Mathematica: A System of Computer Programs

Mathematica is a powerful application package for doing mathematics and is used almost in all branches of science. It has widespread applications ranging from quantum computation, statistical analysis, number theory, zoology, astronomy, and many more. Mathematica gives a rich set of programming extensions to its end-user language, and it permits us to write programs in procedural, functional, or logic (rule-based) style, or a mixture of all three. For tasks requiring interfaces to the external environment, mathematica provides mathlink, which allows us to communicate mathematica programs with external programs written in C, C++, F77, F90, F95, Java, or other languages. It has also extensive capabilities for editing graphics, equations, text, etc. Starting from the basic level of mathematica here we illustrate how to use a mathematica notebook and write a program in the notebook. Following with this, we also describe very briefly about the importance of the local and global variables those are used in writing programs in mathematica. Next, we investigate elaborately the way of linking of external programs with mathematica, so-called the mathlink operation. Using this technique we can run very tedious jobs quite efficiently, and the operations become extremely fast. Sometimes it is quite desirable to run jobs in background of a computer which can take considerable amount of time to finish, and this allows us to do work on other tasks, while keeping the jobs running. The way of running jobs, written in a mathematica notebook, in background is quite different from the conventional methods i.e., the techniques for the programs written in other languages like C, C++, F77, F90, F95, etc. To illustrate it, in the present article we study how to create a mathematica batch-file from a mathematica notebook and run it in the background. Finally, we explore the most significant issue of this article. Here we describe the basic ideas for parallelizing a mathematica program by sharing its independent parts into all other remote computers available in the network. Doing the parallelization, we can perform large computational operations within a very short period of time, and therefore, the efficiency of the numerical works can be achieved. Parallel computation supports any version of mathematica and it also works significantly well even if different versions of mathematica are installed in different computers. All the operations studied in this article run under any supported operating system like Unix, Windows, Macintosh, etc. For the sake of our illustrations, here we concentrate all the discussions only for the Unix based operating system.