A computer algebra user interface manifesto

Abstract

Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and allowing easy fine grain control over the form of the result -- even by amateurs. This wizard integrates ideas including: flexible subexpression selection; complete control over the ordering of variables and commutative operands, with wellchosen defaults; interleaving the choice of successively less main variables with applicable function choices to provide detailed control without incurring a combinatorial number of applicable alternatives at any one level; quick applicability tests to reduce the listing of inapplicable transformations; using an organizing principle to order the alternatives in a helpful manner; labeling quickly-computed alternatives in dialog boxes with a preview of their results, using ellipsis elisions if necessary or helpful; allowing the user to retreat from a sequence of choices to explore other branches of the tree of alternatives -- or to return quickly to branches already visited; allowing the user to accumulate more than one of the alternative forms; integrating direct manipulation into the wizard; and supporting not only the usual input-result pair mode, but also the useful alternative derivational and in situ replacement modes in a unified window.