How can I find the answer to this inequality for Lambda?
Abs[8 \[Eta]^2 \[CapitalLambda]^2 + 8 \[Pi] \[Eta] \[Mu] + (
16 \[Pi]^2 \[Mu]^2)/\[CapitalLambda]^2]/Abs[
4 \[Pi] \[Eta] - (8 \[Pi]^2 \[Mu])/\[CapitalLambda]^2]<1
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$\begingroup$ @MariuszIwaniuk: I want to have a region plot that determines the area where this condition is established. The answer of this command is somehow complicated $\endgroup$– Perfect FluidCommented Jul 24, 2018 at 17:16
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1 Answer
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sol = Reduce[(Abs[8 η^2 Λ^2 + 8 π η μ + (16 π^2 μ^2)/Λ^2]/Abs[4 π η - (8 π^2 μ)/Λ^2] //
FullSimplify) < 1, Λ, Reals] // Simplify
(* long expr *)
RegionPlot3D[sol, {η, -3, 3}, {μ, -3, 3}, {Λ, -3, 3}, AxesLabel -> Automatic]
answered Jul 24, 2018 at 18:02
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$\begingroup$ +1. Although much slower,
RegionPlot3D[ sol, {\[Eta], -3, 3}, {\[Mu], -2, 2}, {\[CapitalLambda], -3, 3}, AxesLabel -> Automatic, PlotPoints -> 75, MaxRecursion -> 6] // Quietis far smoother. $\endgroup$ Commented Jul 24, 2018 at 18:34 -
$\begingroup$ @BobHanlon,Thanks for smoother 3DPlot
:)$\endgroup$ Commented Jul 24, 2018 at 18:41