This directory contains the Mathematica packages for Hypercad, plus
some example packages for use with Hypercad.  Hypercad itself
consists of the files Hypercad.m, RH2.m, and Complex.m.  All the
other files are examples which use Hypercad.

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Hypercad.m:
	The main Hypercad file.  This file defines the interface
	with the graphics program.

RH2.m:
	Hyperbolic plane computation package.  This can be used
	independently from Hypercad.	

Complex.m:
	Complex numbers package; RH2.m uses this.

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Pencil.m:
	Functions for computing and drawing hyperbolic pencils.

Triangle.m:
	Functions for computing and drawing equilateral triangles.

Parallels.m:
	Functions for computing and drawing lines through a point
	which do not intersect a given line; illustrates the fact
	that Euclid's fifth postulate does not hold in hyperbolic
	geometry.

GroupTheory.m:
	Package for enumerating free groups and semigroups.

Dirichlet.m:
	Package for computing the Dirichlet region of an
	array of points.


Tessellations.m.tpl:
	Template for Tessellations.m, a package for computing discrete
	group tessellations.  This file is distributed in template
	form because it needs to know the exact pathname of the
	'separate' executable.  Use the Makefile to create a copy
	Tessellations.m containing the pathname appropriate for your
	system.

Beardon.m:
	This file contains various functions for interactively
	verifying/illustrating some of the theorems in chapter 7 of
	Beardon's book "The Geometry of Discrete Groups" (Springer).
	It is by no means complete and is not documented; I used it as
	a test for Hypercad and am distributing it simply for the
	benefit of those who might like to play with it.

