Introduction

  Experimentation has a distinguished tradition in mathematical research. Experiments often play an important role in formulating new conjectures and discovering paths toward the proof of such conjectures and of other results. As computational resources have become more powerful in recent years, this domain of activity is growing into a mathematical field in its own right, called experimental mathematics. There is a perceived need for a standardization so that experiments made by one researcher can be repeated or modified by others with minimal effort.

The Oorange project is a response to this challenge. It is an initiative of the Sonderforschungsbereich 288 of the Technical University Berlin, "Differential Geometry and Quantum Physik". The project development commenced in September 1994, the first beta version was release Christmas 1995, and Version 1.0 is slated for release in October 1996. We postpone an account of previous work until Section 5 in order first to introduce the terminology in which comparisons and historical influences can be expressed.

The key impulse behind the project is to create a framework for experimental mathematics that is appropriate to the contents of this science. Since the field of experimental mathematics is modeled on the traditional models of physical sciences, we found it useful to maintain the correspondences to that realm. With this in mind, the following seven-fold subdivision of a mathematical experiment is helpful:

Object of study: High level software classes

Laboratory equipment: Foundation software classes and function libraries

Configuration of specific experiment: Computational network composed of objects

Monitor and control: Object inspection; 2D and 3D viewers

Running the experiment: Animation objects

Recording the experiment: Archiving and scripting

Disseminating result: Documentation

The correspondence to traditional experimental practice is only approximate; significant differences arise from the non-physical nature of software. For example, there is a further level of design necessitated by the fact that there is no physical laboratory to hold all these components. Oorange is accordingly organized as a virtual laboratory, which presents a unified user interface integrating all the above components.

In order to motivate the detailed discussion of the components we first introduce the virtual laboratory.

Copyright © 1997 Sonderforschungsbereich 288, Differential Geometry and Quantum Physics, TU-Berlin