5
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Look at these two examples:

In[1]:=Select[f[i], MatchQ[_f]]
Out[1]:=f[]

In[2]:=Cases[f[i],_f]
Out[2]:={}

It seems that the Select take $f[i]$ as List, but Cases do not.

I also can not understand why the first gives that answer.

Thanks.

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  • 1
    $\begingroup$ ref / Select / Generalizations&Extensions / #1. $\endgroup$ – Kuba Jan 11 at 7:58
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  1. Select preserves the head of the original expression, while Cases always returns the result in a List.

  2. Select operates only at level one, whereas Cases accepts a levelspec.

Specifically your first output is equivalent to these:

Part[f[i], {}]

Delete[f[i], 1]

The second can be made to match by expanding the levelspec to include level zero:

Cases[f[i], _f, {0, 1}]
{f[i]}

Recommended reading:

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  • 3
    $\begingroup$ The essence of (1) is that Select[f[i], MatchQ[_f]] matches nothing and only returns an empty expression with head f. It is the same as Select[f[i], MatchQ[_somethingelse]]. The recommended answers are very informative btw. $\endgroup$ – Theo Tiger Jan 11 at 10:04

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