
RealHyp/:


This directory contains the files relevant to Ch 5 of the paper.

The first file  <relations>,  does all the computations from
Ch 5.2 in the paper.  This file is not called by any other
files and does not call any other files.  It is completely
isolated.



The file <algebra> contains the basic algebraic routines
used be the other files.  Each routine (or small
group of routines) is followed by a routine which
checks that it is correct.


The file <group_elements> defines the group elements relevant
to Ch. 5.2.  The first few lines are a repeat from the
file <relations>.  Two kinds of elements are defined:
the halfturn pairings and the auxilliary commuting
halfturns.  Each halfturn pairing commutes with one of
the auxilliary pairings.  

The significance of the auxilliary elements is as follows:
We do not have a routine which computes the action of a
mobius transformation on H^3.  Rather we represent a
point in H^3 as the intersection of two geodesics.  We
then move around the geodesics (by their endpoints) and
recompute the intersection point as necessary.  In
all cases we will choose for our geodesics the fixed
axes of commuting halfturns.   The corresponding points
in H^3 are the points of symmetry discussed in Ch 5.3.



The file <special points> defines all the special points
from Ch 5.3.  Needless to say, it uses the files
<group_elements> and <algebra>.



The file <tiles> defines the tiles from Ch 5.3.  It also
contains some routines for plotting the tiles both
in Mathematica and in tcl.  We plot in tcl for the
purposes of exportation.  The <tiles> file is the
only one the user really needs to use in order to
see pictures.  Just load it into Mathematica.  Assuming
that one of the plotting commands is uncommented, you
will see a picture of a tile or a tiling.




The file <out_to_tcl> is a date file, outputted from <tiles>
when the tcl routines are invoked.  
The file <tcl_plotter> is the tcl plotter which plots the
date in <out_to_tcl>.



The file <aux_plots> makes a few auxilliary plots and
calculations, which serve as sanity checks for the
other programs in this directory.
