For questions regarding the underlying implementation of built-in functions.
2
votes
1answer
64 views
What is the underlying algorithm for GroupElementToWord?
What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
1
vote
0answers
58 views
What algorithm is Mathematica using for FirstPassageTimeDistribution[]?
What algorithm is Mathematica 9 using for FirstPassageTimeDistribution[]? Is it attempting to use PseudoInverse[] on the ...
1
vote
1answer
56 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? ...
6
votes
0answers
57 views
Apart may use Padé method: what's that?
How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
1
vote
0answers
61 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 ...
5
votes
0answers
90 views
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 ...
1
vote
0answers
167 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 ...
19
votes
3answers
272 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 ...
6
votes
1answer
162 views
What algorithm is Mathematica 9 using for “SpectralEmbedding” of graphs?
When I specify that a graph should be realized using the "SpectralEmbedding" procedure, what paper / algorithm for spectral embedding is this based on? I was unable to find any documentation for ...
2
votes
1answer
117 views
Implementation of Decompose
I'm curious as to how Decompose works so I decided to use Trace with the option ...
2
votes
1answer
77 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 ...
5
votes
3answers
142 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.
11
votes
1answer
142 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 ...
13
votes
2answers
288 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:
...
4
votes
2answers
290 views
Any ideas on how GeneralMiniMaxApproximation is implemented?
GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
21
votes
0answers
383 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 ...
20
votes
2answers
301 views
How to retrieve the parameters calculated and used by ImageAdjust?
When ImageAdjust is called with an image, i.e. with one parameter, it returns an automatically adjusted Image. I would like to ...
8
votes
1answer
119 views
Algorithm used by IsomorphicGraphQ
I'd like to know which algorithm is used to test if two graphs are isomorphic?
1
vote
0answers
85 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 ...
6
votes
0answers
250 views
Does Mathematica use the Elliptic Curve Method (ECM) in FactorInteger[]?
I'm not a mathematician, and I'm not even going to pretend that I understand anything of the ECM. But I know it can be a fast method for factorization.
I benchmarked the factorization of ...
3
votes
1answer
104 views
Identifying `Indeterminate` elements [closed]
I want to identify if a variable, which is the result of a calculation, is Indeterminate. I was trying to do this using If[]. ...
5
votes
1answer
77 views
What is the simplest way to determine which call to a superfunction has generated a Message?
I have a complicated function which contains many calls to NIntegrate, NSolve, FindRoot and ...
5
votes
1answer
179 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 ...
10
votes
1answer
212 views
Why doesn't Mathematica pack Boolean arrays?
I've been wondering about this for a while now, so I'm going to ask. This is a question about the design of Mathematica, which perhaps cannot be directly answered by anyone but the designers, however ...
4
votes
2answers
245 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? ...
3
votes
2answers
185 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
...
2
votes
2answers
160 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:
...
16
votes
1answer
275 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 ...
11
votes
1answer
661 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 ...
5
votes
1answer
185 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 ...
17
votes
1answer
2k 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 ...
26
votes
3answers
791 views
What is the most convenient way to read definitions of in-memory symbols when we don't have the source files?
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 ...
21
votes
1answer
339 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 ...
7
votes
1answer
222 views
How to check for Mathematica’s definition of XY?
The question is: Can I ask the Mathematica kernel directly what it takes as the definition of the built-in symbol XY? After all this has to be in the kernel. And if the documentation is not giving any ...
