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I'd need to apply all functions in a list to a BlankNullSequence (___)
But when I tried
Through[{Abs, Dot, Plus, Power, Times}[___]]
(*{Abs[___], ___, ___, ___, ___}*)
it works well only with Abs. I'd like to have the result
{Abs[___], Dot[___], Plus[___], Power[___], Times[___]}
How can I have this as an output?
Why in my example there is a difference among Abs, Dot, Plus etc.?
It is important to understand that functions will attempt to operate on pattern objects (like ___) as they will any other, and sometimes this confounds the intent you had for them (the pattern objects).
Consider for example:
Plus[_, _, _]
3 _
This evaluates to 3 _ (FullForm Times[3, Blank[]]), which is not a pattern expression that will match x + y + z, because _ is not treated specially in evaluation, so it is just like Plus[x, x, x] evaluating to 3 x.
Now consider:
Abs[x]
Dot[x]
Plus[x]
Power[x]
Times[x]
Abs[x] x x x x
What to do about this will depend on why you are preparing these patterns.
If you want to use all patterns at once I would suggest Alternatives:
pat = (Abs | Dot | Plus | Power | Times)[___]
(* unchanged by evaluation *)
Now e.g.
MatchQ[a^b, pat]
True
If you really need individual pattern expressions you will need to prevent evaluation from making undesired changes. The canonical method for that is HoldPattern as proposed by MB1965 in a comment:
HoldPattern[#[___]] & /@ {Abs, Dot, Plus, Power, Times}
{HoldPattern[Abs[___]], HoldPattern[Dot[___]], HoldPattern[+___], HoldPattern[Power[___]], HoldPattern[Times[___]]}
Note: +___ is due to an output formatting rule and not evaluation itself, and the pattern will still match a + b etc. See Returning an unevaluated expression with values substituted in for more on this.
Recommended reading:
Possible duplicate:
Through[{Abs, Defer[Dot], Defer[Plus], Defer[Power], Defer[Times]}[___]]? $\endgroup$Absholds its argument if it's non-numeric. That's your issue here. TheDeferkglr proposes will work. An alternative is to use(HoldPattern[#[__]]&)/@<funcs>because you probably want that for pattern matching anyway. $\endgroup$Deferis only for formatting within notebooks. Unless the output is copied and pasted back, the headDeferwill stay in the expression. $\endgroup$BlankNullSequence.Plus[x]will evaluate toxfor anyx. It can't be kept asPlus[x]unless it wrapped withHoldor similar. What are you actually trying to do? Perhaps you wantHoldPattern. $\endgroup$ComplexExpand[Conjugate[ff[x]], {ff[x]}]and I have to specify that the functions inside ff are complex; for example:ComplexExpand[Conjugate[Abs[x]+Dot[x, y]], {x, y,Dot[___],Abs[___],Plus[___]}]. My idea is to search the functions (Symbol) that are inside ff, append to them the [___] and put the list inComplexExpand$\endgroup$