Processing Textbook-Style Matrices

In mathematical textbooks matrices are often represented as objects of indefinite size containing abbreviations. To make the knowledge implicitly given in these representations available in electronic form they have to be interpreted correctly. We present an algorithm that provides the interface between the textbook style representation of matrix expressions and their concrete interpretation as formal mathematical objects. Given an underspecified matrix containing ellipses and fill symbols, our algorithm extracts the semantic information contained. Matrices are interpreted as a collection of regions that can be interpolated with a particular term structure. The effectiveness of our procedure is demonstrated with an implementation in the computer algebra system Maple.