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

learn more… | top users | synonyms

17
votes
1answer
2k views

How was Mathematica built?

I've been wondering this for a while now: How was Mathematica built? Is it written in Haskell? C++? I'd love to get a taste of the wizardry behind this incredible software.
2
votes
1answer
77 views

Is there a method to look inside at the internal code of Built-In functions? [duplicate]

How can I look at the code of built-in functions? Is there something like this: LookInsideFunction[SubsetQ] RETURNS ...
17
votes
2answers
339 views

What algorithm do the Compress and Uncompress functions use?

Compress and Uncompress are used internally by Mathematica to compress things like 3D data in notebook files - data that I'd like to read independently. Does anyone have any idea if the compression ...
5
votes
0answers
72 views

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  (...
5
votes
2answers
172 views

Why this upvalue doesn't escape from Sum?

Probably a hard question, but I decide to cry out loud :). This is actually another problem I encountered when answering this question. Consider the following transform rule stored as an upvalue: <...
5
votes
1answer
172 views

BoxWhiskerChart Notched: how is the notch calculated?

I am aware of one convention for the uncertainty in a median: it is 1.58 * IQR / Sqrt[n], where IQR is the inter-quartile range and n is the number of data points. This was proposed by McGill, Tukey, ...
6
votes
0answers
75 views

What is the underlying algorithm to simplify sums of reciprocals of polynomials?

Flipping through Wolfram's blog entry on Leibniz, W noted Huygens' interview test for the young Leibniz, namely to determine: $$ \sum_{n\ge2} \frac{1}{{n \choose 2}} $$ It's one thing to do this by ...
16
votes
1answer
2k views

What are the algorithm details of FindRoot?

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

How to show steps of Integrate[Exp[-(I*(s*t))]/(Sqrt[2*Pi]*Sqrt[s]), {s, 0, Infinity}]? [duplicate]

I am trying to use Wolfram Alpha in Mathematica 10.2 to show me the steps for calculating the integral in the title, i.e I have written the following command: show steps of ...
3
votes
1answer
113 views

How does Matematica compute the CDF of the binomial distribution?

I want to know, how Mathematica actually implements the cumulative distribution function of the binomial distribution. Which algorithm does Mathematica use to compute ...
6
votes
1answer
321 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 ...
9
votes
2answers
177 views

Does LinearSolve know that I gave it a Sparse lower triangular matrix?

Let $\mathbf L$ be a nonsingular numeric (non-symbolic) large, lower triangular sparse matrix. Let $\mathbf b$ be an appropriately sized vector. I want to solve $\mathbf L\mathbf x=\mathbf b$. ...
8
votes
1answer
155 views

What values of $\delta$ and $\eta$ are being used in LatticeReduce?

The Lenstra–Lenstra–Lovász algorithm has a parameter $\delta$ with $1/4 < \delta < 1$, where roughly speaking the closer $\delta$ is to 1 the longer it takes, but the better basis reduction you ...
12
votes
1answer
715 views

What type of solver does Mathematica use in LinearSolve

I have a question regarding linear equation solvers. For a specific 9-diagonal matrix, every method I tried in C++ (Gaus, GCC, BICGTAB) didn't work (even though they worked for other matrices). But in ...
6
votes
2answers
566 views

Any ideas on how GeneralMiniMaxApproximation is implemented?

GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
6
votes
1answer
249 views

Default algorithm in NonlinearModelFit

Does anyone know the default algorithm used in NonlinearModelFit? The documentation gives several possible algorithms, but I can't figure out what it uses if you do not specify the algorithm. Thanks.
21
votes
1answer
756 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 ...
1
vote
0answers
97 views

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 ...
3
votes
2answers
393 views

How does Accumulate work?

Accumulate can be used to compute the partial sums of a list. The partial sums can also be computed using a For loop but this ...
8
votes
1answer
964 views

The difference between “SymbolicProcessing” -> 0 and restricting the function definition to numeric values only

The Documentation tells us that there are two ways to disable symbolic processing of the integrand by the NIntegrate function when it is known that it just slows ...
2
votes
0answers
56 views

SetSystemOptions is obsolete? What is next? [closed]

When running the following code on Mathematica 10.2 SetSystemOptions[ "CompileOptions" -> "CompileReportExternal" -> True]; I received the message: ...
1
vote
1answer
122 views

What methods does Maximize use like $\mathtt{Maximize}\left[\left\{3 x^2+2 \sqrt{2} x y,x^4+y^4=1\right\},\{x,y\}\right]$

I used Maximize for the maximum value of $3 x^2+2 \sqrt{2} x y$ when $x^4+y^4=1$ , $x>0,y>0$. What methods does Maximize ...
9
votes
1answer
155 views

Apart may use Padé method: what's that?

How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
7
votes
0answers
151 views

How does Mathematica resolve symbolic systems of inequalities? [closed]

Before getting into my question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A major part of the ...
0
votes
1answer
151 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 ...
9
votes
1answer
269 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 suppose)...
1
vote
0answers
105 views

How to find matrix exponential using RootSum? [duplicate]

From what I've been able to deduce, Mathematica uses a root sum scheme to determine the exponential of a matrix. Can someone please explain to me the theory behind this? I've searched, but have had no ...
1
vote
1answer
700 views

FindMinimum [] methods [closed]

Which algorithm is used when we do not use the option Method of FindMinimum[] function. FindMinimum[f,{x,x0}]
10
votes
2answers
499 views

How to interpret the FullForm of a SparseArray?

SparseArrays are atomic objects, but they do have a FullForm which reveals information about them. What is the meaning of the ...
6
votes
2answers
197 views

How does Mathematica calculate LaguerreL

About the function LaguerreL[n,a,x], the helping documents in Mathematica only say that this function satisfies equation $xy^{\prime\prime}+(a+1-x)y^\prime+ny=0$. ...
6
votes
0answers
72 views

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 (...
2
votes
0answers
81 views

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 ...
3
votes
0answers
92 views

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 ...
5
votes
1answer
176 views

References on functions FindGraphPartition and FindGraphCommunties

Does somebody have some interesting references on the FindGraphPartition and FindGraphCommunties[.., Method -> "Spectral"] ...
5
votes
2answers
1k views
9
votes
3answers
726 views

The default bandwidth of the SmoothKernelDistribution function

I am researching the Silverman rule of thumb for bandwidth selection. Below is a sample of my code, from which it seems that BW=63 is close to the default parameter given by Mathematica (2 images are ...
2
votes
1answer
52 views

Documentation for the Bounded option of SmoothKernelDistribution

I have found the Bounded option useful in the SmoothKernelDistribution function, but I can't find any documentation for exactly ...
10
votes
1answer
335 views

How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
29
votes
2answers
1k views

How does Plot work?

I considered the following function: sin[x_] := Module[{}, Print["x=", x]; Sin[x] ] in Mathematica. Next, I tried to plot it using: ...
4
votes
1answer
617 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 ...
3
votes
1answer
812 views

Specific Mathematica algorithms, for example LU Decomposition

Where I can find detailed information on algorithms used by Mathematica, especially for numerical methods. The Manual doesn't seem to iclude specifics in most cases. For example I get a different LU ...
12
votes
1answer
606 views

What function generates random numbers in a compiled function?

I am writing a simulation for 2D random walk. I wrote several version of code, and found that the speed is like this (fastest to slowest): C++, Mathematica compiled procedural code, Mathematica ...
9
votes
1answer
532 views

How to know the internal algorithms of functions like Predict or Classify?

The document centre seems only explain how to use these functions, but just in an very brief way. I know Mathmatica is not open source, so we can not expect to see the code of the function, but are ...
6
votes
1answer
370 views

Algorithms behind implemented Mathematica functions [duplicate]

When I use Mathematica for analysis and I write a publication, readers often ask me: "What is the algorithm behind your calculation?". I answer that I did it with Mathematica and if they are ...
43
votes
3answers
3k views

How to find out which method Mathematica selected?

There are commands like NonlinearModelFit[] or NDSolve[] that have the option Method it ...
4
votes
1answer
2k 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 ...
10
votes
1answer
1k views

How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
5
votes
0answers
176 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 ...
4
votes
1answer
146 views

What is the formula Mathematica uses for ZetaZero?

What is the formula/algorithm Mathematica uses for the ZetaZero command?
5
votes
3answers
298 views

How could I implement the equivalent of NextPrime

I would like to know what an implementation of the function NextPrime would look like if it were implemented in Mathematica's core language.