So I have the following expression that derives from previous computations:

aux=(Sqrt[Im[Rout]^2+Re[Rout]^2])/(\[Sqrt]((-2000 f \[Pi] Im[L1]-2000 f \[Pi] Im[L3]+f^3 \[Pi]^3 (-8000000000 Im[C2] Im[L1] Im[L3]+8000000000 Im[L3] Re[C2] Re[L1]+8000000000 Im[L1] Re[C2] Re[L3]+8000000000 Im[C2] Re[L1] Re[L3])+Re[Rin]+f^2 \[Pi]^2 (4000000 Im[L3] Im[Rin] Re[C2]+4000000 Im[C2] Im[Rin] Re[L3]+4000000 Im[C2] Im[L3] Re[Rin]-4000000 Re[C2] Re[L3] Re[Rin])+Re[Rout]+f^2 \[Pi]^2 (4000000 Im[L1] Im[Rout] Re[C2]+4000000 Im[C2] Im[Rout] Re[L1]+4000000 Im[C2] Im[L1] Re[Rout]-4000000 Re[C2] Re[L1] Re[Rout])+f \[Pi] (2000 Im[C2] Im[Rin] Im[Rout]-2000 Im[Rout] Re[C2] Re[Rin]-2000 Im[Rin] Re[C2] Re[Rout]-2000 Im[C2] Re[Rin] Re[Rout]))^2+(Im[Rin]+Im[Rout]+2000 f \[Pi] Re[L1]+2000 f \[Pi] Re[L3]+f^3 \[Pi]^3 (Im[L3] (8000000000 Im[L1] Re[C2]+8000000000 Im[C2] Re[L1])+(8000000000 Im[C2] Im[L1]-8000000000 Re[C2] Re[L1]) Re[L3])+f^2 \[Pi]^2 (Im[Rin] (4000000 Im[C2] Im[L3]-4000000 Re[C2] Re[L3])+(-4000000 Im[L3] Re[C2]-4000000 Im[C2] Re[L3]) Re[Rin])+f^2 \[Pi]^2 (Im[Rout] (4000000 Im[C2] Im[L1]-4000000 Re[C2] Re[L1])+(-4000000 Im[L1] Re[C2]-4000000 Im[C2] Re[L1]) Re[Rout])+f \[Pi] (Im[Rout] (-2000 Im[Rin] Re[C2]-2000 Im[C2] Re[Rin])+(-2000 Im[C2] Im[Rin]+2000 Re[C2] Re[Rin]) Re[Rout]))^2))

Because all variables are real and positive I do this:

aux = Simplify[aux, {Rin,L1,C2,L3,Rout} \[Element] PositiveReals];

And obtain

Abs[Rout]/Sqrt[(Rin-4000000 C2 f^2 L3 \[Pi]^2 Rin+Rout-4000000 C2 f^2 L1 \[Pi]^2 Rout)^2+4000000 f^2 \[Pi]^2 (L1+L3-4000000 C2 f^2 L1 L3 \[Pi]^2+C2 Rin Rout)^2]

Now why in the world is Mathematica doing Abs[Rout] instead of Rout, how can I bypass this?

My version is

  • 3
    $\begingroup$ With v13.2.1, I cannot reproduce your problem. Have you tried starting with a fresh kernel or restarting Mma? $\endgroup$
    – Bob Hanlon
    Feb 20, 2023 at 2:45
  • 3
    $\begingroup$ On v12.2.0 Win7-x64, I see this. $\endgroup$
    – Syed
    Feb 20, 2023 at 3:14
  • 1
    $\begingroup$ Please edit your question to include further details, like the output of $Version and if you have tried this with fresh Kernel or not. Problem can't be reproduced on 13.2.0 for Linux x86 (64-bit) (December 12, 2022) . $\endgroup$
    – rhermans
    Feb 20, 2023 at 16:31
  • $\begingroup$ Just updated the version $\endgroup$ Feb 20, 2023 at 22:52
  • $\begingroup$ @GrangerObliviate in 12.0 on a mac there's no problem. What I mean is that I don't get Abs[Rout] $\endgroup$
    – bmf
    Feb 21, 2023 at 6:26

1 Answer 1


I have the same version,, on Linux, and the issue does not reproduce. That said the code technically does not seem correct (unless I've missed that feature in the documentation): the code says that a list is an element of PositiveReals instead of saying that each individual element of that list is a positive real number. To make sure it is not the issue, can you try the following?

aux = Simplify[aux, And@@(Element[#,PositiveReals]&/@{Rin,L1,C2,L3,Rout})];
  • 1
    $\begingroup$ It's easier to write (Rin | L1 | C2 | L3 | Rout) \[Element] PositiveReals. $\endgroup$ Feb 21, 2023 at 13:20

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