Questions tagged [implementation-details]

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

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29 views

What are the valid options for the “ParametricCaching” option in ParametricNDSolve?

I am using ParametricNDSolve as part of the calculation of an objective function for an optimization, so I am trying to strike a balance between memory usage and ...
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2answers
124 views

How does Plot choose the points in a figure?

Taking a simple example, ...
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Is anyone aware of Mathematica implementation of OpenAI's GPT-3 API?

Is anyone aware of Mathematica's implementation of OpenAI's GPT-3 API?
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2answers
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How do the functions Reap and Sow actually work behind the scenes?

I have read that using Reap and Sow to generate a list of unknown length is much more efficient than using AppendTo over and over. I believe AppendTo works by creating a new list that is one element ...
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1answer
59 views

AsymptoticOutputTracker to Matlab-Simulink

What is the structural scheme for AsymptoticOutputTracker in Mathematica? I need this in order to transfer the feedback signals received with the help of ...
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3answers
256 views

Why does ReliefPlot not have a version for functions?

TL, DR: Use the LightingAngle option to DensityPlot to achieve the same shadows effect as ...
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1answer
70 views

GroebnerBasis internals and runtime dependence on variable list ordering

I have a problem I have reduced to asking for a Gröbner basis. For some reason, Mathematica is able to solve this in minutes, while other programs more dedicated to these types of calculations run for ...
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1answer
122 views

Automatic Method for FindMinimum with constraints

What is the default method used by FindMinimum with constraints? The documentation says: "Currently, the only method available for constrained optimization is ...
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58 views

NMinimize differential evolution: how do search points and initial points really work?

I am puzzled by the settings of a specific method for NMinimize called DifferentialEvolution, given for example here. The ...
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62 views

Algorithm used by Mathematica for evaluating partial sums

Today, while using mathematica, I entered the command Sum[1/Factorial[n], {n, 0, x}] and found that: $$\sum_{x\geq n\geq0}\frac{1}{n!}=\frac{e\Gamma(x+1,1)}{\Gamma(...
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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 ...
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1answer
161 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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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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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
343 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 ...
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1answer
219 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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42 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 ...
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1answer
82 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 ...
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1answer
109 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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55 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: ...
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1answer
198 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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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: ...
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2answers
349 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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94 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
83 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: ...
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1answer
78 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 ...
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1answer
128 views

Algorithms used for DelaunayMesh

Is it possible to find what algorithms are used for Delanunay triangulations?
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71 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 ...
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62 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) ...
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1answer
150 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
107 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? ...
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1answer
172 views

Conflict with hidden names

The following code hangs Mathematica 12.0.0: ...
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1answer
204 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 *) ...
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3answers
374 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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81 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 ...
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2answers
208 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 ...
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1answer
227 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: ...
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1answer
393 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 ...
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2answers
875 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 ...
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1answer
127 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 ...
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1answer
64 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 ...
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1answer
297 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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43 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 ...
2
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1answer
82 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 $...
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1answer
453 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 ...
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1answer
389 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 ...
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1answer
226 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 ...
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4answers
1k 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, ...
7
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1answer
474 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^{-...
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324 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 ...

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