# Tagged Questions

For questions regarding the underlying implementation of built-in functions.

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### What is the most convenient way to read definitions of in-memory symbols when we don't have the source files? (Spelunking tools)

Note: I put Simon's implementation on GitHub. Contributions welcome! When trying to read the definition of already defined (package or built-in) symbols using ...
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### What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
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### How to find out which method Mathematica selected?

There are commands like NonlinearModelFit[] or NDSolve[] that have the option Method it ...
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### Where can I get detailed information on how the Plot command works?

The command Plot[x^2, {x, -3, 3}, PlotStyle -> Arrowheads[{-.025, .025}]] /.Line -> Arrow produces this output. What I don't understand is what ...
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### How does Plot work?

I considered the following function: sin[x_] := Module[{}, Print["x=", x]; Sin[x] ] in Mathematica. Next, I tried to plot it using: ...
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### How does Mathematica integrate?

Basically, this question can be considered to be an extenstion to my other question. What I wanted to do was this integral as homework (it is indefinite BTW so no approximations using Simpson's Rule ...
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### How to interpret the FullForm of a SparseArray?

SparseArrays are atomic objects, but they do have a FullForm which reveals information about them. What is the meaning of the ...
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### Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...
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### How is pattern specificity decided?

Mathematica has a notion of pattern specificity, which is a partial ordering on patterns. The rules (e.g. DownValues, SubValues,...
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### How are MemberQ and FreeQ so fast?

I would like to understand the implementation that allows MemberQ and FreeQ to be as fast as they are. I noticed this thanks to ...
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### Why does list assignment with a packed array result in unpacked values?

Bug introduced in 5.2 or earlier and fixed in 10.1.0 This is another question on the design choices in Mathematica. I understand that without direct reply from the developers it may not be ...
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### Blend code for built-in ColorData schemes

Hi I want to get a blend similar to "SunsetColors". To make those slight modifications, I would like to know the precise blend of that color scheme. My try: <...
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### Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
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### How does Interpolation really work?

I'm looking for some explanation or advice, not help in solving something. Recently I finished my program and my supervisor said "Ok, now it's time for your first paper: write a scientific text about ...
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### How to implement FittedModel like objects

In the course of making some RLink wrappers I want to have some richer containers like Mathematica does with its FittedModel ...
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### Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
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### How to determine BLAS/LAPACK implementation used internally for numerical matrix operations?

Is there a command which reveals which implementation of BLAS and LAPACK are used in Mathematica's matrix operations such as Eigensystem? I asked a related question ...
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### How to know the internal algorithms of functions like Predict or Classify?

The document centre seems only explain how to use these functions, but just in an very brief way. I know Mathmatica is not open source, so we can not expect to see the code of the function, but are ...
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### What is the real default CellEvaluationFunction?

The default CellEvaluationFunction is Identity but one can quickly see that this is handled specially as an equivalent function, ...
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### How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
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### The difference between “SymbolicProcessing” -> 0 and restricting the function definition to numeric values only

The Documentation tells us that there are two ways to disable symbolic processing of the integrand by the NIntegrate function when it is known that it just slows ...
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### What is the default ColorFunction for Image3D?

What is the default ColorFunction for Image3D? I find it a bit confusing that the most intense colour is not shown where the ...
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### What are the limits of the Prime-functions? [duplicate]

Will Prime and PrimePi test up to 3 * 10^12? Where can I find the limits for these funtions? ...
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### What is behind experimental function: FindFormula?

In version 10.2 there is a new experimental function: FindFormula[]. I suspect that a genetic programming algorithm (symbolic regression) is behind this new ...
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### Why does't SeedRandom work here?

From the docs on SeedRandom, SeedRandom[] resets the generator, using as a seed the time of day and certain attributes of ...
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### Why does iterating Prime in reverse order require much more time?

Say I would like to display the $10$ greatest primes that are less than $10^5$. I could do the following: ...
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### What does “suitable for symbolic manipulation” in the documentation mean?

This question is related to this other one I posted on Stack Overflow some time ago. There, in a beautiful answer, acl (with some unhumble editing done by me) showed that the derivative of ...
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### What governs images resizing in the FrontEnd environment

What is responsible for the middle Row images' size? And why single image row is different? ...
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### How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
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### Why NIntegrate is badly-behaved on $J_{\frac{9}{2}}(x)$ by default?

A friend of mine showed me this example: Plot[BesselJ[9/2, x], {x, 0, 1}, PlotLabel -> Style["The integrand seems to be simple", 14]] ...
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### Citation of the algorithms used in FindGraphCommunities

For my research work I need to put a comparison of different community detection algorithms. Instead of implementing all those algorithms once again, I would like to use the methods already provided ...
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### References on functions FindGraphPartition and FindGraphCommunties

Does somebody have some interesting references on the FindGraphPartition and FindGraphCommunties[.., Method -> "Spectral"] ...
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### How does Mathematica determine that an evaluation should be terminated?

How exactly does Mathematica determine that evaluation of particular expression should be finished and the result should be returned? Here are some examples of unclear behavior which have arisen, ...
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### Efficiently appending points to a NearestFunction

I have a program which works with a list of points (in 3D, but it could be in 1D as well, it won't make a difference). Within a loop, it keeps adding new points to the list. To calculate the ...
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### What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...
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### What is the simplest way to determine which call to a superfunction has generated a Message?

I have a complicated function which contains many calls to NIntegrate, NSolve, FindRoot and ...
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### How to retrieve the parameters calculated and used by ImageAdjust?

When ImageAdjust is called with an image, i.e. with one parameter, it returns an automatically adjusted Image. I would like to ...
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### How does Mathematica automatically choose which classifier method to use?

I'm interested in what heuristics are used in Classify's choice of method.
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### What calendar is Mathematica using for dates in the distant past?

It appears that Mathematica treats all dates as proleptic Gregorian dates by default, a hypothesis that can be easily tested by using AbsoluteTime to compute the ...
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### Algorithm used by IsomorphicGraphQ

I'd like to know which algorithm is used to test if two graphs are isomorphic?
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### what is The Formula behind the Kolmogorov-Smirnov test statistics?

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
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### What method does NDSolve use for solving PDEs?

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. ...
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### How to check for Mathematicaâ€™s definition of XY?

The question is: Can I ask the Mathematica kernel directly what it takes as the definition of the built-in symbol XY? After all this has to be in the kernel. And if the documentation is not giving any ...
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### Get name of hidden inbuilt functions (like Ticks drawing)

how do I get the name and definition of a builtin Mathematica functions? For instance, I would like to see how default Tick plotting function is implemented. However, it is not clear where it is and ...
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### Algorithm in RandomChoice[{w1,w2,…}->{e1,e2,…},n]?

I wonder if someone happens to know the actual algorithm implemented in the particular overload of RandomChoice that handles explicitly presented discrete ...
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### The default ColorFunction of DensityPlot before v10?

The default ColorFunction of Plot, Plot3D before v10 is respectively mentioned here and here,...
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### How does Mathematica calculate $\sin(\pi/5)$?

Consider: Sin[Pi/5] which returns: $$\sqrt{\frac58-\frac{\sqrt5}{8}}$$ Does anyone know how to figure out the trigonometric identities used by Mathematica to ...
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### Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...