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

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2
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0answers
67 views

FrobeniusSolve: how does it work?

Can someone suggest any reference to read? I would like to understand how the algorithm works.
2
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0answers
23 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 ...
8
votes
1answer
102 views

Accuracy of PrimeQ function

Using PrimeQ in Mathematica 10 on integers up to $2\cdot 10^{5717}$ the function appears to work. The Documentation for Mathematica 5 says that ...
5
votes
1answer
125 views

Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
0
votes
0answers
64 views

Meaning of the character sequence after an Entity's name

Mathematica can interpret an entity when you type Ctrl+=, like this: Then we'll get an entity We can get the InputForm You will get a canonical name ...
9
votes
2answers
112 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 ...
8
votes
1answer
296 views

Show how Mathematica defines a function

Is there a way to show how Mathematica defines a function, such as In: Something[Sqrt], Out: Sqrt[x] -> x^(1/2) As far as I understand it the command ...
3
votes
1answer
84 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 ...
2
votes
0answers
61 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 ...
7
votes
1answer
77 views

Is the Method -> Automatic option for Classify not deterministic?

I just prepared an (well known) example in machine learning, the weather dependent determination of whether to play golf or not, as shown in this picture (of a corresponding Dataset) Now I set up ...
3
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0answers
63 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 ...
2
votes
1answer
56 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. ...
3
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0answers
67 views

The implementation of FunctionRange

How exactly does the FunctionRange work? What kind of algorithm does it use? I looked it up in the manual but it doesn't provide any references or even a name of ...
5
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0answers
51 views

How many clusters does DominantColors return?

Is there any documentation on how it automatically chooses the number of colors - does it use X-means or some other heuristic to determine the number of clusters it automatically returns?
13
votes
1answer
219 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? ...
17
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1answer
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.
2
votes
1answer
69 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 ...
17
votes
2answers
285 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 ...
8
votes
1answer
192 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 ...
4
votes
1answer
83 views

What is the default ColorFunction for MatrixPlot?

I think the the default ColorFunction for ArrayPlot is ...
5
votes
0answers
70 views

How does Plus work on machine precision Real arguments?

I thought Kahan's summation method would make a nice example for students to use to think about round-off error [W. Kahan, Pracniques: Further Remarks on Reducing Truncation Errors, Commun. ACM 8  ...
5
votes
0answers
70 views

What is the underlying algorithm to simplify sums of reciprocals of polynomials?

Flipping through Wolfram's blog entry on Leibniz, W noted Huygens' interview test for the young Leibniz, namely to determine: $$ \sum_{n\ge2} \frac{1}{{n \choose 2}} $$ It's one thing to do this by ...
2
votes
0answers
74 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 ...
1
vote
1answer
100 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 ...
5
votes
2answers
163 views

Why this upvalue doesn't escape from Sum?

Probably a hard question, but I decide to cry out loud :). This is actually another problem I encountered when answering this question. Consider the following transform rule stored as an upvalue: ...
8
votes
1answer
154 views

What values of $\delta$ and $\eta$ are being used in LatticeReduce?

The Lenstra–Lenstra–Lovász algorithm has a parameter $\delta$ with $1/4 < \delta < 1$, where roughly speaking the closer $\delta$ is to 1 the longer it takes, but the better basis reduction you ...
1
vote
0answers
67 views

What's the algorithm behind markov classifier in Classify function for text classification?

https://www.wolfram.com/mathematica/new-in-10/highly-automated-machine-learning/find-which-author-wrote-a-text.html The above url show the use of Classify ...
9
votes
2answers
167 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 $\mathbf L\mathbf x=\mathbf b$. ...
2
votes
0answers
55 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: ...
1
vote
1answer
117 views

What methods does Maximize use like $\mathtt{Maximize}\left[\left\{3 x^2+2 \sqrt{2} x y,x^4+y^4=1\right\},\{x,y\}\right]$

I used Maximize for the maximum value of $3 x^2+2 \sqrt{2} x y$ when $x^4+y^4=1$ , $x>0,y>0$. What methods does Maximize ...
6
votes
0answers
82 views

Heliocentric coordinates in PlanetData

I tried to use planets' HeliocentricLongitude and I wonder if anyone has any insight on what coordinate system they use. I took vernal equinox times from http://ns1763.ca/equinox/eqindex.html and ...
15
votes
1answer
218 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 ...
6
votes
2answers
184 views

How does Mathematica calculate LaguerreL

About the function LaguerreL[n,a,x], the helping documents in Mathematica only say that this function satisfies equation $xy^{\prime\prime}+(a+1-x)y^\prime+ny=0$. ...
3
votes
0answers
84 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 ...
2
votes
1answer
48 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 ...
3
votes
1answer
106 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 ...
34
votes
3answers
769 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 ...
13
votes
1answer
585 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 ...
6
votes
0answers
69 views

Functionality of FindMaximumFlow

I know that the superseeded function NetworkFlow (needs Combinatorica) uses Goldberg-Tarjan's Push-Relabel-Algorithm but i cant find any information on Mathematica's built-in-function (...
6
votes
1answer
345 views

Algorithms behind implemented Mathematica functions [duplicate]

When I use Mathematica for analysis and I write a publication, readers often ask me: "What is the algorithm behind your calculation?". I answer that I did it with Mathematica and if they are ...
5
votes
1answer
129 views

Actual bins used for Pearson Chi Square Test

PearsonChiSquareTest[data, dist] computes bins for data as a step towards calculating the test statistic. For continuous ...
-2
votes
1answer
175 views

Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: $$ \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } $$ That is: ...
8
votes
1answer
291 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 ...
2
votes
0answers
146 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?
5
votes
1answer
159 views

BoxWhiskerChart Notched: how is the notch calculated?

I am aware of one convention for the uncertainty in a median: it is 1.58 * IQR / Sqrt[n], where IQR is the inter-quartile range and n is the number of data points. This was proposed by McGill, Tukey, ...
3
votes
0answers
87 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.
5
votes
0answers
149 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
1
vote
0answers
55 views

Algorithm for converting truth tables to Boolean functions

The function BooleanFunction is able to convert a truth table into a Boolean function. Does anyone know what is the mathematical background and/or algorithm that ...
0
votes
0answers
54 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 ...
-3
votes
1answer
127 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: ...