# Tagged Questions

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

436 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, ...
52 views

### How to make work Plus function? [duplicate]

I have a little problem. I have k = 1.56343*10^9; r = 9.10492*10^18. And I should receive a (2*r*r-k*k)/2*r*r, it equals to ...
476 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 ...
856 views

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

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

### Pick bug? level 0 matching

A previous discussion of this issue (Is there a bug in Pick?) accepted that matching at level 0 is not a bug in Pick. Was that correct? I am not yet persuaded. ...
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 ...
71 views

### Miller-Rabin algorithm [closed]

I want to implement the Miller-Rabin algorithm in Mathematica to check if a number is prime with at least 99.99% probability. I used this: ...
99 views

### PlotRange->Automatic the exact function used to calculate outliers

I know that PlotRange->Automatic does the following: "the distribution of coordinate values is found, and any points sufficiently far out in the distribution ...
138 views

### Derivative of Vectoral NDSolve Interpolated Function / Rule Solutions,/., and Vector NDSolve [duplicate]

I need to find the instantaneous phase and instantaneous frequency for a rotating system. I am having difficulty making the math work with interpolating functions. First, here is a problem without ...
69 views

### Plot function failure, and understanding how mathematica selects recursion points for correction

I think it is best to start out by directing everyone to this link. The discussion concerns why the Plot function fails to accurately generate a simple sine wave for given parameters. The answer given ...
225 views

### 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 ...
37 views

### Apparent issue with derivative of FractionalPart [duplicate]

This issue came to my attention from Math.SE: http://math.stackexchange.com/questions/1015325/is-the-derivative-of-x-on-0-1-always-equal-to-1/1015342#1015342 To summarize, it appears that ...
263 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 ...
61 views

### Birch clustering in Mathematica

I want to implement birch clustering in Mathematica. MAthematica only has 4 methods of clustering, is there any implementation for Birch clustering? Birch clustering is much faster than K means ...
188 views

### Distance Time Warp (DTW) function implementation in mathematica

The DTW (Distance time warp) is given here http://en.wikipedia.org/wiki/Dynamic_time_warping There is an implementation of DTW in R as well as MATLAB. However i am unable to find something for DTW in ...
269 views

### 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 ...
54 views

### Implementation of Series function

I'm trying to evaluate the partial derivatives of some function F[x,y] at some point, i.e. ...
383 views

### Use of Strassen's algorithm

Strassen's algorithm is an algorithm for matrix multiplication that is asymptotically faster than the naive one. In practice, the matrices involved have to be quite large before Strassen's algorithm ...
901 views

### Find the smallest positive integer that satisfies a certain condition

I know Mathematica is really powerful when it comes to functional operations like applying a list of tasks to a list of variables. Sometimes I feel like it isn't the most powerful tool when it comes ...
283 views

### What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
163 views

### Finding hidden treasure (aka finding undocumented functions) [duplicate]

I was searching for a way to determine if a point is within a polygon and stumbled upon rm -rf's answer. (actually, I really wanted to find a point within a ...
370 views

### How to generate a unique file name similar as that created by CreateTemporary

CreateTemporary can generate a unique file name like ...
131 views

### Given two samples, how does LocationTest select its AutomaticTest?

How does LocationTest select its "AutomaticTest" when testing two samples? Background: A previous post poses a similar question ...
492 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 ...
63 views

I would like to obtain a "slick" implementation of A*-search algorithm on Graph objects, using the built-in BreadthFirstScan (if that is possible at all). I noticed that BreadthFirstScan is static in ...
136 views

### 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 ...
120 views

510 views

### Method used by FindFit

Using FindFit, Mathematica selects an optimal algorithm when Automatic is selected. I'd like to know the name of the method ...
758 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: ...
37 views

### Internals of Prime function [duplicate]

Does anyone knows how exactly Prime works ? For example how Prime[1000000000] is calculated ? The only information I found was ...
97 views

### 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? ...
271 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 ...
2k views

### 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 ...
89 views

### JewishNewYear date limitation

The documentation for the function "JewishNewYear" in the "calendar" package declares that the year argument must be between 1900 and 2100. No explanation is given for this limitation. The function ...
136 views

### How does Mathematica solve eigenvalues? [on hold]

I believe mathematica uses some techniques beyond our book. According to the text book it is not possible to solve eigenvalues of which the matrix has not completely eigenvectors, or of those matrix ...
4k 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 ...
431 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 ...
708 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, ...
1k views

### How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
392 views

### Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
287 views

### Daubechies scaling function

In Mathematica in wavelet package with the following codes Phi[x_, j_, k_] := 2^(j/2) WaveletPhi[DaubechiesWavelet[3], 2^(j) x - k] Mathematica computes ...
568 views

### How does Mathematica's LowpassFilter work?

I don't really understand the documentation for the LowpassFilter[] function in Mathematica. In the course I have about signal processing, low-pass filters come in ...
449 views

### How does Mathematica calculate the nth prime?

When I enter Prime[2000000000000], the two-trillionth prime, Mathematica gives 61427839512211 for the answer after several ...
480 views

### Any ideas on how GeneralMiniMaxApproximation is implemented?

GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
156 views

### Implementation of Decompose

I'm curious as to how Decompose works so I decided to use Trace with the option ...
84 views

### What algorithm is Mathematica using for FirstPassageTimeDistribution[]?

What algorithm is Mathematica 9 using for FirstPassageTimeDistribution[]? Is it attempting to use PseudoInverse[] on the ...
369 views

### How does FindShortestTour work?

How are FindShortestTour and the algorithms therewithin implemented internally? Also: Can I access some form of incremental, in-progress result during evaluation? ...
111 views

### Design considerations behind O (a.k.a. BigOh, a.k.a. Landau Order)

This works without any warnings: O[Log[x]]. This raises a warning: O[x^2]. I have a few questions around this: Why is it a ...