Mathics - A free, light-weight alternative to Mathematica with support for Sage
mathics.org
mathics.org
I don't know, but this is what I've always assumed.
Sum[x^2,{x,1,y}]-y*(y+1)*(2*y+1)/6
$ math
Mathematica 8.0 for Mac OS X x86 (64-bit)
Copyright 1988-2010 Wolfram Research, Inc.
In[1]:= Sum[x^2,{x,1,y}]-y*(y+1)*(2*y+1)/6
Out[1]= 0
Sum::iterb: Iterator does not have appropriate bounds.
Sum::iterb: Iterator does not have appropriate bounds.For comparison, similar software companies include MathWorks, the publishers of Matlab, with 2,400 employees and SAS Institute with 12,000 employees.
Totally made up numbers, but any chance I'm within a factor of 2? Posted only so somebody who knows what they're talking about can ridicule me with actually realistic numbers.
Mathematica development is split into two main groups. The Math Kernel group has about 20-30 engineers, and the FE group is around 10-15. There's a handfull of developers floating around that work on mathlink (a communication lib that allows external apps to hook into the math kernel).
Overall, they're actually a fairly efficient company. I can't speak to the current state of their finances, but I do know that about ten years ago (just after Methematica 5) they were running at about $24M gross anual revenue for the U.S, about $30M for asia, and $12M for U.K.
Because mathematica is actually really a pretty great math program.
The vast majority of students in my program are non-programmers. The only 'programming language' they know is mathematica which I think is a real shame.
Worse than that is that most of them have developed a dependence on Mathematica; without it they are severely limited in what they can do. We are provided with free copies (student version), but once we graduate will have to pay the full price if we want to continue using it.
I guess I just don't like having my abilities to solve problems tied to an expensive, closed source program. I do admit, it is very powerful.
Mathematica is a real functional programming language. It's a lisp with CamelCase builtins and consistent naming. And that's without any of its math goodness. It has superb documentation and a huge standard library. If you master it, you can master any lisp with a simple translator. matlab is a toy by comparison.
Yes, it has lambdas and first-class functions, but that's it. What about closures, for example? Therefore one would better not call Mathematica "a real functional programming language".
BTW, rule-based paradigm and pattern matching is a standard feature of languages from Lisp family, e.g. Scheme. From that point of view Mathematica is not something unique.
Mathematica is a term-rewriting system. This is a fundamentally different model of computation from the lambda calculus.
There are many practical consequences of this, in terms of the design of individual language constructs, and in how the language is used generally.
That's interesting. Can you say what some of these consequences are?
If it's about programming and math, Python really plays its strengths: Clean syntax, functional programming features, numpy, sympy, linalg, etc.
As author(s) of Mathics will surely discover very soon, the devil is in details. There are lots of corner cases and improvement opportunities that takes many man-years to implement. It may seem easy to get 50% of functionality quickly; getting the other half is much trickier.
This is not an issue if you use that software for dicovering stuff. But it is a huge problem for e.g. mathematical proofs, or statistical analysis in other fields.
Note that I'm not saying that proprietary software has more bugs. But it's a problem if your result depends on using a black-box whose creators hide their implementation from you. Also, even if your may read their code, this is worthless unless you are allowed to compile your own version from that.
Also note that the same issue exists with hardware, but the question whether your processor adds and multiplies correctly is on a totally different level than whether complex algorithms have been implemented correctly.
In reality, they make experiments more repeatable, not less. The real offender is the in-house, proprietary software developed by individual research groups. It is almost never open sourced. And it is far more likely to be riddled with bugs.
Computer experiments are just that: experiments. Any real researcher employs multiple methods to confirm their results.
No, but I will celebrate a decent open source alternative, which is what the root was probably suggesting as well. Mathematica is great as an entry software - much like MS Word for word processing. But having LibreOffice is good.
I just don't think the reproducibility of experiments is a valid argument against commercial scientific software.
It's an age-old purist argument. In the meantime, people have been getting stuff done. And without those tools, the "huge problem" would be even huge-er.
The real problem isn't reproducibility, it is extensibility. The development agenda isn't under your control. So if you get to the edge of a field, you might find you hit a wall.
I think its both. Extensibility is obviously an issue. But so is extensibility, I will give two reasons for it:
1. Easy reproducibility is necessary for extensibility. Firstly, academia is not very good at publishing their tools or their codebases. We have given so much weight to the concept behind the implementations and not the implementations themselves, that most people skip publishing implementations. What it means is that the next research group now has to start from scratch in implementing the concepts before they can think of extending the work. Reproducibility is not only to verify previously reported results, but also to create a starting point for further work. Secondly, given that the tools that the researcher is using is proprietary, the trend is to make it closed source. It may be because the tool is not ubiquitous and hence the researcher sees no point in distributing his/her implementations - or because he had not followed any guidelines (or in case of Matlab and Mathematica - they didn't exist/were-not-popular). He might not be sure about his implementations, and hence cannot publish them.
2. Reproducibility has always been the base for science. I don't need to trust the work a random researcher that I don't personally know. I can just verify his/her findings myself. The requirement of commercial software creates a huge monetary barrier in this. It is wasteful of me to buy a licence for a simple verification that I am not planning to extend. Given that non-academic licenses of most of these softwares are insanely expensive, it makes this verification to be confined to researchers from big research groups in large companies.
Not being plain text is usually my biggest gripe with proprietary software, they don't cooperate with source control systems and are completely useless without the software.
I'm not sure what they are using in undergraduate courses, but I think the toolchain by Wolfram has really advanced the way scientists work. It's far from perfect, but it is an amazing tool.
One of Mathematica's authors offers an unexpected non-solution to that:
http://www.reddit.com/r/programming/comments/7gue5/the_incre...
"You know it's only $139 for students for the full Mathematica, and if you're not a student you can always pirate it."
Wolfram is aware of that issue, they haven't found a solution.
http://www.reddit.com/r/IAmA/comments/tmutz/stephen_wolfram_...
"But we're still trying to figure out the best ways to make Mathematica as a language be as fully open as possible"
When given the tradeoff between keeping their company running and risk losing language integrity, they rather keep the company running. That's fine for me, but that means that in the meantime I'd use something else. Mathics might change that.
Its not only gratis, its libre.
Try
Plot[Sin[x], {x, -5, 200}]
The plot is all over the place. In Mathematica it is a smooth sine wave.
You can put the same input into Wolfram Alpha and see how it looks there.
Sounds,like the sort of thing an opposition lawyer would bring up in IP proceedings in a "so you copied the implementation and interface" sort of way ...
Edit:
Here they are:
http://rpy.sourceforge.net/rpy2.html http://rpy.sourceforge.net/rpy.html
There is a need for a Mathematica-like syntax parser.
(Edited)