StuffThatMatters: Mathematics & Computing
For mathematicians, chemists, engineers and physicists alike, calculations are a must. And doing lengthy calculations by hand is both tiresome and error-prone. This is why Computer Algebra Systems (CAS) are important.
What are Computer Algebra Systems?
But for starters, here's an introduction to CAS. Basically, a Computer Algebra System is a piece of software that can work with equations, matrices, graphs and other mathematical constructs, because a CAS is specially designed for one single purpose - manipulation of mathematical constructs.
You can always calculate a large but straightforward arithmetic problem with nothing but a calculator, or the usual software on your computer, but what about the roots of an equation, say x^3 + 7x^2 + 9x + 10? Or, what if I ask you to invert a 4 x 4 matrix? This is where CAS software come into play, it can just take the equation, solve it instantly and return you the result, and even tell you the steps (in some commercial software).
Some examples of what a CAS can do for you
1. Solving linear, quadratic, differential equations etc.
2. Differentiating/integrating functions.
3. Expanding/simplifying expressions.
4. Plotting/graphing functions.
5. Manipulate special types of data, such as matrices, arrays, intervals etc.
Free CAS software you can download now
Now, for those who use CAS, Mathematica and Maple are like the Holy Grails of CAS. But not everyone can afford them, especially since those software are pretty aggressively priced. And being an advocate of open-source and software freedom, I always look out for better, open-source alternatives.
Of course, there are many, many features which Mathematica and Maple offer, that will never be found in the free software I mention below, but unless you're really, really serious about your mathematical computation, I believe things like Maxima, Sage etc will work flawlessly for you. Be warned though, there's a bit of learning curve in each of them, but plenty of online documentation and volunteers are available to help you.
So, here they are.
1. Maxima
Maxima is my personal favourite, when it comes to open source CAS software. It's fast, it's comprehensive and it's expandable, plus there's a great deal of information about it online.
Maxima was originally based on Macsyma (hence the name), but the original CAS got discontinued, and Maxima survives today. It includes a powerful mathematical programming language, that you can use to code scripts (executable via maxima interpreter).
Learning it is pretty straightforward, plus it's available on a variety of platforms. Be sure to use a GUI if you plan to install Maxima, such as wxMaxima, GMaxima (on GTK+ interface) etc. Also, for Linux users, KDE's fantastic front-end Cantor can be linked with Maxima, which is perhaps the best combination.
Download: http://ift.tt/1gN7Yno (check the Downloads section)
2. Sage (System for Algebra and Geometry Experimentation
Sage is in itself a complete package, and much more complete than Maxima so far as the integrated GUI is concerned. But here's the catch - instead of packing a GUI of its own, Sage makes use of your existing browser to give you a notebook-like interface, that you can use for all your calculation needs.
The notebooks of Sage are a delight to use, and there's an integrated tutorial that guides you well. Even better, you can keep the entire installation as a binary on your pen-drive, and then access it on each machine you own. Recently, an online version of Sage is also being developed, with a native Android app for easy access.
One problem, however, is the lack of any Windows version of Sage.
Download: http://sagemath.org/ (for Linux & Mac systems)
3. Mathomatic
Mathomatic is a general purpose CAS, and it excels with regards to its size. It's really lightweight and small, but this comes at a price. It can only deal with elementary algebra, and it doesn't have a GUI.
Instead, mathomatic makes use of your terminal (DOS-like prompt in Windows), and requires you to use its specialized syntax.
But yes, mathomatic is available for almost all OSes out there. Linux users can install a PPA to stay updated, and Windows users can just follow the old .exe download + installation process.
Download: www.mathomatic.org
4. Reduce
Reduce was previously a commercial CAS, but since 2008 (IIRC) it's open-source. It's primarily meant for physics, especially astronomy-related calculations. It's a brilliantly programmed software, and has been developed for over a long time, since the 1960s. This gives it an edge over other, newer solutions.
Reduce is also available for a variety of platforms.
Download: http://ift.tt/1vhjRsC
5. OpenAxiom
OpenAxiom, or simply Axiom (following the publication of its code). Like Reduce, it too has been in development for a long time. However, it's perhaps the most frequently developed one in the list.
I confess, that unlike the other four in the list, I haven't used Axiom well enough. In fact, I just downloaded it day before yesterday, and decided to give it a shot. But from what I've seen, other than the lack of a GUI, it's quite powerful. Also, as the website states, work is under way, to develop the software into a fully usable GUI-backed solution for computational needs.
Download: http://ift.tt/1mTdkoF
Conclusion
Well, these software are nowhere near Maple or Mathematica, but then again, the total price you'll have to pay for all these 5 software is $0.00. And that amounts to something, I guess.
These glorious software demonstrate the beauty of open-source and the idea of software freedom. Thousands of volunteers are working hard so that we may use them, and the makers get nothing in return. In fact, I believe they are somewhat like me, since I maintain this page only for sharing what little I know with everyone, without any commercial interests. Only, they are much, much, much better than I am, because what they've designed is million times better than my act of spreading the word.
If these software benefit you, please be sure to spread the word.
References
http://ift.tt/1mTdkoH
#freesoftware #linux #math #science #opensourcesoftware
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