What is in your Mathematica tool bag? [closed]

Question

We all know that Mathematica is great, but it also often lacks critical functionality. What kind of external packages / tools / resources do you use with Mathematica?

I'll edit (and invite anyone else to do so too) this main post to include resources which are focused on general applicability in scientific research and which as many people as possible will find useful. Feel free to contribute anything, even small code snippets (as I did below for a timing routine).

Also, undocumented and useful features in Mathematica 7 and beyond you found yourself, or dug up from some paper/site are most welcome.

Please include a short description or comment on why something is great or what utility it provides. If you link to books on Amazon with affiliate links please mention it, e.g., by putting your name after the link.

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Packages:

1. LevelScheme is a package that greatly expands Mathematica's capability to produce good looking plots. I use it if not for anything else then for the much, much improved control over frame/axes ticks. Its newest version is called SciDraw, and it will be released sometime this year.
2. David Park's Presentation Package (US$50 - no charge for updates)
3. Jeremy Michelson's grassmannOps package provides resources for doing algebra and calculus with Grassmann variables and operators that have non trivial commutation relations.
4. John Brown's GrassmannAlgebra package and book for working with Grassmann and Clifford algebras.
5. RISC (Research Institute for Symbolic Computation) has a variety of packages for Mathematica (and other languages) available for download. In particular, there is Theorema for automated theorem proving, and the multitude of packages for symbolic summation, difference equations, etc. at the Algorithmic Combinatorics group's software page.

Tools:

1. MASH is Daniel Reeves's excellent Perl script essentially providing scripting support for Mathematica v7. (Now built in as of Mathematica 8 with the -script option.)
2. An alternate Mathematica shell with a GNU readline input (using python, *nix only)
3. ColourMaths package allows you to visually select parts of an expression and manipulate them. http://www.dbaileyconsultancy.co.uk/colour_maths/colour_maths.html

Resources:

1. Wolfram's own repository MathSource has a lot of useful if narrow notebooks for various applications. Also check out the other sections such as

   • Current Documentation,
   • Courseware for lectures,
   • and Demos for, well, demos.

2. The Mathematica Wikibook.

Books:

1. Mathematica programming: an advanced introduction by Leonid Shifrin (web, pdf) is a must read if you want to do anything more than For loops in Mathematica. We have the pleasure of having Leonid himself answering questions here.
2. Quantum Methods with Mathematica by James F. Feagin (amazon)
3. The Mathematica Book by Stephen Wolfram (amazon) (web)
4. Schaum's Outline (amazon)
5. Mathematica in Action by Stan Wagon (amazon) - 600 pages of neat examples and goes up to Mathematica version 7. Visualization techniques are especially good, you can see some of them on the author's Demonstrations Page.
6. Mathematica Programming Fundamentals by Richard Gaylord (pdf) - A good concise introduction to most of what you need to know about Mathematica programming.
7. Mathematica Cookbook by Sal Mangano published by O'Reilly 2010 832 pages. - Written in the well known O'Reilly Cookbook style: Problem - Solution. For intermediates.
8. Differential Equations with Mathematica, 3rd Ed. Elsevier 2004 Amsterdam by Martha L. Abell, James P. Braselton - 893 pages For beginners, learn solving DEs and Mathematica at the same time.

Undocumented (or scarcely documented) features:

7. How to customize Mathematica keyboard shortcuts. See this question.
8. How to inspect patterns and functions used by Mathematica's own functions. See this answer
9. How to achieve consistent size for GraphPlots in Mathematica? See this question.
10. How to produce documents and presentations with Mathematica. See this question.

Answer 1

It is possible to run MathKernel in batch mode by using undocumented command-line options -batchinput and -batchoutput:

math -batchinput -batchoutput < input.m > outputfile.txt

(where input.m is the batch input file ending with the newline character, outputfile.txt is the file to which the output will be redirected).

In Mathematica v.>=6 the MathKernel has undocumented command-line option:

-noicon

which controls whether the MathKernel will have visible icon on the Taskbar (at least under Windows).

The FrontEnd (at least from v.5) has undocumented command-line option

-b

which disables the splash-screen and allows to run the Mathematica FrontEnd much faster

and option

-directlaunch

which disables the mechanism which launches the most recent Mathematica version installed instead of launching the version associated with .nb files in the system registry.

Another way to do this probably is:

Instead of launching the Mathematica.exe binary in the installation directory, launch the Mathematica.exe binary in SystemFiles\FrontEnd\Binaries\Windows. The former is a simple launcher program which tries its hardest to redirect requests for opening notebooks to running copies of the user interface. The latter is the user interface binary itself.

It is handy to combine the last command line option with setting global FrontEnd option VersionedPreferences->True which disables sharing of preferences between different Mathematica versions installed:

SetOptions[$FrontEnd, VersionedPreferences -> True]

(The above should be evaluated in the most recent Mathematica version installed.)

In Mathematica 8 this is controlled in the Preferences dialog, in the System pane, under the setting "Create and maintain version specific front end preferences".

It is possible to get incomplete list of command-line options of the FrontEnd by using undocumented key -h (the code for Windows):

SetDirectory[$InstallationDirectory <> 
   "\\SystemFiles\\FrontEnd\\Binaries\\Windows\\"];
Import["!Mathematica -h", "Text"]

gives:

Usage:  Mathematica [options] [files]
Valid options:
    -h (--help):  prints help message
    -cleanStart (--cleanStart):  removes existing preferences upon startup
    -clean (--clean):  removes existing preferences upon startup
    -nogui (--nogui):  starts in a mode which is initially hidden
    -server (--server):  starts in a mode which disables user interaction
    -activate (--activate):  makes application frontmost upon startup
    -topDirectory (--topDirectory):  specifies the directory to search for resources and initialization files
    -preferencesDirectory (--preferencesDirectory):  specifies the directory to search for user AddOns and preference files
    -password (--password):  specifies the password contents
    -pwfile (--pwfile):  specifies the path for the password file
    -pwpath (--pwpath):  specifies the directory to search for the password file
    -b (--b):  launches without the splash screen
    -min (--min):  launches as minimized

Other options include:

-directLaunch:  force this FE to start
-32:  force the 32-bit FE to start
-matchingkernel:  sets the frontend to use the kernel of matching bitness
-Embedding:  specifies that this instance is being used to host content out of process

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Are there other potentially useful command-line options of the MathKernel and the FrontEnd? Please share if you know.

Related question.

Answer 2

I was just looking through one of my packages for inclusion in this, and found some messages that I defined that work wonders: Debug::<some name>. By default, they are turned off, so don't produce much overhead. But, I can litter my code with them, and turn them on if I need to figure out exactly how a bit of code is behaving.