Author Topic: YACAS is an easy to use general purpose Computer Algebra System  (Read 1632 times)

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Software Santa

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YACAS is an easy to use general purpose Computer Algebra System
« on: September 30, 2010, 11:17:28 PM »
YACAS is an easy to use general purpose Computer Algebra System -

https://sourceforge.net/projects/yacas/files/latest/download

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YACAS is an easy to use, general purpose Computer Algebra System, a program for symbolic manipulation of mathematical expressions. It uses its own programming language designed for symbolic as well as arbitrary-precision numerical computations. The system has a library of scripts that implement many of the symbolic algebra operations; new algorithms can be easily added to the library. YACAS comes with extensive documentation (hundreds of pages) covering the scripting language, the functionality that is already implemented in the system, and the algorithms we used.

Downloading the Yacas source code

The source code is offered in a .tar.gz file, with all the source to generate everything relating to Yacas.

The latest version of Yacas is yacas-1.2.2.tar.gz.

Download the documentation

The online documentation in html format can also be downloaded as one tar.gz file, manual.html.tar.gz.

In addition, there is the postscript version, manual.ps.tar.gz, and the pdf version manual.pdf.tar.gz of the manual.
Browse versions for Windows, other operating systems and older versions

Big changes ahead for Yacas

Some of you may have noticed changes that have been made to the Yacas project recently. The structure and look of the web site has changed a lot, as have the contents of the downloadable version of Yacas. The sharp observer might even have noticed that the release discipline has changed too. Yacas had collected a lot of unnecessary weight over the years, and there was room for improvements to the ease of use of Yacas.

The original idea behind open-sourcing Yacas was always to get people to help extend it. My reasoning was that if I wanted such a system, other people were bound to also want it. Wouldn't it be great if all those people helped me extend Yacas, instead of them starting their own system? All I had to do is stop them from starting their own project and work on mine instead. They would thus extend Yacas, improve on it, making the system more valuable as a whole to every one else including me. So Yacas started life as an open-source project, and people did come to help.

In retrospect it is a wonder that people came to help at all! Consider the effort one has to take in order to be able to contribute to Yacas. First, one has to be able to use it, which means:

    * have an interest in math (1 percent of the population, say)
    * be comfortable using a Unix-style system (10 percent of the remaining population, say)
    * download Yacas and compile it yourself, and install it
    * learn a completely new programming language
    * after all of that, you are greeted with a blinking cursor, and you are supposed to think up calculation examples yourself. You have to do all this work, and after that the benefits are not clear, you have to think of what you want to calculate.

Now, that was just to use Yacas. Now, if you want to actually contribute, you have to:

    * get comfortable with using the complex command-line tools called cvs and ssh
    * get aqcuainted with the Yacas system
    * get an account at Sourceforge (will take a day to process)
    * get me to give you write permissions to the cvs repository (again another day of waiting)

People had to be really persistent, they had to really really want to help extend Yacas. It is a miracle people came to help at all.
User interface design to the rescue
User interface design is generally frowned upon in academia. It is not 'smart', does not require 'brains'. If you look at what equivalent projects work on they very rarely spend much time considering the interface to the user, the way the end user is going to communicate with the system. There is a command line, and you type in commands there. If you don't know a command, you look it up in a manual, or worse, the source code because the manual is non-existent or incomplete or not kept up to date. I have seen Google summer of code projects for competing software programs where they sollicited help from computer science students to design a user interface for them. This is akin to, say, asking a student of mathematics to become a cook in a one-star restaurant, tonight, or a photographer, or an artist painter, etcetera. No amount of smarts will allow you to do work instantly that requires skill and years of training. And user interface design is an art, a skill, and it requires knowledge and experience. You can not substitute smartness for that.

But we are not alone any more!

There are two big competing computer algebra systems that Yacas competes with, Axiom and Maxima. Axiom and Maxima have their roots in the seventies, in an era where artificial intelligence was the next big thing. Computers had to second-guess you. You typed in a problem, and the system presented you with the solution. People have come to think of computer algebra systems in that way, as huge databases of mathematical knowledge to query, a search engine of mathematics. That is what they mean when they say Yacas is less powerful than the other systems. People type in some calculation that Axiom and Maxima had entries for in their databases, and Yacas doesn't. These two systems have math knowledge databases that are more extensive than the database of knowledge in Yacas.

When I started Yacas back in 1998, there were no big open-source computer algebra systems. People tend to forget that now with Maxima and Axiom available in open-source form. But we used to be alone. We were this little rowing boat on a big ocean. Suddenly two huge titanic-sized ships named Axiom and Maxima came and floated next to us. Two huge ships faring next to us, and we are in the middle with our tiny little rowing boat named Yacas. These big ships suddenly showed up out of the blue!

The event of the arrival of two big competitors forced me to consider how to compete with them. Do we compete on their turf, or do we do something else? The two classic ways to compete are to compete on features (who has more features?), or to compete by providing something different. Maxima and Axiom have approximately 30 years under their belts. Hundreds of researchers have worked on it. They have both been commercial. Hundreds of man-years of work went in to them. Competing with them on their own turf might be a bad idea. Maxima is understood to be the most powerful system, but Axiom has another dream. Axioms dream is based on strong typing, and the promise of mathematically provable correct code as a consequence. Equally, Yacas will also have to find its niche, its area where it outshines the other systems, if it is to have a reason to exist.

Some other systems are focused on mathematical calculations of the brute-force kind. You have some simple boring repetitive task, and write a computer program specifically optimized for that calculation, and let the computer do the dull grunt work, because that is what computers are good at. This is not something Yacas will typically shine at, since clean code and maintainability are considered more important than raw performance in the Yacas project.

The thing Yacas development will focus on is ease of use. Ease of use is not something you can casually fake. If this is done right other systems can not easily copy it, because making a software program easy to use is hard work. You have to think about the computers people use, the software they have running on it, the operating system they run it on, the tasks they would typically want to perform, their level of knowledge of math and computer-related subjects, even the fonts they have installed. You want to make it as easy as possible for them to start using the system, preferably without having to install software. The web site and application have to be responsive. When they have the system running they should be able to do what they want to do without having to learn too much about the system. People will generally want to do a calculation, or learn some new mathematics. They don't want to learn Yacas-specific details per se. Using Yacas should be effortless in that they have to invest very little in order to start using it.

In a sense, ease of use has always been a focus for Yacas. I always wanted the system to be self-contained, easy to download, easy to install without external dependencies. Yacas was as self-contained as possible. It used its own numerics library, its own array and linked list classes, all so it would not have to depend on external libraries. After installation, the ideal was to only have to write a few lines of code to do complex calculations, in an easy to read programming language. Those are ease-of-use issues, and I have cared for them from the very inception of Yacas.
Javascript to the rescue

For the recent update of the web site I decided that we should use Javascript to make Yacas easier to use. Javascript is now supported by most browsers, it has been around for a long while, so almost every one has access to a computer with a browser with Javascript support. Javascript allows you to make dynamic web pages, where an application runs inside a web browser without needing a constant link to a web server to serve it pages. This causes the web page to feel much more responsive than if it had to get every page through a request to a server. The "on-line application" can be used immediately, without having to download or install anything, thereby removing one hurdle for people to start using the it. They can just run Yacas on-line, from any OS that has a Java and Javascript-capable browser. When entering the Yacas site, one is now one click away from actually using Yacas.

Javascript is used in combination with the Yacas Java applet to bring the on-line version of Yacas to life. One can now program on-line and run your program directly in the Java applet inside your browser, emulating the work-flow of an experienced user of Yacas. In addition, the Yacas web site now also offers an interactive tutorial using Javascript and Java to bring the examples to life. Also, there is a find utility written in Javascript which allows the user to find functions with accompanying descriptions and examples. The find utility allows the user to use the system without having to remember too much. Functions and their calling sequences can be looked up very quickly.
The Big Cleanup

For the long term one has to worry about the maintainability of a system, if the system is to survive over the long haul. Will it still be useful in a few years time? Will it still run on future systems? Will it be easy to maintain by future generations?

The development mailing lists of the two systems Maxima and Axiom are interesting reads. Essentially, you have the next generation of maintainers of these systems communicating with each other there. The original authors have generally moved to greener pastures (or retired?). You have to understand that these systems are huge, and mathematical algorithms are (or can be) highly non-trivial. Taking over maintenance of such a system is not trivial! These more mature systems now seem to have run in to the problem of succession, where the next generation has to take over and maintain the code that was sometimes developed three decades ago, when memory was at a premium and every byte counted and you would rather use a variable name with one letter, and rather not have comments in the code. Looking at these systems gives us a glance at what lies ahead in the future of Yacas (if it survives the next 30 years like these systems have, impressively).

I had the problem of maintainability and succession in small with the Yacas project. I was always willing to give cvs write access to Yacas, to people whose coding expertise I had not checked yet. This resulted in people adding non-trivial parts to Yacas, which was really great because it made the system do more. However, there were now parts of the code I didn't know intimately. Sometimes I didn't agree with the way it was implemented either. But now it was in the system. Leaving it in was easier than removing it. This reduced maintainability from my standpoint. It is easier to maintain code you wrote yourself than it is to write code written by some one else, in another programming language, in another coding style. Most of the people making contributions have now left, leaving me with the task of maintaining what they contributed. Maintenance of parts that I don't understand will cause me to slow down as I have to delve in to understanding that part.

Because the code became harder for me to maintain, I have decided to do a big cleanup. If I am going to commit to maintaining this system for the next 50 or so years, I should be allowed to decide on what I will be maintaining. I need to be quick, flexible, efficient. Yacas needs to grow, become more useful. That is not going to happen if I get slowed down in to trying to understand obscure code. I am in the process of removing things that we don't need. It is funny to see that I can remove enormous amounts of files and Yacas still does what it used to do! It still passes all the tests! Apparently we didn't need plugins. Apparently we didn't need an fltk-based user interface. The list goes on. Removing big parts will also make it easier for others to understand the system, and will hopefully make the succession problem less severe for Yacas in 50 years.

The policy for accepting contributions has changed also. I have become more strict. I now reserve the right to referree, review and edit everything that goes in to the Yacas branch that I maintain. Every one is free to maintain a different branch, or an addition to Yacas, but control over the branch that I maintain is going to rest with me.

Contributions are very welcome. If you have any suggestions for improvements, please don't hesitate to send an email! This is about making it easier for you (yes, you) after all. I can not promise that I can accommodate every wish, but feedback on how the system can be improved is much appreciated. Feedback is a contribution too. I am interested in the types of calculations you want to do, problems you experience while using Yacas either on-line or off-line, or even plain simple bugs or typos in the manual. Yacas will change some more in the near future, and it can improve a lot with your help. If you are a good writer or expert on a specific topic in mathematics, contributed articles are also very welcome.

Releases are now very frequent, with a new release being made a couple of times each week. The idea behind this is that since there are a lot of improvements in the system, user interface, web log, and documentation and such, it would be a pity if others would have to wait in order to be able to use the new and improved version. People don't have to download and install anything any more in order to be able to use Yacas on-line. People who visit the web site use the version that is on the web site at that moment. Updating that version frequently means that people other than me have instant access to the latest version also.
A final word

Big changes have been made recently to Yacas to improve its ease of use and maintainability. I hope you enjoy the changes I made. The plan is to step up the effort and make more improvements in the near future. So watch this space!

Ayal

https://sourceforge.net/projects/yacas/

http://yacas.sourceforge.net/homepage.html
« Last Edit: March 26, 2014, 10:50:07 PM by Software Santa »

 

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