# Questions tagged [implementation-details]

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

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### Complex Airy function implementation in Mathematica?

Which algorithm does Mathematica use for double-precision N[*,16] computation of the AiryAi and AiryAiPrime functions? Are there any references? Any TOMS number or libraries?
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### Choice of initial values for FindMinimum

I have been using the FindMinimum function in Mathematica to implement nonlinear regression (for function $f(x,y)$, say). I am curious to find how the starting ...
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### Are derivatives from interpolating functions created by NDSolve using derivatives of the spline or numerics from solving DE

For example given the code: ...
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### Theory behind CountRoots

According to this page, one can compute the number of zeros of a meromorphic function over an interval in Mathematica. I am working with univariate functions of x, which are meromorphic elementary ...
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### Is K is a function? [duplicate]

Some of the capitalized single letters are functions. Starting a fresh kernel and typing in the 24 capital letters, the following letters turn black since they are special functions, ...
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### How does FindRoot decide if a solution has converged?

I am solving a 1D non-linear differential equation using the finite element method with NDSolve. From the documentation I understand that the equation is discretized and then solved with FindRoot, I ...
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### Mathematica internal source code for a numerical method

I read this (Six Reasons Why the Wolfram Language Is (Like) Open Source), which inspired me to re-investigate Mathematica's implementation of some numerical methods. I would like to see the code that ...
1 vote
108 views

### How is MatrixPower computed?

How does Mathematica compute MatrixPower[m,n]? The documentation states it is equivalent to Dot @@ ConstantArray[m, {n}], but ...
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### Why does NMinimize using NelderMead without PostProcessing always stop at the nearest decade of iterations, e.g. 100, 110, 120

Why does NMinimize using NelderMead without PostProcessing always stop at the nearest decade of iterations, e.g. 100, 110, 120... Perhaps Catch Throw can prevent this e.g., see this answer, but that ...
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### RandomReal vs Random[Real

Let's say I need random numbers with increasing precision to simulate a particular function, so I try: ...
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### My construction of additive compound matrices doesn't work sometimes; why?

Using the multiplicative compound matrix --see definition at Are compound matrices implemented in mathematica? one may define also additive compound matrices ...
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### Construction of an additive compound matrix

I want to construct an additive compound matrix which has the following form as output : ...
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1 vote
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### Can LinearOptimization (ex. LinearProgramming) support other methods (Ellipsoid method)?

Can LinearOptimization (ex. LinearProgramming) support methods other than "InteriorPoint", "Simplex", "RevisedSimplex"? Specifically, I need the Ellipsoid Method. Are ...
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1 vote
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### Spelunking yields <<kernel function>> [closed]

This is in the spirit of the old but excellent thread: What is the most convenient way to read definitions of in-memory symbols when we don't have the source files? (Spelunking tools) Using ...
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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 ...
397 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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1 vote
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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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### 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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