# Questions tagged [implementation-details]

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

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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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### 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 ...
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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Algorithms used for DelaunayMesh

Is it possible to find what algorithms are used for Delanunay triangulations?
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### 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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### 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 & ...
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### 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) ...
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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### 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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### Conflict with hidden names

The following code hangs Mathematica 12.0.0: ...
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### 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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### 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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### 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 ...
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, ...
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^{-...
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 ...
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: ...
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### 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 ...
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### 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, ...
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### 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 : ...
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### 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 ...
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### 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 ...