# Tag Info

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

In version 10.1, I've built something like Spelunk into GeneralUtilities. To use it, run ...
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### Where can I get detailed information on how the Plot command works?

I can add to Mr.Wizard's answer that when InputForm is wrapped by any head like List (...
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### Why Except is so slow as compared to equivalent RegularExpression?

Using StringPatternPatternConvert we can find the regexp into which Mathematica converts the original string expression: ...
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### How was Mathematica built?

In the Mathematica book (5th edition), Stephen Wolfram writes the following (sec. 1.12.4): The Software Engineering of Mathematica Mathematica is one of the more complex software systems ever ...
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### What's behind Method -> {"EquationSimplification" -> "Residual"}

This post contains several code blocks, you can copy them easily with the help of importCode. As mentioned in the comment above, the answer is hidden in this ...
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### How was Nothing implemented?

Ok, I failed to find a duplicate so here is my comment: I don't know how Nothing is internally implemented but you can do something like this with ...
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### What's the default colormap (or color scheme) used in mathematica?

"DefaultColorFunction" /. (Method/. ChartingResolvePlotTheme[Automatic, ContourPlot]) "M10DefaultDensityGradient" ...
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### How to know the internal algorithms of functions like Predict or Classify?

If you want to have a description of the method used by a given ClassifierFunction you can do: ...

### Mathematica's morphological thinning algorithm

Prologue Some five years ago I have asked exactly this question to the Wolfram support people. Below I have taken their respective answers (one sentence for each ...
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### What algorithm do the Compress and Uncompress functions use?

It is using the zlib format followed by Base64 coding, and then preceding the resulting string with "1:". So to use it externally, you can strip the "1:", do Base64 decoding, and feed the result of ...
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### What algorithm do the Compress and Uncompress functions use?

After a bit of poking around, it looks like the binary format is pretty simple to parse. Mark Adler's answer is correct - the strings Compress[] returns are just ...
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The definition used (motivated by exterior calculus) is as follows: Given a rectangular array $a$ of depth $n$, with dimensions $\{d, ..., d\}$ (so there are $n$ $d$'s) and a list $x = \{x_1, ..., ... • 5,635 20 votes Accepted ### Why does setting SyntaxInformation add a definition to DefaultValues In my view, the Mathematica front end would have needed a complete rewrite a long time ago to be in a shape where it can compete with modern UI's. Looking at MATLAB, it's clear that you always find ... • 111k 19 votes Accepted ### What is behind experimental function: FindFormula? The Experimental function FindFormula[] at the moment is using a combination of different methods: it combines non linear regression with Markov chain Monte Carlo ... • 206 19 votes ### NDSolve uses different difference order for different spatial derivative when solving PDE Note: fix is broken since v11.3, a new question has been started aiming at upgrade it. Here's my approach for fixing the difference order. The key idea is ... • 52.5k 18 votes ### Is there a "precedence table" for the canonical Sort ordering? So I think the docs are mostly clear, if hard to visualize. Here's my version of such a table: ... • 45.5k 18 votes ### How to determine BLAS/LAPACK implementation used internally for numerical matrix operations? As indicated in the comments, machine-precision linear algebra operations in Mathematica use the Intel MKL library optimized implementation of BLAS/LAPACK. That is the case for all platforms where ... • 25.1k 17 votes Accepted ### Why is FreeQ so much faster for some specific variable names? TLDR: If you run into performance issues related to symbol names, rename your symbols such that SystemPrivate`GetContentCode returns different values for each ... • 7,666 17 votes ### What's the principle behind the new MoleculeRecognize function? Using ResourceFunction["PrintDefinitions"][MoleculeRecognize], one can determine that the source implementation is MolVec. The specific source code is: ... • 12.6k 17 votes ### How do the functions Reap and Sow actually work behind the scenes? I do not know how Sow and Reap are actually implemented, but to show you that it isn't magic, I can provide the following toy ... • 95.6k 16 votes ### What algorithms does NSolve use? In at least the univariate case, the guess of "Newton-Raphson" is not too far off. Daniel mentions the three possible methods supported by NSolve[]/... 16 votes ### How does Mathematica calculate$\sin(\pi/5)\$?

In the course of answering this question, I ran into a little bit of weirdness that doesn't square with my experience with previous versions of Mathematica. I think writing this answer is as good a ...
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### How does Mathematica solve a certain differential equation?

@Nasser's method seems to be what Mathematica does internally. The following gives hints of the steps taken, and one can see the elements of Nasser's solution. Some is left to the user to guess. The ...
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### How does Mathematica calculate the Standard error during a non linear fit?

Rather than give formulas here is how to duplicate the results (coefficient estimates and standard errors) from NonlinearModelFit. First show the example from <...
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### What stopwords list is the Wolfram language using?

A little spelunking of the code for DeleteStopwords[] yields the internally used stopword list: ...
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### Evaluated vs. unevaluated Association

Summary The confusion we observe here is largely due to ambiguous use of the symbol Association as an expression head. On the one hand, ...
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### Where can I get detailed information on how the Plot command works?

As far as I know the specific output format of Plot (and similar commands) is not documented. I believe it has changed between versions therefore any post-...
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### Show how Mathematica defines a function

This isn't necessarily how these functions are implemented, but MathematicalFunctionData gives a way to access definitions that are equivalent to the ones ...
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### How does FunctionDomain work?

Evaluate ((x - 2) (x + 1))/((x - 2) (x + 3)) and see what it gives. It automatically simplifies to (1 + x)/(3 + x). The second ...
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