

A possible solution for the more general problem described in the comments would (perhabs) be:

Replace[F2, a_*w_Wedge -> CustomSimplify[a]*w, {1}]

which applies some custom simplifications to the coefficients of the Wedge-products. One can change the pattern to a_. if the coefficient 1 should also be transformed.

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  • $\begingroup$ Yes, but my question is a simplified version of my real needs :) I need to simplify the expressions but Mathematica finds simplifying p-forms very difficult to do, so my strategy is to extract coefficients, simplify them individually and then recombine them; so, I need to track what the coefficients are in front of also. Probably I'm still doing it inefficiently, though... $\endgroup$ – Zorawar Mar 2 '16 at 22:05
  • $\begingroup$ In effect, for F2 above, what I need is something like: Simplify[2] d[x] ^ d[y] + Simplify[3] d[x] ^ d[z]. But where the actual coefficients are functions of the variables x, y, z, ... and not just 2 and 3 :) $\endgroup$ – Zorawar Mar 2 '16 at 22:08
  • $\begingroup$ I changed my reply a bit. Those patterns with default values are neat way to simplify code, see the tutorial on Patterns and Transformation Rules. $\endgroup$ – Berg Mar 2 '16 at 23:19
  • $\begingroup$ Interesting. Thanks! I'm going to delete the question soon, but thanks for the suggestion! $\endgroup$ – Zorawar Mar 3 '16 at 20:31

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