Bill Casselman's Servlet Page

The PrintServlet

The PrintServlet is a servlet which allows certain applets on this server to get a printed version of themselves. Eventually, the package will be made publicly available, and should be easy to port to other servers. In particular, writing applets that use it should be extremely simple, and will require no understanding of servlets. At the moment it has been run only with ApacheJServ running as an extension of the Apache server.

This project involves three basic Java programs: (1) the PrintableApplet, an abstract class requiring a method toHTML(); (2) the HttpMessage class from the book Java Servlets Programming (Jason Hunter with help from William Crawford, published by O'Reilly); (3) the PrintServlet, which receives printing requests from a PrintableApplet and then displays a printable version of the applet on a new browser window.

A sample printable applet

Source code: (1) PrintableApplet.java; (2) TestPrint.java (a sample PrintableApplet) (3) PrintServlet.java

An Internet spreadsheet

One of the most interesting applications of the PrintServlet will be used to allow users of the Internet spreadsheet being developed by David Austin and myself to get printed output from the spreadsheet.

The Coxeter group servlet

There are several programs which allow one to work with Coxeter groups and in particular to calculate Kazhdan-Lusztig polynomials.

The symbolic program GAP can also calculate KL polynomials to a limited extent, but it is terribly slow. On the other hand, the output can be integrated easily with other data from the GAP interpreter.
Mark Goresky wrote a well known one in Pascal somewhat later, and although his program is rather slow, it was the first to provide widely circulated data (in the well know "Green Book"). He has made these data available for several groups, including a few affine Coxeter groups that were not accounted for in the original distribution.
The original efficient program for this purpose was written by Dean Alvis, I believe in FORTRAN, but does not seem to have been made publicly available. Its greatest accomplishment was to verify that the Kazhdan-Lusztig polynomials for the group H4, which is not associated to a flag manifold, have non-negative coefficients. Even nowadays calculating the KL polynomials for H4 is a highly non-trivial achievement. The cause of the difficulty is that although the group is not large (14,400 elements), the length of its longest element is quite large, which means that the recursive calculation of KL polynomials is tedious.
The most notable one is the program coxeter developed by Fokko DuCloux, written originally in C and then rewritten in C++. It is ridiculously fast and publicly available, compiles easily on most computers, and has output which is convenient for humans to read. Its worst drawbacks are that it deals only with finite Coxeter groups, that the output is not so easy to scan by computer, and that it is difficult to modify.

I have written a suite of programs in Java that will calculate various things about Coxeter groups. They are a bit slower than DuCloux's program, but still fairly efficient, and at the moment wasteful in memory use. Eventually they should be modular enough to be easily incorporated into other Java programs, but that is not so at the moment. They will, at any rate, work for any Coxeter group described by its Coxeter matrix, as well as for any root system described by its Dynkin diagram. They are at the moment too cumbersome to be run as an applet except for rather small groups, but in the near future I will collect output for various groups at this site. These would be convenient to have available in HTML format, so one could locate data by traversing hypertext links, but the HTML files for even a small group would to large to allow this (several megabytes for F4, for example). On the other hand, the basic data files are quite small. So I intend to write a collection of applets and servlet which will provide the data as a simulated HTML file (or set of such files), which should be almost as useful in allowing one to navigate the data - chasing around the W-graph, for example.