front end - Usage of [InvisibleApplication] and other related invisible characters

From the front end, \[InvisibleApplication] can be entered as Esc @ Esc, and is an invisible operator for @!. By an unfortunate combination of key-presses (there may have been a cat involved), this crept up in my code and I spent a great deal of time trying to figure out why in the world f x was being interpreted as f[x]. Example:

enter image description here

Now there is no way I could've spotted this visually. The *Forms weren't of much help either. If you're careful enough, you can see an invisible character between f and x if you move your cursor across the expression. Eventually, I found this out only by looking at the contents of the cell.

There's also \[InvisibleSpace], \[InvisibleComma] and \[ImplicitPlus], which are analogous to the above. There must be some use for these (perhaps internally), which is why it has been implemented in the first place. I can see the use for invisible space (lets you place superscripts/subscripts without needing anything visible to latch on to), and invisible comma (lets you use indexing like in math). It's the invisible apply that has me wondering...

The only advantage I can see is to sort of visually obfuscate the code. Where (or how) is this used (perhaps internally?), and can I disable it? If it's possible to disable, will there be any side effects?

Answer

It is used in TraditionalForm output, e.g. here:

TraditionalForm[ Hypergeometric2F1[a,b,c,x] ]

Without \[InvisibleApplication] it would probably be hard for Mathematica to parse it back to InputForm. Probably it is used in more places internally.

In order to get rid of it:

Locate the file UnicodeCharacters.tr in /usr/local/Wolfram/Mathematica/8.0/SystemFiles/FrontEnd/TextResources (or the equivalent under Windows or MacOSX), make a backup of the file, open it and delete the line

0xF76D         \[InvisibleApplication]         ($@$ ...

Then your cat can jump on the keyboard again.

Comments

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....

Blog

Search This Blog