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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
Fateman, R.: Manipulation of matrices symbolically (January 9 2003), Available from http://http.cs.berkeley.edu/~fateman/papers/symmat2.pdf
Fitting, M.: First-Order Logic and Automated Theorem Proving. Springer, Heidelberg (1990)
Heck, A.: Maple Manuals, 3rd edn. Springer, Heidelberg (2003)
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1990)
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)
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)
Sexton, A., Sorge, V.: Semantic analysis of matrix structures. In: International Conference in Document Analysis and Recognition. IAPR (2005) (to appear)
Snyder, W.: A Proof Theory for General Unification, Birkhäuser. Progress in Computer Science and Applied Logic, vol. 11 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sexton, A., Sorge, V. (2006). Processing Textbook-Style Matrices. In: Kohlhase, M. (eds) Mathematical Knowledge Management. MKM 2005. Lecture Notes in Computer Science(), vol 3863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11618027_8
Download citation
DOI: https://doi.org/10.1007/11618027_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31430-1
Online ISBN: 978-3-540-31431-8
eBook Packages: Computer ScienceComputer Science (R0)