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022 - Programming Principles for Visualisation in Mathematical Research

Abstract

We describe programming principles for visualization under development at the University of Warwick. These exploit systems of definitions - resembling the formulae that define the values of cells in a spreadsheet - to specify the structure and interrelationship between mathematical images such as Hasse and Cayley diagrams. The use of a prototype visualization system incorporating the definitive (ie "definition-based") notations ARCA and DoNaLD - for graphics - and SCOUT - for screen layout - is illustrated using a specific mathematical research problem involving combinatorial analysis of planar arrangements of lines. We briefly discuss the practical potential of our methods and possible directions for further development.

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