Analysis of Mathematica 7 Symbols and Functions

By Nasser M. Abbasi
Updated November 17,2009

Introduction

The following is quantitative analysis of Mathematica 7.0 in terms of what functions and symbols it contains. This includes all the AddOns package which come with Mathematica7.0 outside of the kernel and have to be loaded to be used. These packages are standard packages that come with Mathematica, but are not inside the kernel itself.

Finding a list of just the functions (i.e. not just Symbols) is a bit tricky.  This is how this information is found: Call SyntaxInformation[] on each symbol, and look for the result. If the result is non-empty, then this symbol is a Function, else it is not.  This is becuase for any function say Cos[], SyntaxInformation[Cos] will return {ArgumentsPattern -> {_}} and for anything else, the empty list {} is returned.

For finding which symbols are functions when looking at the AddOns packages, a different approach from the above is used. In this case, the usage message for each symbol is printed and saved to a text file. Then this file is read and each line is parsed to look for a pattern where the line starts with a name followed immediatly by a "]". If this pattern is found, then the "name" is considered a function name.

Thanks for John R. Fultz for suggesting in the Math group to use SyntaxInformation[] and the Usage message to help determine which Symbols are functions and which are not.

Table showing number of Symbols in System and all other AddOns Packages

Finding the functions in System and all other AddOns packages

We be in the same folder as the data file, this command below changes directories so that the current directory becomes the same as where this notebook is saved. Which should be also the same folder where this text file is.