# Tagged Questions

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

3k views

### 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 ...
1k views

### 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,...
1k views

### What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
3k views

### How to find out which method Mathematica selected?

There are commands like NonlinearModelFit[] or NDSolve[] that have the option Method it ...
5k views

### 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 ...
819 views

### 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 ...
794 views

### 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 ...
1k views

### 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: ...
713 views

### 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 ...
509 views

### 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 ...
553 views

### 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: ...
520 views

### 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 ...
417 views

### 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 ...
931 views

### 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: <...
956 views

### 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 ...
499 views

### 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 ...
734 views

### 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 ...
564 views

### 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 ...
319 views

### What algorithm do the Compress and Uncompress functions use?

Compress and Uncompress are used internally by Mathematica to compress things like 3D data in notebook files - data that I'd like to read independently. Does anyone have any idea if the compression ...
2k views

### How was Mathematica built?

I've been wondering this for a while now: How was Mathematica built? Is it written in Haskell? C++? I'd love to get a taste of the wizardry behind this incredible software.
2k views

### 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 ...
456 views

### 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 ...
495 views

### 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: ...
2k views

### 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 ...
234 views

### 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 ...
891 views

### 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, ...
3k views

### 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. ...
442 views

### 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, ...
277 views

### Why do big-O terms disappear in definite integrals since Mathematica 9?

In Mathematica 8, when I computed the following input: Integrate[Series[Cos[x], {x, 0, 2}], {x, 0, a}] Mathematica returned an expression that had a O[a^4] in ...
396 views

### 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 ...
596 views

### What function generates random numbers in a compiled function?

I am writing a simulation for 2D random walk. I wrote several version of code, and found that the speed is like this (fastest to slowest): C++, Mathematica compiled procedural code, Mathematica ...
224 views

### What governs images resizing in the FrontEnd environment

What is responsible for the middle Row images' size? And why single image row is different? ...
709 views

### What type of solver does Mathematica use in LinearSolve

I have a question regarding linear equation solvers. For a specific 9-diagonal matrix, every method I tried in C++ (Gaus, GCC, BICGTAB) didn't work (even though they worked for other matrices). But in ...
119 views

### 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]] ...
491 views

### 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 ...
202 views

### 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 ...
195 views

### Algorithm used by IsomorphicGraphQ

I'd like to know which algorithm is used to test if two graphs are isomorphic?
155 views

### 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 ...
318 views

### Possible Method for MatrixExp

Well, probably a hard question, but I think it's better to cry out loud :). I noticed that MatrixExp owns Method option when ...
1k views

### How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
331 views

### How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
117 views

### The theory/algorithm knowledge behind the built-in Discretize* and Boundary*

The ComputationalGeometry package was built-in in V10 distribution. In classical computational geometry field, the following questions were investigated. Convex ...
518 views

### 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 ...
721 views

### The default bandwidth of the SmoothKernelDistribution function

I am researching the Silverman rule of thumb for bandwidth selection. Below is a sample of my code, from which it seems that BW=63 is close to the default parameter given by Mathematica (2 images are ...
175 views

### Does LinearSolve know that I gave it a Sparse lower triangular matrix?

Let $\mathbf L$ be a nonsingular numeric (non-symbolic) large, lower triangular sparse matrix. Let $\mathbf b$ be an appropriately sized vector. I want to solve $\mathbf L\mathbf x=\mathbf b$. ...
263 views

### What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I suppose)...
310 views

### What algorithm does Plot use to determine abscissas?

(I'm hoping this question is not hopelessly naive...) My understanding is that Plot's strategy is to generate a list of abscissas, evaluate the argument expression ...
346 views

### 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 ...