Questions tagged [implementation-details]

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

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1answer
40 views

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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1answer
55 views

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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0answers
59 views

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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0answers
101 views

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 ...
2
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1answer
111 views

How FunctionConvexity is implemented in Wolfram Mathematica?

I am wondering how FunctionConvexity was implemented in Wolfram Mathematica. I am trying to prove the convexity of the function $A(v)$: $$ A(v) = -\dfrac{k-1}{\...
2
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1answer
148 views

How is this asymptotic expansion of an integral calculated?

I am strongly impressed by this example from New in 13 as = AsymptoticIntegrate[ (t^10 + 3) Exp[I λ (t^5 + t + 1)], {t, -2, 2}, {λ, Infinity, 2} ] <...
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1answer
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Exactly recreating image NetEncoder output

I need to run an exported NetChain in ONNX, surprisingly the model exports and runs successfully, but there's a discrepancy in the image loading stage (the NetEncoder'ing that must be written manually)...
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0answers
72 views

How does Mathematica numerically evaluate Gaussian Hypergeometric function $_2F_1(a,b,c,z)$ where $a,b,c \in \mathbb{C}$ [closed]

Gaussian hypergeometric function $_2F_1(a,b,c,z)$ usually takes $a,b,c \in \mathbb{R}$ and $z \in \mathbb{C}$. But using Barnes integral representation, one can analytically continue the $_2F_1(a,b,c,...
4
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1answer
50 views

`NetNestOperator` with custom input / output ports

I'd like to use NetNestOperator on a NetGraph that has custom input / output port names, such as ...
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0answers
39 views

How is the Riemann-Siegel Z function evaluated in Mathematica?

How is the Riemann-Siegel Z function evaluated in Mathematica? Is it calculated using the first so many terms of its power series or by other means?
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2answers
345 views

How does mathematica numerically evaluate the Meijer G-function?

The Meijer G-function is defined as a contour integral in the complex plane. Mathematica is able to numerically evaluate such a function quickly and accurately. How does she do that?
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0answers
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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
128 views

How does Plot choose the points in a figure?

Taking a simple example, ...
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0answers
113 views

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
1k views

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
67 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
268 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 ...
6
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1answer
110 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 ...
9
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1answer
140 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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0answers
91 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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0answers
68 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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0answers
100 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
192 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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0answers
92 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 ...
2
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0answers
42 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 ...
8
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3answers
367 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
300 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
46 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
91 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
125 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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0answers
72 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
201 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
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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: ...
14
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2answers
381 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
95 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
86 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
88 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
140 views

Algorithms used for DelaunayMesh

Is it possible to find what algorithms are used for Delanunay triangulations?
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0answers
88 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 ...
5
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0answers
63 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) ...
19
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1answer
161 views

Why does setting SyntaxInformation add a definition to DefaultValues

Before setting any definitions to the symbol f, the DefaultValues of f is empty: ...
2
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1answer
111 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
174 views

Conflict with hidden names

The following code hangs Mathematica 12.0.0: ...
2
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1answer
221 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
437 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
85 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
252 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
231 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: ...
27
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1answer
401 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 ...
12
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2answers
886 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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