What is the best open-source equivalent for Mathematica? My requirements are:
(most important) Must be a real computer algebra system (CAS). Notably, I don't want Matlab clones -- I want something that can, at least, symbolically differentiate and integrate.
Must be programmable. A functional-programming view of the world, like Math...

Does anybody know if there is a built-in function in Mathematica for getting the lhs of downvalue rules (without any holding)? I know how to write the code to do it, but it seems basic enough for a built-in
For example:
a[1]=2;
a[2]=3;
BuiltInIDoNotKnowOf[a] returns {1,2}
...

If you have Mathematica code in foo.m, Mathematica can be invoked with -noprompt
and with -initfile foo.m
(or -run "<<foo.m")
and the command line arguments are available in $CommandLine (with extra junk in there) but is there a way to just have some mathematica code like
#!/usr/bin/env MathKernel
x = 2+2;
Print[x];
Print["There were ",...

I'd like something like this:
ForEach[i_, {1,2,3},
Print[i]
]
Or, more generally, to destructure arbitrary stuff in the list you're looping over, like:
ForEach[{i_, j_}, {{1,10}, {2,20}, {3,30}},
Print[i*j]
]
(Meta-question: is that a good way to call a ForEach loop, with the first argument a pattern like that?)
ADDED: Some a...

Consider the following dialog with the command-line interface to the kernel:
$ math
Mathematica 6.0 for Linux x86 (32-bit)
In[1]:= p = Plot[x^2, {x,-1,1}]
Out[1]= -Graphics-
In[2]:= Export["foo.png", p]
Out[2]= foo.png
That works fine on a machine with $Version = 6.0 for Linux x86 (32-bit) (June 2, 2008) but fails on a machine with ...

F# has a bunch of standard sequence operators I have come to know and love from my experience with Mathematica. F# is getting lots of my attention now, and when it is in general release, I intend to use it frequently.
Right now, since F# isn't yet in general release, I can't really use it in production code. LINQ implements some of th...

What is the equation of a helix parametrized by arc length (i.e. a function of arc length) between any two points in space? Is there any function for this ? How do i implement the same using matlab or mathematica ?
...

I am going to start learning Abstract Algebra- Groups, Rings,etc. I am interested to know any programming language, if at all which can help me learn/try the concepts I learn in theory.
EDIT: I am not really looking at implementing what I learn. I am interested to know any language which already supports them.
Thank You.
...

I have something like the following in a string:
blah blah
BEGINIGNORE
this stuff should get stripped out
ENDIGNORE
more stuff here
I would like to do this (perl syntax): s/BEGINIGNORE.*ENDIGNORE//s -- namely, strip out everything between BEGINIGNORE and ENDIGNORE, inclusive.
You would think the following would do that in Mathema...

In Mathematica
a = FactorInteger[44420069694]
assigns
{{2, 1}, {3, 1}, {7, 1}, {11, 2}, {13, 1}, {23, 2}, {31, 1}, {41, 1}}
to a. Now instead of the factors with their exponents I would like each of those lists expanded. The above factorization would then become
{2, 3, 7, 11, 11, 13, 23, 23, 31, 41}
I wrote the following functio...

I use Mathematica with JLink for a research project, which involves a lot of computation. Mathematica is used as a graphical frontend for entering the parameters, and later plotting the results. The actual algorithms are located in Java Classes, which are called via JLink.
The "link" is an instance named evalFrontend. On the press of a ...

I need to set an environment variable from a Mathematica notebook.
Environment["VARIABLE"]
gives the value of the variable. But is it possible to set a variable, too?
...

I have a 15-day trial of Mathematica and need to evaluate it, and see if it can be used to help created algorithms for some games we are working on.
Are there any good resources that will teach me some basics and let me explore the application.
...

Hi All
I am trying to use GraphPlot function to build a Graph, where each node is an image. I wanted to display the image as my vertex. Does anybody know how to do this?
I tried something like this:
GraphPlot[ Map[If[# > 2.0 , 0, 1] &,
imgDistT, {2}],
VertexRenderingFunction -> (Inset[imgs[[#2]], #1, Center] &) ]
But this does ...

Hi all
does anybody here do computer vision work on Mathematica? I would like to know what external libraries are available for doing that. The built in image processing functions are not enough. I am looking for things like SURF, stereo, camera caliberation, multi-view geometry etc..
How difficult would it be to wrap opencv for use in...

When generating a png image file in Mathematica on a linux box running X, there's no problem. Doing the same on a linux machine without X but instead Xvfb the png generates fine but the colors are all screwed up. We tried changing the pixel depth from the default of 8, to no avail. Any other tweaks that might make Xvfb mimic normal X ...

I am doing a computing-intensive benchmark using Mathematica and its J/Link Java interface.
The benchmark grinds to a halt if a memory footprint of about 320 MB is reached, since this seems to be the limit and the garbage collector needs more and more time and will eventually fail.
The Mathematica function ReinstallJava takes the argum...

Hello,
I have a 3D math problem which I just can't seem to solve.
I have data of 3 points. The data is a (2D) coordinate on a plane, floating somewhere in 3D space. I also know the (2D) coordinate of the projection. That results in the following array of data:
[[[x1,y1], [px1,py1],
[[x2,y2], [px2,py2],
[[x3,y3], [px3,py3]]
Where t...

Can anybody recommend a pattern for unit-testing code within a Mathematica notebook? I am familiar with the unit testing infrastructure in Wolfram Workbench, but I would also like to have a good approach that can be used within simple notebooks in the regular GUI.
I've been using a simple "Expect" function as demonstrated below. But t...

Mathematica's notebook front end has provided a hugely productive next-generation development environment for over 13 years, particularly suited to technical computing but also more widely applicable.
What other languages have IDEs that allow code to be typeset and have inline graphics?
...