MKM 2005: Mathematical Knowledge Management pp 111-125

# Processing Textbook-Style Matrices

• Alan Sexton
• Volker Sorge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3863)

## Abstract

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.

## Keywords

Interpolation Function Input Matrix Concrete Term Mathematical Text Weighted Directed Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
Char, B.W., Geddes, K.O., Gonnet, G.H., Leong, B., Monagan, M.B., Watt, S.M.: Maple V: Language Reference Manual. Springer, Heidelberg (1991)Google Scholar
2. 2.
Fateman, R.: Manipulation of matrices symbolically (January 9 2003), Available from http://http.cs.berkeley.edu/~fateman/papers/symmat2.pdf
3. 3.
Fitting, M.: First-Order Logic and Automated Theorem Proving. Springer, Heidelberg (1990)
4. 4.
Heck, A.: Maple Manuals, 3rd edn. Springer, Heidelberg (2003)Google Scholar
5. 5.
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1990)
6. 6.
Kanahori, T., Suzuki, M.: A recognition method of matrices by using variable block pattern elements generating rectangular areas. In: Blostein, D., Kwon, Y.-B. (eds.) GREC 2001. LNCS, vol. 2390, p. 320. Springer, Heidelberg (2002)Google Scholar
7. 7.
Pollet, M., Sorge, V., Kerber, M.: Intuitive and formal representations: The case of matrices. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 317–331. Springer, Heidelberg (2004)
8. 8.
Sexton, A., Sorge, V.: Semantic analysis of matrix structures. In: International Conference in Document Analysis and Recognition. IAPR (2005) (to appear)Google Scholar
9. 9.
Snyder, W.: A Proof Theory for General Unification, Birkhäuser. Progress in Computer Science and Applied Logic, vol. 11 (1991)Google Scholar