I have a complicated complex function containing some other ones that are real, f=f(A,B,C,...) ,where A=A(r) and it is real, for example. When I do Conjugate[f] I get something like Conjugate[f]=f*=f*(Conjugate[A],Conjugate[B],...), I mean those internal function arent interpreted as real.
I tried ComplexExpand to work with it by assuming that those internal functions are real, but it does not work. I also tried $Assumptions={A,B,...}\[Element] Reals at the beginning of the nb, and nothing.
What I want is to Simplify some expressions like (-I A)(I A)=A^2, but I only get Conjugate[A] A.
Is there some way to declare these internal functions as real, even they are part of a larger more complicated complex function?
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2 Answers
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Your assumption should be made on the value of g[_], not of plain g. Otherwise, your assumption can be introduced globally through $Assumptions, or as a second argument to Simplify, or using Assuming, all with the same result.
Clear[f, g, r]
f[arg_] := a - I arg
Conjugate[f[g[r]]]
(* Out: Conjugate[a] + I Conjugate[g[r]] *)
Assuming[g[_] ∈ Reals, Simplify[ Conjugate[f[g[r]]] ] ]
(* Out: Conjugate[a] + I g[r] *)
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$\begingroup$ You probably meant
$Assumptions$\endgroup$ Commented Jul 6, 2015 at 6:02 -
$\begingroup$ @belisarius I certainly did! Thanks for catching that. $\endgroup$– MarcoBCommented Jul 6, 2015 at 6:04
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Here is another possible solution which doesn't require you to use Simplify:
Clear[f, a, g, r]
f[arg_] := a - I arg
Conjugate[g[r_]] ^:= g[r]
Conjugate[f[g[r]]]
(* ==> Conjugate[a] + I g[r] *)
This uses UpSetDelayed to make the desired assumption part of the definitions associated with g.
