map - Element-wise test on List elements

This question could sound pretty silly but I can't find a way to apply element -wise tests to a list.

For example if I digit

{0.6, 1.2}>1
{{0.6,1.2},{5,0.1}}>1

I would expect to obtain

{False,True}
{{False,True},{True, False}}

respectively, but it is not the case.

Of course I can define a function or using Map, but I can't believe there is not a core function providing this kind of result. Thank you for any indication

Answer

To my knowledge, there aren't built-in versions for comparison operators that would be automatically threaded over lists. One reason for that is that Mathematica is a symbolic system, and every auto-simplification has a cost, because there may be cases when this isn't desirable.

It is relatively easy however to construct the behavior you want:

ClearAll[l];
l[f_] := Function[Null, f[##], Listable]

Now, you can call:

{{0.6, 1.2}, {5, 0.1}} ~ l[Greater] ~ 1

(* {{False, True}, {True, False}} *)

and similarly with other comparison operations.

Note that, since you didn't mention efficiency, I intentionally left this aspect out. If you have large numerical lists, there are vastly more efficient ways to perform the comparisons, making use of vectorization and packed arrays.

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