Skip to main content

kernel - All value types for a symbol?


Robby Villegas here shows a nice way to see all the types associated with a symbol. He sets a symbol, valueTypes, to an explicit list of the values types in version 3.0 of Mathematica (I took off his dollar sign (he wrote $ValueTypes) so as not to give the false impression that valueTypes is provided by the system --- Robby just writes it out from some other source, maybe just deep knowledge or the source code):


valueTypes = {Attributes, DefaultValues, DownValues, FormatValues, 
   Messages, NValues, OwnValues, Options, SubValues, UpValues};
Through[valueTypes[Unevaluated[E]]]



{{Constant, Protected, ReadProtected}, {}, {}, {HoldPattern[MakeBoxes[E, _]] :> 
"\[ExponentialE]"}, {HoldPattern[E::usage] :> "E is the exponential constant 
\[ExponentialE] (base of natural logarithms), with numerical value 
\[TildeEqual] 2.71828."}, {}, {}, {}, {}, {}}

This was way back in version 3. We're at version 10.2, now, and I wonder whether any new "value types" have been added to the system.


Is there an authoritative list of these types, either in the documentation or in a system-supplied symbol I can inspect?



The question "Copying one symbol into another" is about a similar, but non-identical problem. Why is my question not a duplicate? The solution to copying involves the function Language`ExtendedDefintion, which explicitly lists the following value types:


In[1]:= Language`ExtendedDefinition[f]


Out[1]= Language`DefinitionList[HoldForm[f] -> 
  {OwnValues -> {}, SubValues -> {}, UpValues -> {}, 
   DownValues -> {}, NValues -> {}, FormatValues -> {}, 
   DefaultValues -> {}, Messages -> {}, Attributes -> {}}]

Note that it does not list Options. Options are instead stored within DefaultValues for some reason:


In[2]:= Options[f] = {a -> 1};
In[3]:= Language`ExtendedDefinition[f]


Out[3]= Language`DefinitionList[HoldForm[f] -> 
      {OwnValues -> {}, SubValues -> {}, 
       UpValues -> {}, DownValues -> {}, NValues -> {}, 
       FormatValues -> {}, DefaultValues -> {HoldPattern[Options[f]] -> {a -> 1}}, 
       Messages -> {}, Attributes -> {}}]

This shows that Options and Default are somehow different from the other value types, and they are both stored inside DefaultValues. Yet they still fit the description of "values associated with a symbol" (and are listed by Definition). I would like to have a full list of such value types, including Options and Default.




Comments

Post a Comment

Popular posts from this blog

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}]
Post a Comment
Read more

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}]
Post a Comment
Read more

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....
Post a Comment
Read more