Notations for Active Mathematical Documents

Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent throughout the document and with their own prior publications. In print media where notations are fixed at publication time, this is an over-constrained problem. In active documents notations can be adapted at reading time, taking reader preferences into account. We present a representational infrastructure for notations in active mathematical documents. Mathematical notations can be defined declaratively. Author and reader can extensionally define the set of available notation definitions at arbitrary document levels, and they can guide the notation selection function via intensional annotations. We discuss the management of these declarative specifications with focus on the creation and maintenance of notations. Finally, we describe several interconnected implementations of the various notation-related aspects of active documents.