User Interface Design for Geometrical Decomposition Algorithms in Maple

As computer algebra develops, it handles more sophisticated objects, many of which have no precise parallel in conventional mathematics, since mathematicians have handled the concepts on an ad hoc basis. Furthermore, by definition, computer algebra must handle these objects algorithmically, and present them to the user. This is particularly a challenge when the user may not be intimately familiar with the object, and all the special cases that may occur. We present various issues connected with this in the context of equation solving, and show how the ’piecewise’ construct of Maple [3] can be employed to build representations of solution objects that: 1. Are intuitive in simple cases; 2. Use familiar base constructs; 3. Allow ‘delayed evaluation’ of difficult special cases, which the user may not actually be interested in.