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

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2
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0answers
17 views

Implementation of Series function

I'm trying to evaluate the partial derivatives of some function F[x,y] at some point, i.e. ...
3
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0answers
71 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 ...
0
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0answers
33 views

What Algorithm Does Mathematica use to Calculate Betweenness Centrality for Unweighted Graphs?

Recently asked this question http://math.stackexchange.com/questions/888369/betweenness-centrality-how-long-does-mathematica-take on the Mathematics SE. Does anyone know, as a follow up, what ...
4
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1answer
198 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 ...
5
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2answers
203 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 ...
6
votes
9answers
814 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 ...
1
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1answer
103 views

What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
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2answers
68 views

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

CreateTemporary can generate a unique file name like ...
0
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0answers
121 views

What algorithms does NSolve use?

I've been using NSolve to find roots and now I've been wondering what underlying algorithm mathematica uses. It's probabaly similiar to ...
4
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0answers
88 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 ...
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0answers
53 views

Can BreadthFirstScan be modified?

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 ...
0
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1answer
94 views

Open an MX file used by the kernel [closed]

I am working on a graph, and I am using Mathematica function FindGraphCommunities to analyze the properties of this graph, but I have no idea about the algorithm ...
6
votes
2answers
96 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 ...
9
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1answer
92 views

Why does $Failed have attribute HoldAll?

Why does $Failed have attribute HoldAll? Are there typical situations where $Failed is ...
1
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0answers
208 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 ...
65
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2answers
734 views

Why are numeric division and subtraction not handled better in Mathematica?

There is something that has been troubling me for a while. At least in version 7, the performance of a / b and a - b is not ...
8
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1answer
250 views

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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0answers
30 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 ...
2
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0answers
80 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? ...
9
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1answer
121 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 ...
6
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1answer
515 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 ...
4
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0answers
83 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 ...
6
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0answers
144 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 ...
0
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0answers
117 views

How does Mathematica solve eigenvalues?

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 ...
18
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2answers
540 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: ...
17
votes
1answer
346 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 ...
12
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1answer
315 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, ...
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0answers
554 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 ...
19
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0answers
269 views

Why does list assignment with a packed array result in unpacked values?

This is another question on the design choices in Mathematica. I understand that without direct reply from the developers it may not be possible to give a definitive and exhaustive answer to "why" ...
2
votes
1answer
240 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 ...
24
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1answer
429 views

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

I'm curious what's inside the InterpolationFunction object? For example: ...
2
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1answer
189 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 ...
4
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1answer
303 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 ...
3
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1answer
282 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 ...
8
votes
3answers
432 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 ...
6
votes
2answers
241 views

What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
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0answers
77 views

What algorithm is Mathematica using for FirstPassageTimeDistribution[]?

What algorithm is Mathematica 9 using for FirstPassageTimeDistribution[]? Is it attempting to use PseudoInverse[] on the ...
1
vote
1answer
175 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? ...
7
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0answers
104 views

Apart may use Padé method: what's that?

How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
1
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1answer
326 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 ...
6
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0answers
108 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 ...
4
votes
1answer
928 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 ...
21
votes
3answers
347 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 ...
6
votes
1answer
232 views

What algorithm is Mathematica 9 using for “SpectralEmbedding” of graphs?

When I specify that a graph should be realized using the "SpectralEmbedding" procedure, what paper / algorithm for spectral embedding is this based on? I was unable to find any documentation for ...
2
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1answer
142 views

Implementation of Decompose

I'm curious as to how Decompose works so I decided to use Trace with the option ...
5
votes
2answers
262 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 ...
5
votes
3answers
197 views

How could I implement the equivalent of NextPrime

I would like to know what an implementation of the function NextPrime would look like if it were implemented in Mathematica's core language.
20
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2answers
431 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 ...
14
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2answers
418 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: ...
4
votes
2answers
381 views

Any ideas on how GeneralMiniMaxApproximation is implemented?

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