Which condition?

Question

I want to substitute integers in a list with theirs square, I tried these

Cases[{{1, 2, 3}, a, {4, 5}}, t__ /; Element[t, Integers] :> t^2]
(*{{1, 4, 9}, {16, 25}}*)
Cases[{{1, 2, 3}, a, {4, 5}}, t__ /; IntegerQ[t] :> t^2]
(*{}*)

Why the first code works and the second doesn't? What is the difference between Element and IntegerQ?

Answer 1

basically if you deconstruct you will see that Element in your case operates on the sublist level

{1, 2, 3} ∈ Integers
(* True *)

a ∈ Integers (* does not result in a boolean *)

{4,5} ∈ Integers
(* True *)

in second case your integers are present at level 2 and therefore you need to define the appropriate level in Cases

Cases[{{1, 2, 3}, a, {4, 5}}, t__ /; IntegerQ[t] :> t^2, {2}]
(* {1,4,9,16,25} *)

Note: this will not give the same form as Cases with Elements because you are matching objects at a different level

If you need a similar result with your second case, consider using this:

Cases[{{1, 2, 3}, a, {4, 5}}, pat : {__Integer} :> pat^2]
(* {{1, 4, 9}, {16, 25}} *)

with the named pattern pat your pattern matches at the same level as your Elements case