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

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4
votes
1answer
149 views

The algorithm of ListGraphs[n,m]

I'm not sure if this is a Mathematica problem, math problem or a CS problem, so if this is off-topic please transfer it. In the package Combinatorica there is a ...
4
votes
1answer
531 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 ...
4
votes
1answer
94 views

What is the default ColorFunction for MatrixPlot?

I think the the default ColorFunction for ArrayPlot is ColorNegate[RGBColor[{#, #, #}]] &...
4
votes
1answer
74 views

Classifying text and number features

I am new to the ML algorithms and I am checking the Classify function of Mathematica. I understand the math for the random forest algorithm, but I have a question ...
4
votes
1answer
283 views

Root finding: zeroes of Mathieu function

I am finding the roots of the Mathieu sine function, and find Mathematica and Maple do not agree on the solutions. For example, consider the solutions of ...
4
votes
1answer
2k views

How does Mathematica estimate error on fit parameters?

When performing a fit using NonlinearModelFit (or any of Mathematica fitting functions, but I am particularly interested in nonlinear models), Mathematica makes a ...
4
votes
0answers
91 views

Why patterns names aren't scoped by default?

In a recent question [1] OP asked how to make Module scope working inside Set, so how to get: ...
4
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0answers
143 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 ...
4
votes
0answers
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 ...
3
votes
2answers
393 views

How does Accumulate work?

Accumulate can be used to compute the partial sums of a list. The partial sums can also be computed using a For loop but this ...
3
votes
2answers
221 views

How does RootOfUnityQ work?

How does Mathematica's RootOfUnityQ function work? That is, how does Mathematica know if a number is a root of unity? Example: Let $x = \frac{1-i \sqrt{2+\sqrt{5}}}{1+i \sqrt{2+\sqrt{5}}}$. Then <...
3
votes
1answer
313 views

What method does NIntegrate use by default?

There is a variety of algorithms for performing numerical integration (See wiki). What method does NIntegrate use by default? I looked at the documentation page ...
3
votes
1answer
334 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 ...
3
votes
1answer
113 views

How does Matematica compute the CDF of the binomial distribution?

I want to know, how Mathematica actually implements the cumulative distribution function of the binomial distribution. Which algorithm does Mathematica use to compute ...
3
votes
1answer
812 views

Specific Mathematica algorithms, for example LU Decomposition

Where I can find detailed information on algorithms used by Mathematica, especially for numerical methods. The Manual doesn't seem to iclude specifics in most cases. For example I get a different LU ...
3
votes
1answer
91 views

What kind of preprocessing does Mathematica do when I use EdgeDetect on an image?

I am doing my own implementation of Canny and Sobel in another language (not in Mathematica). I was testing the EdgeDetect method (Sobel and Canny), and my own, and ...
3
votes
0answers
43 views

What is the Chebyshev method for `InterpolationFunction`?

With InterpolationOrder -> All, some methods of NDSolve returns interpolations with ...
3
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0answers
94 views

FrobeniusSolve: how does it work?

Can someone suggest any reference to read? I would like to understand how the algorithm works.
3
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0answers
30 views

Where do DistributeDefinitions and ParallelNeeds put their definitions for newly-launched kernels to find

I'm sorry to keep banging on the definition distribution bell, but here is another (hopefully well-focused enough) question on that vein. If one is trying to distribute the definitions in a package ...
3
votes
0answers
72 views

What CPU instruction set extensions does Mathematica support?

Most CPUs in desktops and laptops nowadays are backwards compatible with the x86-64 instruction sets. But newer CPUs also have additional instruction set extensions like AVX 2, FMA3, and BMI/BMI2 ...
3
votes
0answers
92 views

What am I missing in this highly oscillatory integral?

I want to numerically integrate this equation (in python without calling Mathematica): $\int_0^\infty {\rm d}k f(k) J_v(r k) J_n(s k)$ where $f(k)$ is a non-smooth function, $J_v$ are the Bessel ...
3
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0answers
94 views

How does Mathematica automatically choose which classifier method to use?

I'm interested in what heuristics are used in Classify's choice of method.
3
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0answers
150 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 ...
3
votes
0answers
272 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 ...
3
votes
0answers
72 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 ...
2
votes
1answer
490 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? (...
2
votes
1answer
73 views

What is the encoding used when exporting images as MOV with “VideoEncoding” -> “MPEG-4 Video”?

I have a few rasterised images generated in Mathematica, and I want to output them in a video file, ideally using H.264 encoding. I found the following command. ...
2
votes
1answer
77 views

Is there a method to look inside at the internal code of Built-In functions? [duplicate]

How can I look at the code of built-in functions? Is there something like this: LookInsideFunction[SubsetQ] RETURNS ...
2
votes
1answer
161 views

Implementation of Decompose

I'm curious as to how Decompose works so I decided to use Trace with the option ...
2
votes
1answer
35 views

What is the default `SignificanceTest` setting for `FindClusters` with `Optimize` method?

According to the documentation, the default value of FindCluster's Method option is Optimize....
2
votes
2answers
200 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 ...
2
votes
1answer
158 views

Anyone knows the algorithm used by NullSpace function?

NullSpace function gives a list of vectors that forms a basis for the null space of the input matrix. When the rank of the input argument matrix $M_{m\times n}$ is ...
2
votes
1answer
52 views

Documentation for the Bounded option of SmoothKernelDistribution

I have found the Bounded option useful in the SmoothKernelDistribution function, but I can't find any documentation for exactly ...
2
votes
1answer
504 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 ...
2
votes
1answer
660 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 ...
2
votes
0answers
56 views

Rationalize error

The docs state that "Rationalize[x,dx] yields the rational number with smallest denominator that lies within dx of x." However, testing this out it appears to be false. ...
2
votes
0answers
95 views

How does Mathematica compute the determinant of a matrix? [closed]

I have been trying to write efficient code for calculating the matrix determinant for some time now. I noticed last night that Mathematica is able to compute the determinant of a $200 \times 200$ ...
2
votes
0answers
63 views

Algorithm used by Fit[]

Does anyone know what algorithm Mathematica's basic Fit[] function uses? Is it proprietary? I'm trying to do some pretty basic, linear, polynomial data fitting (...
2
votes
0answers
78 views

How can I access the Criterion function of KI method in `FindThreshold` for a dataset?

I want to find a threshold for some data set, using Kittler-Illingworth minimum error thresholding method (KI method). To do so, I use the Mathematica built-in function ...
2
votes
0answers
56 views

SetSystemOptions is obsolete? What is next? [closed]

When running the following code on Mathematica 10.2 SetSystemOptions[ "CompileOptions" -> "CompileReportExternal" -> True]; I received the message: ...
2
votes
0answers
170 views

The idea behind Stiffness switching method with NDsolve [closed]

Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?
2
votes
0answers
55 views

Implementation of Series function

I'm trying to evaluate the partial derivatives of some function F[x,y] at some point, i.e. ...
2
votes
0answers
81 views

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

I recently asked this question on the Mathematics SE. Does anyone know, as a follow up, what algorithm Mathematica uses to calculate the betweenness centrality vector (of $N$ elements) for an ...
2
votes
0answers
103 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? ...
2
votes
0answers
171 views

PowersRepresentations Algorithm

I'm trying to understand the mathematics behind counting the number of representations of a positive integer by $n$ distinct $k$th powers, i.e. I would really like to know how to do the Mathematica ...
1
vote
2answers
124 views

NIntegrate evaluates its 1st argument while it has the attribute HoldAll?

NIntegrate owns the attribute HoldAll: Attributes@NIntegrate (* {HoldAll, Protected} *) ...
1
vote
1answer
700 views

FindMinimum [] methods [closed]

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
1
vote
2answers
103 views

Does FindFit use symbolic differentiation?

Does FindFit use symbolic differentiation when optimizing by least squares a non-linear function?
1
vote
1answer
119 views

How to show steps of Integrate[Exp[-(I*(s*t))]/(Sqrt[2*Pi]*Sqrt[s]), {s, 0, Infinity}]? [duplicate]

I am trying to use Wolfram Alpha in Mathematica 10.2 to show me the steps for calculating the integral in the title, i.e I have written the following command: show steps of ...
1
vote
2answers
629 views

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

CreateTemporary can generate a unique file name like ...