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

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5
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1answer
248 views

Can we know the background code associated with basic mathematica functions

I wanted to know how computers calculate basic functions like Sqrt so first I checked how humans do it I found that they use something called "Newton's method" that ...
5
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1answer
80 views

Actual bins used for Pearson Chi Square Test

PearsonChiSquareTest[data, dist] computes bins for data as a step towards calculating the test statistic. For continuous ...
5
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0answers
93 views

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 ...
5
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0answers
201 views

Citation of the algorithms used in FindGraphCommunities

For my research work I need to put a comparison of different community detection algorithms. Instead of implementing all those algorithms once again, I would like to use the methods already provided ...
5
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0answers
303 views

How to determine BLAS/LAPACK implementation used internally for numerical matrix operations?

Is there a command which reveals which implementation of BLAS and LAPACK are used in Mathematica's matrix operations such as Eigensystem? I asked a related question ...
4
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2answers
329 views

Implementation of builtin function Fold

In the documentation for fold, it says Fold[f,x,list] gives the last element of FoldList[f,x,list]. But this is surely not the way it is implemented, right? ...
4
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1answer
135 views

What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
4
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2answers
464 views

Any ideas on how GeneralMiniMaxApproximation is implemented?

GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
4
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1answer
345 views

Use of Strassen's algorithm

Strassen's algorithm is an algorithm for matrix multiplication that is asymptotically faster than the naive one. In practice, the matrices involved have to be quite large before Strassen's algorithm ...
4
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1answer
135 views

The default ColorFunction of DensityPlot before v10?

The default ColorFunction of Plot, Plot3D before v10 is respectively mentioned here and ...
4
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1answer
419 views

How does Mathematica calculate the nth prime?

When I enter Prime[2000000000000], the two-trillionth prime, Mathematica gives 61427839512211 for the answer after several ...
4
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1answer
156 views

What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I ...
4
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1answer
1k views

How does Mathematica estimate error on fit parameters?

When performing a fit using NonlinearModelFit (or any of Mathematica fitting functions, but I am particularly interested in nonlinear models), Mathematica makes a ...
4
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0answers
126 views

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 ...
4
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0answers
88 views

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 ...
3
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2answers
226 views

What does MinimalPolynomial do?

suppose $x^5-x-1=0$, $y^7-y-1=0$ and $z=x+y$. I want to find a minimal polynomial expression of $z$, such that $p(z)=0$, and the code can be written like this: ...
3
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3answers
143 views

Pick bug? level 0 matching

A previous discussion of this issue (Is there a bug in Pick?) accepted that matching at level 0 is not a bug in Pick. Was that correct? I am not yet persuaded. ...
3
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2answers
209 views

How does RootOfUnityQ work?

How does Mathematica's RootOfUnityQ function work? That is, how does Mathematica know if a number is a root of unity? Example: Let $x = \frac{1-i \sqrt{2+\sqrt{5}}}{1+i \sqrt{2+\sqrt{5}}}$. Then ...
3
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1answer
208 views

What method does `NIntegrate` uses by default?

There is a variety of algorithm for performing numerical integration (See wiki). What method does NIntegrate uses by default? I looked on the documentation page and I saw that the function ...
3
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1answer
273 views

Daubechies scaling function

In Mathematica in wavelet package with the following codes Phi[x_, j_, k_] := 2^(j/2) WaveletPhi[DaubechiesWavelet[3], 2^(j) x - k] Mathematica computes ...
3
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1answer
155 views

Root finding: zeroes of Mathieu function

I am finding the roots of the Mathieu sine function, and find Mathematica and Maple do not agree on the solutions. For example, consider the solutions of ...
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0answers
49 views

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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0answers
160 views

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 ...
2
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1answer
331 views

How does FindShortestTour work?

How are FindShortestTour and the algorithms therewithin implemented internally? Also: Can I access some form of incremental, in-progress result during evaluation? ...
2
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1answer
154 views

Implementation of Decompose

I'm curious as to how Decompose works so I decided to use Trace with the option ...
2
votes
2answers
120 views

Derivative of Vectoral NDSolve Interpolated Function / Rule Solutions,/., and Vector NDSolve [duplicate]

I need to find the instantaneous phase and instantaneous frequency for a rotating system. I am having difficulty making the math work with interpolating functions. First, here is a problem without ...
2
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1answer
103 views

Anyone knows the algorithm used by NullSpace function?

NullSpace function gives a list of vectors that forms a basis for the null space of the input matrix. When the rank of the input argument matrix $M_{m\times n}$ is ...
2
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1answer
356 views

Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
2
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0answers
49 views

The idea behind Stiffness switching method with NDsolve [closed]

Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?
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0answers
80 views

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 ...
2
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0answers
52 views

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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0answers
58 views

Can BreadthFirstScan be modified?

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 ...
2
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0answers
84 views

What are the limits of the Prime-functions? [duplicate]

Will Prime and PrimePi test up to 3 * 10^12? Where can I find the limits for these funtions? ...
2
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0answers
147 views

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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2answers
95 views

Does FindFit use symbolic differentiation?

Does FindFit use symbolic differentiation when optimizing by least squares a non-linear function?
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2answers
299 views

How to generate a unique file name similar as that created by CreateTemporary

CreateTemporary can generate a unique file name like ...
1
vote
1answer
462 views

Method used by FindFit

Using FindFit, Mathematica selects an optimal algorithm when Automatic is selected. I'd like to know the name of the method ...
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0answers
29 views

Apparent issue with derivative of FractionalPart

This issue came to my attention from Math.SE: http://math.stackexchange.com/questions/1015325/is-the-derivative-of-x-on-0-1-always-equal-to-1/1015342#1015342 To summarize, it appears that ...
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0answers
143 views

How to write my own interpolation method

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use ...
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0answers
36 views

Internals of Prime function [duplicate]

Does anyone knows how exactly Prime works ? For example how Prime[1000000000] is calculated ? The only information I found was ...
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0answers
1k views

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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0answers
83 views

What algorithm is Mathematica using for FirstPassageTimeDistribution[]?

What algorithm is Mathematica 9 using for FirstPassageTimeDistribution[]? Is it attempting to use PseudoInverse[] on the ...
0
votes
1answer
73 views

Mathematica Lattice Reduce Command

I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice. I'm on chapter 3, and ran into the LatticeReduce ...
0
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0answers
34 views

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 ...
0
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0answers
52 views

How to make work Plus function? [duplicate]

I have a little problem. I have k = 1.56343*10^9; r = 9.10492*10^18. And I should receive a (2*r*r-k*k)/2*r*r, it equals to ...
0
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0answers
61 views

Plot function failure, and understanding how mathematica selects recursion points for correction

I think it is best to start out by directing everyone to this link. The discussion concerns why the Plot function fails to accurately generate a simple sine wave for given parameters. The answer given ...
0
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0answers
61 views

Birch clustering in Mathematica

I want to implement birch clustering in Mathematica. MAthematica only has 4 methods of clustering, is there any implementation for Birch clustering? Birch clustering is much faster than K means ...
0
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0answers
55 views

What Algorithm Does Mathematica use to Calculate Betweenness Centrality for Unweighted Graphs?

Recently asked this question http://math.stackexchange.com/questions/888369/betweenness-centrality-how-long-does-mathematica-take on the Mathematics SE. Does anyone know, as a follow up, what ...
0
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0answers
292 views

What algorithms does NSolve use?

I've been using NSolve to find roots and now I've been wondering what underlying algorithm mathematica uses. It's probabaly similiar to ...