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Here is the expression. the expression

I want to extract the coefficient just as the table showing below. the coefficient

I can do it by hand, but I expect a code that can automatically identify how many differenct terms there are ,what is its coefficient and show them all in a table.

this is the expression for Mma.

expr= (3 Subscript[1, b] Subscript[2, a])/8+1/8 E^(I [Theta]) Subscript[1, b] Subscript[2, a]+1/8 E^(2 I [Theta]) Subscript[1, b] Subscript[2, a]+3/8 E^(3 I [Theta]) Subscript[1, b] Subscript[2, a]-(3 Subscript[1, a] Subscript[2, b])/8+1/8 E^(I [Theta]) Subscript[1, a] Subscript[2, b]-1/8 E^(2 I [Theta]) Subscript[1, a] Subscript[2, b]+3/8 E^(3 I [Theta]) Subscript[1, a] Subscript[2, b]-(Sqrt[3] Subscript[3, a])/8-1/8 Sqrt[3] E^(I [Theta]) Subscript[3, a]+1/8 Sqrt[3] E^(2 I [Theta]) Subscript[3, a]+1/8 Sqrt[3] E^(3 I [Theta]) Subscript[3, a]+(Sqrt[3] Subscript[3, b])/8-1/8 Sqrt[3] E^(I [Theta]) Subscript[3, b]-1/8 Sqrt[3] E^(2 I [Theta]) Subscript[3, b]+1/8 Sqrt[3] E^(3 I [Theta]) Subscript[3, b]

I think of a example as below:

tab[expr_] := {#, 
     Coefficient[
      expr, #]} & /@ (expr // 
       List @@ # & // # /. {Power[_, _] -> 1, Rational[_, _] -> 1, 
         E -> 1} & // Union) // Grid[#, Frame -> All] &

so, expr//tab will get the table above.

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    $\begingroup$ Use Coefficient. $\endgroup$ – Spawn1701D Apr 25 '13 at 11:25
  • $\begingroup$ It works. But how do I get the terms first? $\endgroup$ – cmc Apr 25 '13 at 11:31
  • $\begingroup$ What do you mean? $\endgroup$ – Spawn1701D Apr 25 '13 at 11:34
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    $\begingroup$ Does that make any sense? Do you want the terms of 3/8? Of Sqrt[3]/8? Of Exp[2 Pi]? $\endgroup$ – bill s Apr 25 '13 at 11:48
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    $\begingroup$ not sure how your expressions look like, not sure what you dislike about your tab, here's another approach, maybe it helps? Voilà: Grid[Transpose@{#, Coefficient[expr, #]} &@Union[Cases[expr, Times[c___ : 1, a : _Subscript, b :___Subscript] :> a b, 2]],Frame -> All] $\endgroup$ – Pinguin Dirk Apr 25 '13 at 12:04
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Let that you have the variables 

vars= {Subscript[1, a],Subscript[1, b],Subscript[2, a],Subscript[2, b],Subscript[3, a],
       Subscript[3, b]}

and 

expr=(3 Subscript[1, b] Subscript[2, a])/8+1/8 E^(I [Theta]) Subscript[1, b] Subscript[2, a]+1/8 E^(2 I [Theta]) Subscript[1, b] Subscript[2, a]+3/8 E^(3 I [Theta]) Subscript[1, b] Subscript[2, a]-(3 Subscript[1, a] Subscript[2, b])/8+1/8 E^(I [Theta]) Subscript[1, a] Subscript[2, b]-1/8 E^(2 I [Theta]) Subscript[1, a] Subscript[2, b]+3/8 E^(3 I [Theta]) Subscript[1, a] Subscript[2, b]-(Sqrt[3] Subscript[3, a])/8-1/8 Sqrt[3] E^(I [Theta]) Subscript[3, a]+1/8 Sqrt[3] E^(2 I [Theta]) Subscript[3, a]+1/8 Sqrt[3] E^(3 I [Theta]) Subscript[3, a]+(Sqrt[3] Subscript[3, b])/8-1/8 Sqrt[3] E^(I [Theta]) Subscript[3, b]-1/8 Sqrt[3] E^(2 I [Theta]) Subscript[3, b]+1/8 Sqrt[3] E^(3 I [Theta]) Subscript[3, b]

to get the first column use the command 

v = List@@Expand[Collect[expr, vars, 1 &]]

now things are easy:

({#,Coefficient[expr,#]}&/@v)// Grid[#, Frame -> All]&

You can tweak the Grid to your liking

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  • $\begingroup$ it help me a lot. Thank you 1701D. $\endgroup$ – cmc Apr 25 '13 at 12:10
  • $\begingroup$ @cmc to create the list vars you can use Cases if it is too long to do by hand. $\endgroup$ – Spawn1701D Apr 25 '13 at 12:12

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