Term rewriting and all that
The Mathematica Book
Application of unspecified sequences in symbolic summation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Abstract matrices in symbolic computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
ACM Communications in Computer Algebra
Functional Decomposition of Symbolic Polynomials
ICCSA '08 Proceedings of the 2008 International Conference on Computational Sciences and Its Applications
SYNASC '08 Proceedings of the 2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Reasoning with Generic Cases in the Arithmetic of Abstract Matrices
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Annals of Mathematics and Artificial Intelligence
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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, non-trivial 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.