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Given input expressions, I want to extract the function and again extract its element.

For example, given my input

 f= b1 g[1, {a1,a2,a3}] + b2 g[1,{a11,a22,a33}] + b3 g[1,{a111,a222,a333}] 

First I want to extract as follows : $\{ \{a1,a2,a3\},\{a11,a22,a33\}, \{a111,a222,a333\} \}$

Since b1,b2,b3 are arbitrary I don't want to use

 coefficient[f,b1] 

Any ideas or comments?

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    $\begingroup$ Just use Cases[f, {__}, {3}] $\endgroup$
    – flinty
    May 5, 2023 at 11:48
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    $\begingroup$ Or, Cases[f, _List, All] $\endgroup$
    – Bob Hanlon
    May 5, 2023 at 15:00

1 Answer 1

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Cases[f, Times[b_. ,  g[k__]] :> {b, Last@k}, 1] // Transpose

{{b1, b2, b3}, {{a1, a2, a3}, {a11, a22, a33}, {a111, a222, a333}}}

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