plotting - How can I customize the tooltips on a ContourPlot?

I have a contour plot and I would like to have finer control over the tooltips that are displayed.

For the sake of argument, suppose that I have the following plot,

ContourPlot[
 Exp[-x^2 - y^2]
 , {x, 0, 2}, {y, 0, 2}
 , PlotRange -> Full
 , Contours -> 10^Range[-4, 0, 0.1]

 ]

Mathematica graphics

and I would like to force scientific notation on the tooltips - say, I'd like every tooltip in the form $10^{-3.7}$. More generally, I would like to apply a user-supplied function tooltipFunction to the value F[x,y] of the plotted function at the contour and display this as the tooltip.

The documentation for ContourLabels hints that this should be possible, via a specification of the form

ContourLabels->{f,g} uses f[x,y,z] as an explicit displayed label, and uses g[x,y,z] as a tooltip for each complete contour line.

However, there are no examples on the documentation and naive implementations of this don't seem to work.

Is there any way to implement this, preferably within the confines of the ContourPlot call?

Comments

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...

How to thread a list

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I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...

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