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Use of Math Languages and Packages in Research?
CEHT asks: "As a research programmer at the university, I have encountered numerous times when I need to choose which language(s) or package(s) to use for different projects. Tradeoffs and performance issues have to be considered: results from one package may be more compatible with the data from other researchers, another package may find the solution faster and use less resources, and so forth. Maple,
Matlab, Magma, and Mathematica
are among the most well-known packages. Libraries such as IMSL is also popular. Of course, there are smaller (and mostly free) packages that tend to target specific types of problem, such as LiDIA, Singular, and LAPACK.
The question is, how useful are these [and other] math packages? Do researchers use only one or two packages for most of their projects? Or do people like to mix things a little by pulling the strength of different packages together to solve a math problem? If not, do researchers write C/C++ programs and use GMP or Matpack to solve math problems?"
Whenever I need to do anything like that, I use Octave.
But masters, remember that I am an ass: though it be not written down, yet forget not that I am an ass.
Now, I'm only in college, but while we did dabble a bit in Maple and a few others that you mentioned, the only Math software package I've used extensively is MathCad. I've found it to be the most user friendly of the bunch, and they have a new version out: MathCad.com
maple and matlab i have found to be useful
but that is only if u are doing a highly intensive amount of math
otherwise it takes longer to figure the gui and usefulness out than to figure out the problem on your own
matlab rules for matrix math
[I can picture a world without war, without hate. I can picture us attacking that world, because they'd never expect it]
I use `expr`.
In Experimental Nuclear Physics (ENP) there is a healthy mix of Fortran , C, and C++ (and some others). There is a healthy schepticism of "black box" programs and libraries so programs like Mathematica and Mathlab are pretty much not used. Also, most of the problems are pretty specific (and time consumming to run) so everyone seems to run specialized code (Example: Radware is very popular in Nuclear Spectroscophy). Of course it helps that most ENP's are pretty competant with computers and electronics (amoung other things).
Galium Arsenide is the material of the future, and always will be.
matlab for design prototypes of numerical algorithms and for visualizing data.
mathematica for doing messy algebra/calculus/differential equations.
my own c/c++ code, with a lapack backend, for doing large-scale computations (matlab and mathematica are too slow for big computations).
So, the answer is e) all of the above!
All is Number -Pythagoras.
Let's not forget about PDL, the Perl Data Language. Think of Matlab combined with the goodness (i.e. CPAN packages) of perl.
"If not, do researchers write C/C++ programs and use GMP or Matpack to solve math problems?"
No! They use FORTRAN!
Surely it's still much better language for numeric stuff
Do any of the listed tools/languages take care of this problem for me? I understand the nature of the problem, but it is still very frustrating. What do the "pure" math programming languages do with this issue?
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Very popular slashdot journal for adul
I have used a few other packages, command-line utilities, which I find useful: Recently I'm using one for my honors research project (I'm an undgergrad): GAP and another I've used which I like: PARI-GP. GAP tends to deal with group-theoretical functions, and GP tends to deal more with number theory, but both shouldn't be ignored.
I find that each package is well suited for a particular use...
MATLAB is great for off-the-cuff research. I can open it up, and program image processing routines in 30 minutes or less. This would take hours in C/C++. Additionally, I can take the M-file and dump it from my computer onto a workstation running MATLAB and get some decent speed and batch processing done.
C/C++, however, gives you so much more control and execution speed, that often you either use the MATLAB --> C compiler, or end up writing a final routine in C directly. I believe for image processing, as an example, you can get over a 100x speed increase just by using the MATLAB --> C compiler.
Just my $0.02.
"Owning a computer is like having your very own TV -- with a built in radio!" - Ed Helms
I've used python and Numeric and coworkers of mine have used them in real physics type stuff and it is great (I think Fermi lab uses Numeric a great deal).
I'm surprised you also haven't mentioned R. It's a stats
package (gpl'd) modled after S. http://www.r-project.org
and it is very powerful with a great community behind it. It's an amazingly powerful tool for analysis.
For my research in mechanical engineering (more specifically regarding tolerances), I use Matlab since it's what I'm most comfortable with. Maple is also used at my Uni, but I don't have much experience with it (other than it's symbolic kernel since it's available with Matlab) so I don't end up using it.
It mostly depends on what you're doing. Depending on your area of research, you may find that one of those is more popular because it solves these types of problem better. If speed is an issue for you, you can easily port your algorithm to a compiled language if you prototyped on an interpreter, even interfacing the two in some cases.
I am not able to articulate this well, but the type of research you are doing is MUCH more important of a consideration than computation speed or resource consumption. If you need supercomputer time, then you had better ask the admin what you need to use. I know a bunch of people that do environmental modelling, and I have never seen or heard of anybody writing their own C++ to do it. Researchers GENERALLY have better things to do than re-invent wheels.
People who think they know everything really piss off those of us that actually do.
For most computer vision code, Matlab is a must for prototyping. It's useful in other areas, and, if you know how to use it, reasonably fast. If you're doing particularly involved matrix manipulations, it takes a lot of work to come up with C/C++ code that will work faster then well-written matlab code.
Personally, I also use Mathematica for doing real math work. If I need to derive something that's particularly complex, then Mathematica's notebook style is really nice to work with, and it makes possible extremely clear and concise mathematical arguments while limiting stupid human errors when doing drudgery like taking derivatives and the like.
I hear Maple and MathCad are both good, too, but I've never used them.
I'm working on a thesis with a math professor here at school. We're working on a mathematical fiber model which requires a whole lot of computation and a whole lot of data. My advisor does all the computations by writing FORTRAN programs and running them on an SGI Octane. Yeah the language is really old an ugly, but it's still useful for mathematics and its what a lot of mathematicians use in academia.
my other penis is a vagina
My experience (Ph.D. in applied mathematics, and employment at a mathematical consulting firm) is that researchers only use their favorite package and will rarely use anything else, despite the fact that their favorite may not be appropriate for the job at hand. To that end, I use Mathematica for nearly all my prototyping, except for brief excursions to Matlab which is much better at image analysis. But both of these have speed issues, and when it came down to serious buisness I would often roll my own C,C++ or FORTRAN code for the problem at hand.
Explain to me how you would do calculus with matlab?
All is Number -Pythagoras.
Just out of curiosity, anyone know what mathematicians, engineers, and phycicists would do in regards to these complex problems before there were these programs mentioned? What about before slide rules?
If brevity is the soul of wit, then how does one explain Twitter?
Having traversed from a predominantly engineering realm (computer science) to a predominantly scientific realm (neurobiology), my observations have been that the tools are selected mostly on habit or previous knowledge rather than fitness for use.
The most commonly-used analytical platform is probably Excel (or some similar tool like Statistica), but the more serious researchers, who are also the more mathematically-aware, nearly all use Matlab in my experience.
When efficiency is an issue, nearly everyone I've worked with turns either to IDL (a Matlab competitor that has more arcane syntax, but much higher processing speed) or writes a C/C++ program by taking algorithms from "Numerical Recipes in C".
Recently, I've also seen a rising use of Visual Basic, especially to do experimental control (although some Matlab hooks do exist for such), and, of course, LabView. Some diehards use LabView for data analysis as well, but their results are suspect just because the tool is so poorly fitted to the task.
And, of course, many data collection hardware manufacturers (CED, National Instruments, TDT, etc.) supply scripting languages to control their hardware and perform rudimentary and sometimes not-so-rudimentary calculations.
The best researchers select the most appropriate tool for the job, but, again in my experience, it seems the selection is normally based on previous experience and inertia. Those who know a particular tool well (eg, Excel, Matlab, SPSS, Mathematica) tend to keep using that tool, even if it is not well-suited. This means you get abberations like Matlab programs that control real-time experiments and LabView programs that do higher-order mathematics.
Why?
Because the largest fraction of a scientists' time should be spent on data collection, not experimental implementation, and the amount of time (for nearly all fields except those with astronomical amounts of data) spent executing code is dwarfed by the time developing it. Clearly this breaks down for certain applications, but most of the science currently being done (read: molecular biology, and no, not bioinformatics) is not algorithm-bound.
Since data analysis is such a huge, broad field, I expect to see radically different answers from other posters!
Put my fist through my alarm clock with its ding-dong death inside my ear. - The Blackjacks.
I use Maxima for my work. It's a continuation of Macsyma, the computer math program that was the inspiration for Mathmatica. Macsyma was tied up in copyrights for a while, but now it's public domain. So Maxima updated it to modern computer environments, added in a GUI (with web browser) and ties to modern programs like GnuPlot, and now there's a good, open-source symbolic math utility / programming language.
Are there any viable open-source solutions to either Mathematica or IDL?
Asking this question is no different from asking, "which programming language should I use?" without stating the purpose. Bash is great for scripting a daily ftp get, but inappropriate for drawing graphics.
I can use Mathematica for almost all of my dabbling. Sometimes I play with MuPAD, R, GnuPLOT, Octave or Mathematica to show a particular problem. Since these are also free (beer or speech, depending on package) I can be reasonably sure that everyone can get a hold of it.
For example, Octave is suitable for matrix manipulation. It does everything that I need it to do and can replace Mathematica for me. It's also fast enough (the longest calculation has taken just over a minute but it was a huge manipulation of some graphic data).
I've dabbled with some of the libraries but only for fun.
I guess what it comes down to is how comfortable are you with the package. By the time I try to write something in C using a dedicated library I can most likely do the same thing in Mathematica in a tenth of the time. Even if the execution speed was 100 times slower, the "real" time may not about to much.
You're talking about two different classes of software: "numerical linear algebra packages" and "computer algebra systems". Maple and Mathematica are the latter, Matlab is the former. I don't know about Magma.
Hardcore numerical programmers use LINPACK/LAPACK with platform-optimized BLAS (this latter is often commercial, or at least proprietary to the platform vendor) directly from Fortran. They usually use modern commercial Fortran 90 or Fortran 95 compilers, too.
On numerical linear algebra stuff where you aren't going to recruit and pay a Fortran programmer with a PhD in applied mathematics, most sane people use Matlab or GNU Octave or one of the many other Matlab clones. A lot of people like Numerical Python, if I had a big new project to do, I'd seriously consider it.
Yes, crazy "researchers" who don't want to learn Fortran and think Matlab is too slow or too expensive will write numerical code in C++. Some of them do fine work, too.
Excel and other spreadsheets are fine for small bits of numerical analysis, too. Don't turn up your nose at 'em, you can email your boss your whole analysis and he doesn't have to learn Matlab to do anything with it. Excel is also slowly replacing Qbasic as the computing lingua franca of the Amateur Radio/hobbyist-electronics community.
The class of people who just doodle out the singular integral equations for the airfoil design they're brainstorming seem to like Mathematica a lot. I wish I were more like that. Maxima is seeing a renaissance now that its licensing and distribution issues are cleared up (it's GPL now). I should check it out. There's also GNU (Emacs) Calc, which I use regularly as an RPN desktop calculator. It is actually much more powerful than that and will do all kinds of HP-calculator-style graphing and computer algebra with a liberal sprinkling of Mathematica-style syntax, but I don't use those features much, because they're wicked slow.
I do lots of geometric work and I depend on vector math.
If I'm not concerned with speed, Python is very nice as I can reuse a module package I wrote that contains my most often used functions. Additionally, the fact that Python is OO is also very helpful.
For speed, such as when I do 10^12+ math operations, I fall back to C. Nothing crunches numbers faster.
Python and C. They're not just for breakfast anymore.
Graham
Linux - Fast Pane Relief
I use MATLAB every day for my neural network simulations. MATLAB is incredibly powerful, incredibly flexible. It is also incredibly expensive. And the decision to port it to OS X was about the best decision The Mathworks has made recently.
MATLAB offers student versions for about $99 a pop, which is dirt cheap considering its $1000 price tag for the retail version. Many universities of course have dramatic discounts, but then, you have to have be affiliated with a univeristy. Even the student version requires you to attest that youre using it for course work or student-level research and not commercial gain.
MATLAB has a number of drawbacks. Price is the largest. To enforce its license, MATLAB requires you to run the onerous and clumsy FlexLM license manager. FlexLM is brought to you by GLOBEtrotter....a division of that bastion of consumer rights, Macrovision. That should speak volumes. The license manager makes doing a lot of simple things stupidly difficult, especially if you're (like me) mobile and have to authenticate with a central server running the license manager. I can get into details if people have questions.
On top of that, MATLAB requires a yearly "maintenance" fee. It's more or less software as a service. Apparently, if you let the maintenance contract lapse, you can still use MATLAB, but you get no more support and cannot apply any new updates. That may be, but the particular license my university employs will cause my copy to simply stop working after April 1 if I don't renew. (April 1 being the beginning of the Mathworks license year. I don't think they see the irony in choosing that date).
The maintenance contract does not apply, AFAIK, to the student version.
On top of THAT, the student version or the $1000 base retail installation just gets you the MATLAB core. Which, granted, is extremely powerful. But the Mathworks also has a couple dozen or so Toolboxes, each with a range of specialized functions and tools (i.e. Signal Processing, Image Processing, MATLAB-to-C Compiler, Symbolic Math, etc. etc.). Each of these comes for an additional price, and its own maintenance fees. IIRC, these are like $500-$700 more each.
Did I mention all these prices are for licenses on a per seat basis? Any institution or company thinking about MATLAB is going to shell out serious bucks for the privelage.
On the other hand...MATLAB is a serious, extensible, highly flexible platform for technical and mathematical computing. I find that I can prototype programs for solving scientific problems in MATLAB far faster than I can in any other language. And its visualization features are truly impressive...even if the Handle Graphics system it uses is SO DAMN KLUDGY to program. You can customize visualizations just about however you can imagine...ALTHOUGH, some simple customizations are going to be UNNECESSARILY tedious to program.
Another drawback to programming in MATLAB is speed. MATLAB ("Matrix Laboratory") is exceptionally optimized for handling calculations of very large matrices. However, because it's interpreted, if you have any loops, it's going to be very slow going. There often many tricks to "vectorize" operations you'd normally do iteratively in other languages, but often the only solution is the ol' for-next or while loop. These are slow. Very very slow. Yes, there's a compiler, but in my experience the compiler isn't that great at optimizing code...and, did I mention it costs extra?
Anyway, MATLAB is amazing in its breadth and depth of power. I haven't even touched on its capabilities for engineers, like the SimuLink system design simulator, and hardware interface toolboxes. I can't imagine a problem needing to use a "mix" of math packages (as the original poster asked) if you're using MATLAB. But the purchase and ownership costs are very steep.
I have a related issue, in this regard. Some of the problems I am working on require arbitrary precision floating point numbers. E.g., one number might be 3.2334, but it needs to be multiplied by 3.4568902349830983945873908730987578439345, and I need all the resultant digits.
The problem is that the output of one calculation is fed into the input stage of another, that output being the input of the first calculation, in a circular style, so that small rounding changes may have a large affect on the final outcome.
Now, at some points, the precision may be truncated (where the effect will be unnoticable to the equations), but at certain points I need the exact number.
I have heard that with Lisp you can have numbers as large as you like, but I don't know how hard it is to perform complex numerical tasks in Lisp. Also, speed is an issue (I want it to be as fast as possible).
Any suggestions as to how to accomplish this?
In the past I've used Matlab, C/C++, and a junkyard of Perl scripts to get things done.
Nowadays I use exclusively Python, with underlying C and C++ components when performance is at a premium. C is easy to call from Python thanks to Swig.
Python is simply unparalleled in its simplicity and elegance, and I find that I can accomplish most of the things that Matlab is good for from a Python interactive shell using Numeric and the other various scientific Python libraries.
I'm a post-doctoral researcher at a engineering college and I use Linux for all of my data acquisition and analysis. The following environments are used:
LabVIEW, PERL, shell scripts, and/or C for data acquisition
C++, MatLAB, and/or shell scripts for data analysis
and you can get some of my codes from Sourceforge:
http://sourceforge.net/projects/qaxa
http://sourceforge.net/projects/ssnooper
and others are available by sending me an email.
Ed
http://cesep.mines.edu/people/hill.htm
I have been using matlab, mathematica, maple and mathcad for different purposes in university and currently in job. I feel matlab by far is the best of the bunch simply because it allows for a more powerful simulation experience using simulink. Here is what I feel about learning these packages vs. coding ...
... maybe its better now ...
:) ob' it may not stand the test of u'r research !!!
1. matlab - hard on newbies' but very powerful and elegant in the hand of intermediate and advanced users. Graphical simulations possible through simulink. Matrix computations are very fast!! and on average it takes the least amount of time to solve the problems compared to mathematica, mathcad and maple.
2. mathcad - the first mathematical software I used, very easy to learn almost instantaneous learning!!! but that was when mathcad was still in dos mode, I saw the windows version out now and they seem to be cumbersome to get around, but then I have not been using it regularly.
3. mathematica and maple - almost similar performance, mathematica has better interface and with a large amount of tutorials and extensive help system is easier to learn than maple.
4. scilab - a matlab clone which is GNU (I think!!) used it couple of years back when it was not as good as matlab graphically
Now, coding - yes it has to be done from time to time but I think due to these softwares it has been relegated to the sidelines when extensive run times are involved and a significant performnace gain can be derived by days of coding. I belive it may be easier given the tons of free libraries available but it still takes longer to code in c/c++ than in a 4GL (generation language) like matlab and mathematica.
Coding still can't beat the quick prototyping mode of these softwares i.e u can do a lot of manipulations in the time u take to write and debug the code. It basically boils down to whether result or way of getting result matter most !!!
and then don't forget sometime those big screen scientific calculators are faster to get quick results than u'r fancy softwares and codes
The other major factor is that nuclear physics is perpetually underfunded and buying commercial software is ussually not nessasary (since we would have to make sure it worked properly anyway).
BTW we do use "building block" type programs and libraries for our interfaces. A good example is SpecTCL at the National Superconductiong Cyclotron Laboratory. I have used GTK/GDK in my applications, others have used Qt. However, the numbercrunching and datacrunching parts are nearly all custom. The data processing is simply too complex and too specialized to trust to prepackaged software. The numbercrunching applications are too time consuming to use a generalized program, everything has to be optimized.
Galium Arsenide is the material of the future, and always will be.
I was taught Matlab in my computational physics graduate class, which biases me toward Matlab in my own research. I also own Mathematica, but have not taken the time to master its language and command structure. Mathematica was an award at a conference where I presented a paper, but I purchased Matlab for myself.
There are two primary advantages which I see in Matlab. The first advantage to me is its abilities with matrices and arrays; it can do things in a couple of lines of code which can take some roundabout programming and subroutines in other more conventional languages.
The second is Matlab's graphical abilities. Display of data is very important, both in the final product (thesis, paper) and in the research process itself. After a brief introduction to graphing in Matlab, it becomes a trivial task to choose and use various display options for your data.
In physics, it seems that we stick with what works until something better is found. That applies to our theories and to our tools. It is not uncommon for us to use Fortran, Pascal, or even various types of Basic to perform simple calculations and experiments.
Much of what one uses may be determined partially by chance--what software package was available at your institution, what professor did you study under, did your undergraduate degree require a programming course? The work involved in switching from one major package to another, for instance from Matlab to Mathematica, simply seems like too much effort for very little sure return.
Jim Deane
It depends on what you want to do.
CHALKBOARD is great for addition and the other basic operations, but if you want to do symbolic algebra, Maple or MathCad are your best bets.
If you want to do some sort of signal processing and/or crazy matrix applications, the Matlab is probably the answer.
If you want to do something with statistics, Matlab or Minitab are the way to go.
MathForge is a project designed to utilize "web services" to provide interfaces to networked and local math tools. The idea being the mathforge architecture "discovers" math services depending on whatever task needs to be done.
The base of the project is a Java environment on which programmers can build tools as needed.
It is GPL'ed software.
Yes, indeed, the latest version (from less than half a year ago) was the first to include a just-in-time transparent compiler by default. Inner loops are so much faster than the old interpreted versions it's not funny.
However, a Matlab clone called MIDEVA had the same thing three years ago. Mathworks bought them out and incorporated their tech.
...for the job at hand.
I'm a graduate student in Mathematics studying (convex) optimization problems so I see a healthy mix of pure and applied math. When I'm doing pure math the best tool for the job is a strongly symbolic math package like Maple (which I use extensively). Maple is also really good for quick visualization and helps gain insight and intuition into problems. Other offerings in this arena include Mathcad and Mathematica (however Mathcad actually uses a smaller version of Maple's symbolic engine).
Similarily, if the task is more numeric, Matlab is the choice (actually, we use Octave, which is a GPL'd and free numeric package that has Matlab syntax; most code written for one runs in the other). I'd say Matlab/Octave are most useful for prototyping numeric algorithms, and solving medium sized numeric problems.
Finally, when a tool is needed that performs well at one specific task (or the problem size gets really large), you can't beat writing your own tools from scratch in the compiled language of your choice. At this point, there are a variety of libraries that one may find useful (for arbitrary precision arithmetic, expression parsing, symbolic manipulation, etc).
So I guess the answer isn't white or black, but rather varying shades of grey (as is always the case).
I don't think anyone has mentioned scilab. It is a good GPL alternative (along with octave) to the expensive (expensive if you are a college student) matlab. It has been a while since I played with them alot but I found that matlab had the best graphing functions.
Anyway the best package for you in part depends on what you are using it for. Matlab, scilab and octave are great for doing linear algebra things -- manipulating matrices and arrays etc. Some people complain about how slow matlab is. I find matlab is pretty fast as long as you use it for what it was designed for. You should use their built in functions as much as possible and use as few loops as possible. If you find yourself using a lot of loops try writing a mex function in C or FORTRAN.
Maple and Mathmatica are great for Calculus differential equations etc. If you are doing a lot of matrix mulitiplies in Maple, you should be using matlab.
Mathcad is user friendly but it is SLOW. Even old people who have been doing insane integrals in their heads since the 50's and refuse to even look at a computer can see a Mathcad print out and tell exactly what the program is doing.
Hope this helps. Personally I like to use Octave and Scilab since they are GPL. Scilab is prettier IMHO but Octave is closer to Matlab (which I am already used to.)
If you have lots of money, use Mathmatica. If you are poor, use PARI.
http://www.gentoo.org/dyn/pkgs/app-sci/octave.xml
A highly unknown but very efficient (faster than Pascal w gc) and easy to program is ML (Meta Language) Seems to be perfect for Math computation.
For example, you can write batch scripts in Maxima a lot more easily than you can in Maple. I have scripts to automatically generate PostScript figures and I'm really not sure I could do the same with Maple.
Maxima has some bugs, some annoyances, but at least, you can report them on sourceforge and they do get fixed. If not, someone will suggest a work-around.
I'm an experimental particle physicist, and most of the mathematics packages I use are home-brew libraries (mostly C++ w/ bits of older Fortran). I think for me a multi-dimensional function minimizer is just about the most complex tool used, and it is used constantly -- tens to thousands of times per day. Unfortunately, it's not a trivial problem and different minimizers will often produce different results. The only one that I know which is semi-free and basically functional is MINUIT, part of CERNLIB (in Fortran). I've recently been searching hard for an open-source minimizer to replace this, written in C/C++. I would also like to see one in Java, for a few reasons (I'd rather an applet than a CGI script).
The GNU scientific library has a very crude minimizer that's too simplistic for my needs (I want things like the curvature at minimum which can be inverted to give a coordinate covariance matrix). I most often use the minimizer to fit various functional forms to observed statistical distributions.
I am surprised at the lack of an up-to-date open-source minimizer, because so many university researchers use these kinds of tools, and are in an environment where commercial solutions are painfully expensive and a schism for any multi-university collaboration. A lot of phycisists write good code prolifically, but far too few support/contribute to open-source projects!
I was reading through Numerical Recipies recently, and was also taken aback by their licensing policies. The algorithms in the book are simple solutions which have been previously published by others in journals and such. And the code is just a direct adaptation (translation really) of the algorithm. Yet somehow their code, or any translations of it, are under copyright? I think it's foul-play like this that are the reason there are so many high-quality commercial mathematics packages, and so few open-source ones.
You can pretty much do everything you want using Python Numeric. It is actually a much nicer language than Matlab if you know your stuff as far as languages are concerned (OOP, functional programming and such).
Also, there is a port of Python Numeric in java (JNumeric) which means that Numeric is extremely portable.
All of that for free. Not just free as in free beer too... free as in free software...you can't beat that!!!
We are trying to get the old site to direct people to the new site. Since the old site is not under our direct control, it isn't as easy as one would hope. (I am the Maxima project leader.)
unfortunately. We were taught it in one of our astronomy classes to analyze and plot data. It has a very arcane syntax and doesn't have a lot of capabilities (no matrices; there is a very crude way to represent square matrices as sets of vectors). I now use Octave or Matlab as much as possible for numerical work. For symbolic math, I mostly use Maple. I also have a little experience with Mathematica, but I like Maple better (although Mathematica looks nice). As far as I know Maxima, it can't do as much as Maple or Mathematica, but it should be good enough for most symbolic computations.
First a global kind of classification.....
octave/matlab... are mostly vector/array oriented languages and are useful for doing work in problems that are suited for such - you can experiment easily, then recode in C,fortran... if needed. apl and j are also in this group and should not be ignored - though they're used a bit less frequently.
Macsyma/mathematica/maple/maxima/derive are symbolic math languages and can solve interestingly sized problems and get symbolic answers (that is, things like sqrt(pi/2)) as well as numeric approximations. This can be a very useful tool to have - depending on what I'm doing I use such things a couple times a week (nice to check results done by hand, or to handle all the crufty part of a solution). Most will emit fortran code which can also be useful.
vtk, opendx/khoros(?) are visualization tools - most of the other packages have some visualization tools packaged in them, but vtk and opendx both offer quite a bit more power.
Now the incredibly non specific recommendation
My suggestion is to pick one of each of these and learn it - do enough in it so you know the language/system well. Otherwise you'll be struggling with the language as well as with the problem - and finding bugs will be close to impossible.
If I put on my "computer science professor" hat (probably a wise thing if I'm to keep the top of my head from turning bright red with sunburn), I usually try to recommend that all CS students learn a smattering of these things as well. When you need one of these tools, knowing its there and how to use it can save large and wonderful quantities of time.
And now some more specific comments
On the whole my choices would be as follows - note the caveats - some of them are pretty cave-rnous (sic). I don't have piles of money to spend, so tend to prefer the open source programs just on that basis.
For array/matrix manipulation I much prefer APL or one of its derivatives (check out aplus on sourceforge). Languages in the APL family are also fun to program once you learn how. However the terseness of the syntax (and with APL itself the odd character set) tends to make these a bit forbidding, so a more popular choice would be octave (open source) or matlab. I've had good luck with octave - it seems to handle most matlab programs well enough. If you've got piles of money, go for matlab.
For symbolic math, maxima (sourceforge) is good. Its commercial cousin Macsyma has usually ranked as about the best symbolic math packages for accuracy and power and seems less expensive than the others. Actually writing programs in either of these requires learning quite a bit about the innards of the system though. My second choice for symbolic math would be Mathematica - its programming language is well integrated with the system as a whole and and for general goodness and niceness of the interface it can't be beat. (The other commercial products are building on the best parts of the Mathematica interface - I've not checked recently, but they're getting much better fast.) The visualization capabilities of Mathematica are also very good. Maple is probably the most popular, so using it will probably make it easier to find someone to help you, but on the whole I've just never found Maple as easy to program as Mathematica and I tend to want to program almost everything.
For visualization both vtk and opendx are very nice systems. vtk is more aimed at a programming interface, opendx has a labviewish kind of programming environment. I like both and have both at hand. Both these systems are big enough that you'll want to make sure you understand them before you tackle a project with them.
They don't scale well, but spreadsheets can be very convenient for small models. Careful though, its easy to have errors even in middlin sized models that can be very hard to find.
Odd Zen Endz
As has been noted there are other systems, some smaller, some more specifically focussed on a single domain. Those tend to be harder to match to a problem - unless the problem is right in the center of the domain in question.
There used to be a program AXIOM which had a lot of nice features, but it seems to have gone to that Big Bit Bucket in the sky - but its base language "Aldor" is now available at aldor.org. I have a copy, but haven't looked deeply at it.
Sourceforge is also hosting a new project "lush" - which is a lisp system that has some integration of some of these features. To the extent that I've used it I'm impressed and will probably spend some time working deeper with it in the hopes that it will prove another valuable tool.
I was in the math software industry for well over a decade. My experience is that each manufacturer is irrationally optimistic about their own package, and irrationally pessimistic about competitors. Kindof like commercial software in general, but the venue is more fuzzy, lending to more irrationality.
:-) It's designed to be interactive, rather than a programming language. Check it out at livemath.com
- the way a user does this or that, varies widely. Often, methods are not obvious, so for one person, "mathblob does gizzyggy calculations" is true, for another, it's false. EG mathcad has (had?) a version of Maple inside, but it was awkward and hokey to use. BUT they could claim all of Maple's capabilities.
- The algorithms vary widely. If MathBlob has a specific optimization for gizzyggy calculations with flipex inversions, then you could say that MathBlob is great at gizzyggy calculations, and the others are useless. These optimizations can easily give you 1000x performance improvement or more (think n^n).
- The domain venues vary widely. Numerical programs typically do zero symbolic stuff, but do the numeric stuff lightyears faster than symbolic programs. A group theory program may have trouble adding floating point numbers. With hardware double floats, you can't get anything past 10^308 or so, which is a disaster to some but no big deal to others. When someone says MathBlob does EVERYTHING, really they mean MathBlob does Everything that I think is important.
So like, I once had Mathematica take like 30 seconds to add 2 + 2. (It had to load in a ton of packages.) Then it reported it was out of memory.
With that said, LiveMath is THE BEST math program in the universe, way better than any of the others here.
(disclaimer: I'm the original author)
Marketing-driven companies end up over-marketing their products. Engineering-driven companies end up over-engineering
If you want to do some statistics, there's also R, a stats analysis package. It's very powerful, but it's designed for experts rather than non-statisticians who occasionally want to crunch some numbers.
Any sufficiently advanced technology is indistinguishable from a rigged demo
--Andy Finkel (J. Klass?)
So from what I have read from most others' posts, there are two camps:
While I agree with #2, it does not really seem to answer the question. The question is: "Do researchers use only one or two packages for most of their projects?" I think the result for the most part is for mathematical calcs, the people that answered the question say most people use different programs for different goals.
Things to think about when you are trying to pick a language:
These are likely to be very similar questions a computer programer asks him/herself when they are starting a new project. Okay, this post really doesn't say anything, but one last note for the major commercial packages: most of them support C/fortran/etc calls so if you are truely interested in efficiency, remember coding efficiency matters too. I am finishing up my Ph.D. Years ago, when I starting simulations for my work, I started working in C. I figured "if I am going to be working on something for X years, I may as well do it right!" While a noble goal, I really didn't know C. I subsequently spent a week trying to do something that took me roughly 2 hours to accomplish the same thing in Matlab (another language that I had no experience in).
So what is the moral of the story?
run... run as fast as you can and don't look back.
Wanna hear something cool?
I just got Octave & Gnuplot running on my Sharp Zaurus. I can do my DSP type calculations, anywhere!
Someone is currently porting gtktiemu, at which point I'll have a TI-89 emulator, which will let me handle just abount any engineering math type stuff I need to do with one pocket-sized deivce.
Now if my fold-up keyboard would just show up.....
Life is too short to proofread.
Well, some did anyway. For example, in the early 1820's, when dealing with solving partial differential equations arising from heat conduction, Joseph Fourier came up with the foundations of Fourier Analysis, which has become an essential tool in a great deal of mathematics, science, and engineering. Where would we be today if he could just plug it into MATLAB and get an approximate numerical solution?
Also, although I do not really know how he did it, I belive that Euler had calculated e to 7+ decimal places in the mid 1700s.
The "maxima community," such as it is, exists on the maxima mailing list. Please follow the links from http://maxima.sf.net for list information, archives, etc.
About keeping important bits of paper. I have MathCAD Pro 2000, and an upgrade to MathCAD 2001, both of which set me back nicely, (though I usually need Mathematica) and when I switched computers in December it was all useless because I can't find the serial number to my MC Pro 2000 disk.
Have you ever tried to build a pyramid without any significant digits. You kids have it so easy these days.
As a statistician, I prefer R. Matlab's approach to statistics is to implement a bunch of formulas one could look up - R (or S-plus - I prefer the open source version) gives an interface that is closer to doing statistics. R has far more routines implemented than minitab (or Matlab, if one sticks to statistics). Additionally, most of the interesting applied statistical research that I've seen is implemented in R.
Quack!Quack!.....QUACK!!
I've done a lot of work in 3D pure mathematical graphics (drawing algebraic surfaces etc), and JavaView and Geomview are nice platforms for viewing 3D data.
There are four sorts of people in the world: fools, lunatics, idiots and morons. - Umberto Eco, Foucaut's pendulum.
Don't underestimate the power of C++: with type checking and overloading, C++ may actually be more convenient to use for many numerical applications that even something like Numerical Python or Octave/Matlab.
Beyond that, yes, obviously, all those libraries are in use by someone if they are maintained. If you have the need to use one of them, you will know. If not, don't worry about it.