# Tagged Questions

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

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### Heliocentric coordinates in PlanetData

I tried to use planets' HeliocentricLongitude and I wonder if anyone has any insight on what coordinate system they use. I took vernal equinox times from http://ns1763.ca/equinox/eqindex.html and ...
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### Functionality of FindMaximumFlow

I know that the superseeded function NetworkFlow (needs Combinatorica) uses Goldberg-Tarjan's Push-Relabel-Algorithm but i cant find any information on Mathematica's built-in-function (...
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### Design considerations behind O (a.k.a. BigOh, a.k.a. Landau Order)

This works without any warnings: O[Log[x]]. This raises a warning: O[x^2]. I have a few questions around this: Why is it a ...
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### How many clusters does DominantColors return?

Is there any documentation on how it automatically chooses the number of colors - does it use X-means or some other heuristic to determine the number of clusters it automatically returns?
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### How does Plus work on machine precision Real arguments?

I thought Kahan's summation method would make a nice example for students to use to think about round-off error [W. Kahan, Pracniques: Further Remarks on Reducing Truncation Errors, Commun. ACM 8  (...
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### Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
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### Given two samples, how does LocationTest select its AutomaticTest?

How does LocationTest select its "AutomaticTest" when testing two samples? Background: A previous post poses a similar question ...
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### JewishNewYear date limitation

The documentation for the function "JewishNewYear" in the "calendar" package declares that the year argument must be between 1900 and 2100. No explanation is given for this limitation. The function ...
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### FrobeniusSolve: how does it work?

Can someone suggest any reference to read? I would like to understand how the algorithm works.
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### Where do DistributeDefinitions and ParallelNeeds put their definitions for newly-launched kernels to find

I'm sorry to keep banging on the definition distribution bell, but here is another (hopefully well-focused enough) question on that vein. If one is trying to distribute the definitions in a package ...
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### What CPU instruction set extensions does Mathematica support?

Most CPUs in desktops and laptops nowadays are backwards compatible with the x86-64 instruction sets. But newer CPUs also have additional instruction set extensions like AVX 2, FMA3, and BMI/BMI2 ...
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### What am I missing in this highly oscillatory integral?

I want to numerically integrate this equation (in python without calling Mathematica): $\int_0^\infty {\rm d}k f(k) J_v(r k) J_n(s k)$ where $f(k)$ is a non-smooth function, $J_v$ are the Bessel ...
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### How does Mathematica automatically choose which classifier method to use?

I'm interested in what heuristics are used in Classify's choice of method.
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### PlotRange->Automatic the exact function used to calculate outliers

I know that PlotRange->Automatic does the following: "the distribution of coordinate values is found, and any points sufficiently far out in the distribution ...
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### Distance Time Warp (DTW) function implementation in mathematica

The DTW (Distance time warp) is given here http://en.wikipedia.org/wiki/Dynamic_time_warping There is an implementation of DTW in R as well as MATLAB. However i am unable to find something for DTW in ...
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I would like to obtain a "slick" implementation of A*-search algorithm on Graph objects, using the built-in BreadthFirstScan (if that is possible at all). I noticed that BreadthFirstScan is static in ...
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### Algorithm used by Fit[]

Does anyone know what algorithm Mathematica's basic Fit[] function uses? Is it proprietary? I'm trying to do some pretty basic, linear, polynomial data fitting (...
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### How can I access the Criterion function of KI method in FindThreshold for a dataset?

I want to find a threshold for some data set, using Kittler-Illingworth minimum error thresholding method (KI method). To do so, I use the Mathematica built-in function ...
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### Implementation of Series function

I'm trying to evaluate the partial derivatives of some function F[x,y] at some point, i.e. ...
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### What Algorithm Does Mathematica use to Calculate Betweenness Centrality for Unweighted Graphs?

I recently asked this question on the Mathematics SE. Does anyone know, as a follow up, what algorithm Mathematica uses to calculate the betweenness centrality vector (of $N$ elements) for an ...
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### PowersRepresentations Algorithm

I'm trying to understand the mathematics behind counting the number of representations of a positive integer by $n$ distinct $k$th powers, i.e. I would really like to know how to do the Mathematica ...
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### Where can I find documentation on the methods/algorithm used in FindGraphPartition in Mathematica 10?

I am working on a graph theoretical project where it would be helpful to know the name of the algorithm used in FindGraphPartition. Question: Where can I find ...
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### Meaning of the character sequence after an Entity's name

Mathematica can interpret an entity when you type Ctrl+=, like this: Then we'll get an entity We can get the InputForm You will get a canonical name ...
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### What's the algorithm behind markov classifier in Classify function for text classification?

https://www.wolfram.com/mathematica/new-in-10/highly-automated-machine-learning/find-which-author-wrote-a-text.html The above url show the use of Classify ...
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### Algorithm for converting truth tables to Boolean functions

The function BooleanFunction is able to convert a truth table into a Boolean function. Does anyone know what is the mathematical background and/or algorithm that ...
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### How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
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### What algorithm is Mathematica using for FirstPassageTimeDistribution[]?

What algorithm is Mathematica 9 using for FirstPassageTimeDistribution[]? Is it attempting to use PseudoInverse[] on the ...
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### What is the default method used by NSolve

I have a system of 6 polynomial equations of the form aijk xi xj + bik xi = ck (k=1,2,...,6; summation convention on i & j) I am using NSolve[{eq1,eq2,...,eq6},{x1,x2,...,x6},Reals] What ...