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

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49
votes
5answers
2k views

What is the most convenient way to read definitions of in-memory symbols when we don't have the source files? (Spelunking tools)

Note: I put Simon's implementation on GitHub. Contributions welcome! When trying to read the definition of already defined (package or built-in) symbols using ...
24
votes
1answer
465 views

What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
12
votes
1answer
1k views

How does Mathematica integrate?

Basically, this question can be considered to be an extenstion to my other question. What I wanted to do was this integral as homework (it is indefinite BTW so no approximations using Simpson's Rule ...
70
votes
2answers
865 views

Why are numeric division and subtraction not handled better in Mathematica?

There is something that has been troubling me for a while. At least in version 7, the performance of a / b and a - b is not ...
26
votes
1answer
570 views

How are MemberQ and FreeQ so fast?

I would like to understand the implementation that allows MemberQ and FreeQ to be as fast as they are. I noticed this thanks to ...
22
votes
2answers
676 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: ...
5
votes
2answers
280 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 ...
21
votes
0answers
296 views

Why does list assignment with a packed array result in unpacked values?

This is another question on the design choices in Mathematica. I understand that without direct reply from the developers it may not be possible to give a definitive and exhaustive answer to "why" ...
18
votes
2answers
584 views

Blend code for built-in ColorData schemes

Hi I want to get a blend similar to "SunsetColors". To make those slight modifications, I would like to know the precise blend of that color scheme. My try: ...
20
votes
2answers
443 views

How to implement FittedModel like objects

In the course of making some RLink wrappers I want to have some richer containers like Mathematica does with its FittedModel ...
14
votes
2answers
432 views

Why does iterating Prime in reverse order require much more time?

Say I would like to display the $10$ greatest primes that are less than $10^5$. I could do the following: ...
26
votes
2answers
3k views

How does Interpolation really work?

I'm looking for some explanation or advice, not help in solving something. Recently I finished my program and my supervisor said "Ok, now it's time for your first paper: write a scientific text about ...
18
votes
1answer
361 views

Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
4
votes
1answer
1k views

Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
16
votes
1answer
381 views

What does “suitable for symbolic manipulation” in the documentation mean?

This question is related to this other one I posted on Stack Overflow some time ago. There, in a beautiful answer, acl (with some unhumble editing done by me) showed that the derivative of ...
14
votes
1answer
353 views

What is the real default CellEvaluationFunction?

The default CellEvaluationFunction is Identity but one can quickly see that this is handled specially as an equivalent function, ...
6
votes
1answer
478 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 ...
5
votes
2answers
246 views

Where can I get detailed information on how the Plot command works?

The command Plot[x^2, {x, -3, 3}, PlotStyle -> Arrowheads[{-.025, .025}]] /.Line -> Arrow produces this output. What I don't understand is what ...
8
votes
1answer
261 views

How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
2
votes
0answers
81 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? ...
22
votes
3answers
361 views

Efficiently appending points to a NearestFunction

I have a program which works with a list of points (in 3D, but it could be in 1D as well, it won't make a difference). Within a loop, it keeps adding new points to the list. To calculate the ...
26
votes
0answers
609 views

What calendar is Mathematica using for dates in the distant past?

It appears that Mathematica treats all dates as proleptic Gregorian dates by default, a hypothesis that can be easily tested by using AbsoluteTime to compute the ...
7
votes
1answer
658 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 ...
7
votes
2answers
477 views

How does Mathematica determine that an evaluation should be terminated?

How exactly does Mathematica determine that evaluation of particular expression should be finished and the result should be returned? Here are some examples of unclear behavior which have arisen, ...
6
votes
2answers
107 views

Algorithm in RandomChoice[{w1,w2,…}->{e1,e2,…},n]?

I wonder if someone happens to know the actual algorithm implemented in the particular overload of RandomChoice that handles explicitly presented discrete ...
9
votes
1answer
156 views

Algorithm used by IsomorphicGraphQ

I'd like to know which algorithm is used to test if two graphs are isomorphic?
5
votes
1answer
233 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 ...
4
votes
0answers
100 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 ...
9
votes
1answer
144 views

What is the default ColorFunction for Image3D?

What is the default ColorFunction for Image3D? I find it a bit confusing that the most intense colour is not shown where the ...