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I have a function, say

minimizeme[ω_][β_][ϵ_] = ϵ^2 ω-Log[2 (Cosh[2 β]+Cosh[2 β ϵ])]/(2 β);

I want to make a high-precision dynamic ContourPlot of it using:

plottricrit[ω_] := ContourPlot[
 D[minimizeme[ω][β][ϵ], ϵ] == 0,
 {β, 0.5, 1.0},
 {ϵ, -3, 3},
 Evaluated -> True, 
 ContourStyle -> Thick, 
 RegionFunction -> Function[
    {β, ϵ}, 
    minimizeme[ω][β][ϵ] < minimizeme[ω][β][0]],
 ImageSize -> Large, 
 PerformanceGoal -> Accuracy,
 WorkingPrecision -> 60]


However, I keep running into a ContourPlot::precw message which tells me that

The precision of the argument function (...) is less than WorkingPrecision.

I have tried several ways to set the right precision (i.e., using With to inject a higher $MachinePrecision, using SetPrecision, using Rationalize, etc.), but I can't seem to get rid of this error. What is the right way to deal with it?

share|improve this question
up vote 5 down vote accepted

New method

I found that using a step value that is arbitrary precision also works:

Manipulate[plottricrit[ω], {ω, 0.217`60, 0.22545`60, 1`60*^-6}]

Old method

For reference this was my original answer, which also works but is less clean:

plottricrit[ω0_] := With[{ω = SetPrecision[ω0, 100]},
   ContourPlot[D[minimizeme[ω][β][ϵ], ϵ] == 0, {β, 0.5, 1.},
   {ϵ, -3, 3}, Evaluated -> True, ContourStyle -> Thick,
   RegionFunction -> Function[{β, ϵ}, minimizeme[ω][β][ϵ] < minimizeme[ω][β][0]],
   ImageSize -> Large, PerformanceGoal -> Accuracy, WorkingPrecision -> 60]
share|improve this answer
Won't SetPrecision get me "virtual" precision? – Andrea Colonna Jul 24 '12 at 14:28
@Andrea I'm sorry, I didn't read your question well enough; I was too busy editing in the Greek letters (I do wish there was a simple way to do that automatically). Yes, this would be "fake" precision, but given that it is originating from a slider I don't see why that matters. What am I missing? – Mr.Wizard Jul 24 '12 at 14:30
Yeah, you are right. I hadn't thought about that. Since it is an input value, it is only as good as I can input it, and as it stands I can still use higher precision numbers via the input field under the slider if needed. Thanks! So, basically, there is no way to tell the Manipulate function to feed higher-precision numbers to its arguments "internally". Is this right? – Andrea Colonna Jul 24 '12 at 14:46
@Mr.Wizard a nice palette for conversion? – Dr. belisarius Jul 24 '12 at 19:11
@Mr.Wizard I usually hate questions with non ascii symbols. Makes more difficult to work with the answers. I am thinking of a palette that when some text is selected and a button pressed changes all greek symbols into something ascii – Dr. belisarius Jul 25 '12 at 3:54

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