Symbolic Algebra Everywhere
Previously in this space, I have covered software packages like Maxima that can be used to solve symbolic mathematics problems. Several packages are available that can do those types of calculations. In this article, I discuss Xcas/Giac. Xcas is the GUI interface to the system. Giac is the command-line program that provides access to the core engine. Xcas has the functionality to handle symbolic algebra, two-dimensional and three-dimensional graphing, spreadsheets and statistics. It even has its own programming language that you can use to add extra functionality of your own. Although you can use the default interface that comes with Xcas, you also can link the CAS (Computer Algebra System) engine as a shared library to your own C++ code.
Packages are available for many different Linux distributions, but they usually aren't available via the default package management systems. For example, in Ubuntu, you need to add an APT source that points to the home page for Xcas. Then you can use the following to install it on your system:
sudo apt-get install giac python-giacpy
Once it is installed and you start it up, Xcas asks what mode you want to work in. You can select from spreadsheet, CAS, programming or geometry. Whenever you start a new session within Xcas, you get this same initial interface. If you want to change it later, select the Cfg→General Configuration menu option. This pops up a new window where you can select the Level option. If you choose the CAS option, you get the starting window shown in Figure 1.
Figure 1. This the opening window in CAS mode.
To open a new tab with the same level, click the File→New Session menu item. You also can open a new tab using any of the available levels, or modes, using menu commands. They are a bit hard to find though. For example, you can get a new spreadsheet with the Spreadsheet→New Spreadsheet menu item.
There is far too much functionality available within Xcas to explain how everything works in such a short article, but I'll try to cover some of the most interesting parts.
Let's start by looking at the command level. This operates in a form similar to the worksheet in Maple or Mathematica. You start with the first empty command line and enter the mathematical expression you want to evaluate. Pressing Enter runs the command, displays the output in a new pane, and creates a new command line and drops the cursor there, ready for your next command. This style should be comfortable to anyone with even a little bit of experience.
The keyboard panel at the bottom of the window gives you a selection of common elements that you will likely use within your commands. If you don't need to use it, you can remove that pane by clicking the Kbd button at the top of your session window.
The library of available commands is very large. Luckily, you can find the majority of them by clicking on the Cmds menu item. Here, you can find sections for several different areas, such as complex numbers, group theory, calculus or probability.
No system has everything that you may possibly need when you start doing any kind of scientific computing. This means that you need to be able to add new functionality of your own devising. With Xcas, you can create a new function by clicking on the Prg→New program menu item. This pops up a new window where you can define the name, arguments, locals and a return value. Once you are happy with these settings and click the OK button, you will get a new program pane with a template ready for you. You then can add in any other code that is required by your new functionality.
Figure 2. You can create your own functions in Xcas.
There are menu options within the programming pane to help you with the syntax of programming structures, such as loops, conditionals and IO. In Xcas, functions need to be compiled before they can be used. This compiling step happens when you click the OK button in the programming pane. If there are any errors, you will get a message in the output pane. If there are no errors, you will get a "Success compiling" message.
You can include graphics inline within a session. If you want a general graphics pane, click the Geo→New figure 2d or Geo→New figure 3d menu item. This gives you a graphics pane along with an associated command pane where you can enter the plotting commands you want drawn. If you have a specific item drawn, you can select one of the other items in the Geo menu section. For example, if you want to graph a function, you can go to Geo→Graph→Function. This pops up a new window where you can enter the function you want to graph, along with the limits of the independent variable. When you click OK, you get the graph drawn inline within your current session.
Figure 3. Graphing functions is pretty easy.
Figure 4. Graphs show up inline within your session.
Xcas is designed to be reasonably good at interacting with other CAS software. With this idea in mind, it is no surprise that you can import and export worksheets using several different formats. Xcas will handle Maple and Mu PAD file formats fairly well. It also can handle the file format used by TI calculators (like the TI-89 or the Voyage 200). With this type of support, you should be able to share your work with many other people.
With Xcas, you can work on almost any system that you have access to. You can use your Linux system to do major amounts of work, and then you can continue that work on your Android or Apple device, or even use your Texas Instruments calculator. Although the interface is a bit confusing, and the learning curve is rather steep, there is no denying just how powerful Xcas is.
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