Introduction

Algebraic or Symbolic computing is very different from the sort of numerical computing you have learned so far. Algebraic computing systems have been available for a long time, almost as long as the older conventional computer languages such as FORTRAN or ALGOL. Systems such as REDUCE or MACSYMA were available on mainframes in the 1960's as general purpose packages. There were also some specialist packages available for various branches of physics and mathematics, such as the program FORM which is widely used in theoretical particle physics (and is available free). With the development of PCs packages such as muMATH became available and more recently MAPLE and MATHEMATICA. In these lectures the examples will be drawn from MATHEMATICA but the discussion will be kept as general as possible.

The newer packages not only perform algebraic manipulations but have powerful built in numerical analysis and plotting capabilities. Most systems can be used as interpreters, with the commands typed in one by one with an instant (?) response, but many also include the possibility to define and run your own macros or procedures, so that they have many of the attributes of a conventional compiler as well.

As many of these packages were designed with different specialised criteria in mind, some packages are better for particular classes of problems than others.