within the next few weeks. Sorry if I don't explain some
or any of the terms I use).
Reading papers is easy ... Reading and Understanding papers is hard.
I currently have about a month (possibly more time but I'm using a
month for approximation purposes) to complete my thesis.
Needless to say, I somewhat underestimated how long it would
take me to get exactly what Casselman was saying in his papers.
Right now I can sum up where I am so far as this:
The key to building the Cayley Graph lies in being
able to do multiplication of a group element by a generator.
Casselman's first paper proposes a group multiplication algorithm
that uses some geometry , orderings, coset factorization ,
the Exchange property and a trick from du Cloux.
It is deeply recursive (and inefficient ) in some cases so even
though I have read about it and have a cursory
understanding of it, I won't be using it.
The other two papers do the group multiplication using a
Minimal Root Reflection Table (mrrt). Once you obtain a
Coxeter group's mrrt, group multiplication is relatively easy.
Note that the set of Minimal Roots is finite.
This doesn't say much about size, but it is a good thing.
So now where are we?
Build Minimal Root Reflection Table ->
Multiplication by generator ->
Build Cayley Graph.
One method for building the mrrt is explained in the
Automata paper. A 2nd is described in more detail in
Casselman's 2nd paper. Now I have two
choices -> Method 1 or Method 2.
The advantage of Method 1 is that if I choose it,
I'll be able to code it up before the semester ends.
It will probably take me all of the rest of the
semester (if not more time) to understand Method 2.
I have been lucky to have been furnished
with java source code from Casselman and so I would still be able
to build Cayley Graphs (even) after picking Method 2.
I have decided to take the risk of attempting
to use Method 2. The reason being that I started
reading Method 2's paper (because it contained some
details needed to implement Method 1) and
inadvertently read more than I intended to:
it wasn't as difficult to understand as I had originally thought.
So I'll be racing against time trying to juggle
my other classes, applications, transition to after-Laf-life,
and this project. I think I should be able to
finish in time though.