Questions tagged [implementation-details]

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

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2
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0answers
70 views

Is there any way to change the box-formatting behavior thoroughly?

Background The box-formmating behavior is affected by the downvalues of the symbol MakeBoxes. But the formatting behavior is not exactly ...
4
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1answer
112 views

Implementation of quantum Uhlmann Fidelity in Mathematica

I want to implement the quantum Uhlmann fidelity $$F(\rho, \sigma) := \mathrm{tr} \left[\sqrt{\sqrt{\rho} \sigma \sqrt{\rho}} \right]^2.$$ in Mathematica as a measure of "closeness" between ...
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86 views

Why Does Subsets[…,{n}] not Output a Packed List, Even Though it Doesn't Unpack?

Assume list is packed. I expect Subsets[] is a structural operation because it depends on the number of elements, not on what ...
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0answers
35 views

How algebraic (or more general) expression is represented (memory level, data structure) in Mathematica?

This is not a question about the usage of Mathematica, it is more about implementation. Mathematica is a very huge system, it can provide a series of very advanced operation against a Mathematica ...
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3answers
314 views

How is Grad defined for array particularly in non-Cartesian coordinates?

This question can be viewed as a follow-up of What is the definition of Curl in Mathematica? First argument of Grad can be an array, but what definition does ...
6
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1answer
133 views

Which methods are available for NDEigensystem?

I am trying to find out what methods/options are available for NDEigensystem and descriptions of their use. Perusing the help, online Q&As, Mathematica's in-...
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0answers
36 views

How does Mathematica determine if a multivariate polynomial is absolutely irreducibile?

I am working with a collection of multivariate polynomials over Q in 5 or more indeterminates, all of which are irreducible over Q. However, after testing their absolute irreducibility via ...
4
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1answer
75 views

What algorithm(s) are used by MoleculeModify's GenerateConformers?

Starting with Mathematica 12, the MoleculeModify function has a "GenerateConformers" option. What is the algorithm used to ...
5
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1answer
92 views

Which algorithm does Mathematica use for FindClique?

Does anyone know which algorithms Mathematica use for computing FindClique[g] and FindClique[g,{n}] (finds a maximal clique ...
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41 views

Method names in FindRoot

Is there any command showing what are the names of all available methods for FindRoot ? (or for any other numerical solving). Where I can find more detailed ...
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0answers
44 views

How to get a method used by ParametricNDSolve?

How to get a method used by ParametricNDSolve for solving a problem? Specifically, a boundary value problem. The code looks like that: ...
4
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1answer
191 views

How do you create the Commonest function

How does the Commonest function work? How can I implement that functionality without using that command?
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0answers
63 views

What's the solver behind Method -> {“EquationSimplification” -> “MassMatrix”}

Related: What's behind Method -> {“EquationSimplification” -> “Residual”} By reading the document carefully, I've learnt that there are 3 possible options in "EquationSimplification" for DAE systems: ...
10
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1answer
282 views

What's the principle behind the new MoleculeRecognize function?

I played a bit with the new MoleculeRecognize function implemented in the newly released WM 12.1: which simply recognizes a molecule in image and returns it as a Molecule object. ...
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0answers
92 views

Pleasantly Dynamic Property of Around

It's a rare occurrence when an improper lexicon is mete with forgiveness when coding. However, I was pleasantly surprised to stumble across the fact that ...
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2answers
78 views

How to know what GraphLayout was used when Method set to Automatic

I was expecting to get the answer to the above by doing either of the following: ...
2
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1answer
70 views

How to know what underlying algorithm mathematica function is using? [closed]

For example Blur, the documentation doesn't seem to tell what is the algorithm it is using (https://reference.wolfram.com/language/ref/Blur.html). Is there any ...
6
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1answer
112 views

Algorithms used for DelaunayMesh

Is it possible to find what algorithms are used for Delanunay triangulations?
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0answers
53 views

Is there a way to get the decision trees used by machine learning methods like `RandomForest`?

I was looking at a tutorial of SimFin, a new German-based financial data provider. There is a nice example of machine learning using sklearn in python. The package ...
0
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0answers
120 views

How does Mathematica implement PrimePi?

I'm attempting to implement a "PrimePi" function from scratch. I have a highly optimized Sieve implemented, and I've read a handful of papers to get a rough idea how to implement the Meissel & ...
5
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0answers
59 views

How Prime[n] is implemented and why is that bounded? [duplicate]

How is Prime[n] implemented in Mathematica? I have just observed that calculating large primes is quite fast (but not in O(1) ...
15
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1answer
133 views

Why does setting SyntaxInformation add a definition to DefaultValues

Before setting any definitions to the symbol f, the DefaultValues of f is empty: ...
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1answer
68 views

Mathematica classify NeuralNetwork default parameters

We have trained a Neural Network on Mathemetica classify with one hidden layer and received good classification results. We would like to know the default parameters beside it has one hidden layer? ...
12
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1answer
172 views

Conflict with hidden names

The following code hangs Mathematica 12.0.0: ...
2
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1answer
178 views

Is NumberForm double rounding numbers?

A number like 0.644696875 is represented internally as 0.6446968749999...: N[FromDigits[RealDigits[0.644696875, 2], 2], $MachinePrecision] (* 0.6446968749999999 *) ...
14
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3answers
327 views

Evaluated vs. unevaluated Association

This question might have a remote connection to my older question, it is also about sameness of expressions and subtle differences observable only in certain forms. I encountered this strange ...
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0answers
80 views

How does Wolfram Language implement for enabling symbols to receive various forms of parameters? [duplicate]

How does the official implement a list/tuple of parameters that can be different in type and quantity as a whole? After re-read @Szabolcs's and @MichaelE2's comments. Finally, I accepted the ...
3
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2answers
156 views

Does Laplacian use first argument “theta” for polar angle or azimuthal angle?

Only example I could find in the help for Laplacian is this My question is, is $\theta$ meant to be the polar or the azimuthal angle? Using $\theta$ for polar is ...
8
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1answer
216 views

Is Mathematica's implementation of convolutional neural networks really inefficient?

I'm surprised how slow ConvolutionLayer works with TargetDevice->"CPU". For instance this code: ...
26
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1answer
389 views

Why is FreeQ so much faster for some specific variable names?

It seems that performance of FreeQ depends on the names of symbols which appear in its arguments. Here is an example of two large expressions which do not contain ...
11
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2answers
849 views

Why does Arg'[1. + I] return -0.5?

From the document we know that Arg[z] gives the gives the argument of the complex number z. Then how about ...
6
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1answer
119 views

What is the algorithm behind ImageRecolor?

I'm wondering which algorithm is implemented, given that recoloring requires a lot of assumptions to really get the desired color. For example, coloring a dark grayscale image into a light green can ...
2
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1answer
63 views

Where to find information about models, data and labels used by Image/AudioIdentify?

I am thinking about using Mathematica 12's ImageIdentify and AudioIdentify functions for an interdisciplinary research project. The social science part of it requires to describe a little bit the ...
11
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1answer
246 views

Meaning of InterpolationOrder -> All for multidimensional interpolation

What specific method does Interpolation use for unstructured multi-dimensional data when we set InterpolationOrder -> All? ...
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0answers
42 views

How is the PowerSpectralDensity function implemented? [closed]

I am working on a signal processing lecture for undergraduate students with Mathematica exercises/examples, and I would like to explain to them what happens when they run the ...
1
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1answer
77 views

StateTransformationLinearize - references?

I am impressed by StateTransformationLinearize, and I feel terribly bad for not having noticed this function before. How does it work? Does it attempt to find a $...
4
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1answer
335 views

Finding NDSolve method details

I have eqs about the NDSolve, I know this code given the solving automatically. How can I find out what method is used behind the scenes? How can I gauge the ...
9
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1answer
305 views

Which FFT algorithm does `Fourier[…]` use?

Does anyone know which Fast Fourier Transform algorithm Mathematica uses to compute a Discrete Fourier Transform using Fourier[...], and is there any option to ...
4
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1answer
175 views

Why does Fourier give me a different picture than ImagePeriodogram?

I want to take a 2D fourier transform of some data, but when I try this I get unexpected results. When I use ImagePeriodogram I get something that looks like I ...
21
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4answers
998 views

What is the definition of Curl in Mathematica?

I have a usual mathematical background in vector and tensor calculus. I was trying to use the differential operators of Mathematica, namely Grad, ...
3
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1answer
325 views

Definition of WignerD function?

On Wikipedia, elements of Wigner's D-matrix are defined as $$D_{m'm}^{j}(\alpha,\beta,\gamma)=\langle jm'|e^{-i\alpha J_z}e^{-i\beta J_y}e^{-i\gamma J_z}|jm\rangle=e^{-im'\alpha}d_{m'm}^j (\beta)e^{-...
2
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0answers
299 views

How to find which automatic method is used by FindMinimum?

This question has already been addressed here and here. The second link consists of an answer by halirutan, which clearly states which method is used in which situation. However, while trying to check ...
12
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2answers
234 views

Listable built-in functions - Why are they so fast on numerical vectors?

Consider the following small example, where I calculate Exp on a large vector by employing the listability which many mathematical built-in functions have: ...
0
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0answers
44 views

Proper implementation of numerically integrated function inside a differential equation

I have a numerically-inverted function TP which is then fed to the differential equation below. My question is: What is the right way to implement this ...
1
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0answers
792 views

Difference between NSolve and FindRoot?

While it is clear what FindRoot does (start at a point and look for local extremum using gradient), how does NSolve work? Also, ...
6
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2answers
212 views

How does CirclePoints function actually work when drawing a polygon?

By reading that CirclePoints gives the positions of n points equally spaced around the unit circle, I understood that : ...
6
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0answers
80 views

Details of NDSolve calling LSODA

Inspired by my question regarding the computation time of NDSolve using the LSODA backend I was wondering how NDSolve is actually calling LSODA (what arguments are sent to LSODA), i.e. what are the ...
7
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1answer
286 views

How does Mathematica determine when to use scientific notation?

I have code that takes an initial guess for a set of parameters to use in a function that I want to minimize, calculates the function, prints the value, recalculates new parameters via the gradient ...
15
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4answers
2k views

What stopwords list is the Wolfram language using?

The documentation of DeleteStopwords only says that it "uses a standard, built-in list of stopwords". So what is it exactly? Update Now that it is said "standard"...
2
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1answer
129 views

“Exporting” Plot Theme “Classic”

I really like the 3D plots in Mathematica with the PlotTheme option set to "Classic". I wonder if there's a way to export the ...

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