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Oliver Goodman
Department of Maths and Stats University of Melbourne Parkville, Vic 3052 AUSTRALIA oag@ms.unimelb.edu.au |
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Oliver Goodman
Department of Maths and Stats University of Melbourne Parkville, Vic 3052 AUSTRALIA oag@ms.unimelb.edu.au |
Snap is a Unix program written in C++ for computing hyperbolic structures and invariants of hyperbolic 3-manifolds. It allows the user to work with a database of low-volume cusped and closed 3-manifolds. It is scriptable and produces graphical output in PostScript (2D) and Geomview format (3D). It is based on Jeff Weeks' program SnapPea and the powerful number theory package Pari.
Pariwrap C++ wrapper for the package
Pari. Pari is a calculator
and library of functions for doing all manner of useful
calculations. In particular it is able to do arithmatic in algebraic
number fields. Pariwrap tries to make Pari easier to use by defining a
class pari which can be manipulated almost like any other
built-in C type such as double. Now distributed as part of snap.
TightSpan Mathematica package for computing tight spans of finite metric spaces. The tight span of a metric space is (roughly) the smallest contractible path geodesic metric space into which the original space embeds isometrically. The package also contains Mathematica functions to compute intersections of half-spaces in any dimension and functions to compute the face lattice of a polytope. See the enclosed README for further details and references. tightspan1.0.tar.Z 17.6K.
Mathpad is an installable external package for Iris Mathematica users. Mathpad provides the user of Mathematica with interactive graphics, a facility which is missing from basic Mathematica. It contains two items: a program which runs alongside Mathematica with a window open in which graphics can be displayed, and a package which aids interaction with the graphics program. mathpad1.0.tar.Z 33.6K.
Hyperbolic.m Mathematica package for carrying out computations in n-dimensional hyperbolic geometry and displaying 2- and 3-dimensional results visually in a variety of models.
CirclePack.m Mathematica package to compute circle packings on geometric surfaces. Those interested in circle-packings should look at Ken Stephenson's much more extensive (UNIX/X-windows) package of the same name.
Geomview conformal model Designed and initially implementated Geomview's Poincare ball model view of hyperbolic 3-space. Geomview is a multi-purpose, multi-platform, free, geometric visualization program. One of its unique features is the ability to view geometric structures in spherical and hyperbolic geometry as well as the more familiar euclidean kind.
tube, an implementation of the
approach of Hodgson and Dowty to determining the hyperbolic Dehn
surgery space of a hyperbolic 3-manifold. In progress. tube.pdf (24k)
Commensurators of cusped hyperbolic manifolds with Heard and Hodgson. An algorithm for computing the commensurator of any non-arithmetic hyperbolic 3-manifold. Preprint. commens.ps (663k) commens.pdf (325k)
Computing Arithmetic Invariants of 3-manifolds with Coulson, Hodgson and Neumann. Describes the theoretical basis of the program snap. Experimental Mathematics 9:1 (2000) 127-152. snap.ps (150k) snap.pdf (239k)
Dehn's algorithm for non-hyperbolic groups with M. Shapiro. A modification of Dehn's algorithm solves the word problem in nilpotent and geometrically finite groups. Preprint. nhdehn_r.ps (138k) nhdehn_r.pdf (221k)
On the tight span of an antipodal graph A study of the tight span construction which provides a route to the computation of the homology a group. antipodal.ps (89k) antipodal.pdf (129k)
An algorithm for computing Andre'ev polyhedra A proof of Andre'ev's theorem and details of an algorithm for carrying out the construction. Preprint (1995). andreev.ps (77k) andreev.pdf (101k)
Metrized Laminations and Quasisymmetric Maps On Thurston's theory of earthquakes and measured laminations. This was my PhD. thesis. qsmap.ps (122k) qsmap.pdf (228k)
Check out my Java Aquarium.