Skip to main content

syntax - What are "" delimiters in box expressions?



If I enter a string (say, "abc") in a cell, and then switch to box representation (Shift+Ctrl+E or menu item Cell ► Show Expression), I see the following:


Cell[BoxData["\"\\""], "Input",
CellChangeTimes->{{3.662918813714031*^9, 3.6629188530623317`*^9}}]

I understand everything in this expression except the delimiters \< and \>. They look like escape sequences (e.g. \\, \") or like symbols used in string representation of boxes (e.g. \(, \!, \*, etc), but I could not find their description anywhere. I experimented a little, and it looks they are ignored within strings (for example StringLength["\<"] evaluates to 0) and rejected as an incorrect input elsewhere.


What do \< and \> mean inside of a string? For what purpose they are automatically added into the low-level representation of a cell? What are their use cases?




$Version 



"10.2.0 for Microsoft Windows (64-bit) (July 7, 2015)"


Answer



Thanks to andre's comment (where this link is provided), I now see the effect of those delimiters (I tested it in Mathematica 11 and also some earlier versions). When I add 2 newlines to the box representation of the cell:


Cell[BoxData["\"\
bc\>\""], "Input",
CellChangeTimes->{{3.662918813714031*^9, 3.6629188530623317`*^9}}]

and switch back using Shift+Ctrl+E, then the cell look like this:



"a

bc"

But if I remove those delimiters:


Cell[BoxData["\"a

bc\""], "Input",
CellChangeTimes->{{3.662918813714031*^9, 3.6629188530623317`*^9}}]


and switch back, then the cell looks like this:


"a  bc"

It seems that the purpose of \<,\> is to delimit ranges within string literals in raw box representations of cells where newlines should be exactly preserved. It looks like they only have effect in that context and are ignored in normal input in newer versions of Mathematica. The legacy documentation suggests that in Mathematica 5 they were significant in all string literals.




Update: I found an old discussion on this topic: [1],[2],[3].


Comments

Popular posts from this blog

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 - 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 - 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.