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Semantic analysis of matrix structures
 In ICDAR’05, p. 1141–1145. IEEE Computer Society
, 2005
"... The automatic interpretation of mathematical text structures has received only limited attention so far. While there has been work on the particularities of the character recognition of two dimensional formulas such as matrices in texts, very little has been done on exploiting their additional seman ..."
Abstract

Cited by 4 (2 self)
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The automatic interpretation of mathematical text structures has received only limited attention so far. While there has been work on the particularities of the character recognition of two dimensional formulas such as matrices in texts, very little has been done on exploiting their additional semantics in order to make them available for further processing. We present an algorithm that provides the interface between the recognition of matrix expressions and their concrete interpretation as mathematical objects. Given an underspecified matrix representation as they commonly appear in textbooks, 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 algorithm can be demonstrated by its ability to derive concrete instances for the processed matrix representations in a symbolic computation system. 1.
Computing with Abstract Matrix Structures
, 2009
"... Classes of matrices are often presented with symbolic dimensions using a mixture of terms and ellipsis symbols to describe their internal structure. While working with such classes of matrices is everyday mathematical practice, it has little automated support. We describe an algebraic encoding of ..."
Abstract

Cited by 3 (2 self)
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Classes of matrices are often presented with symbolic dimensions using a mixture of terms and ellipsis symbols to describe their internal structure. While working with such classes of matrices is everyday mathematical practice, it has little automated support. We describe an algebraic encoding of such matrices in terms of support functions and define the corresponding addition and multiplication algorithms. It is, however, nontrivial to retrieve the structural description of the matrix resulting from these operations. We therefore define an abstract matrix as an encoding of support function combinations that enables simple recovery of the structural properties. This allows us to define arithmetic algorithms for abstract matrices as extensions of those for support function combinations using a normalising term rewrite system.