×

Abstracting symbolic matrices. (English) Zbl 1280.68300

Summary: We present a procedure that allows the abstraction of elements in concrete symbolic matrices to obtain a more compact representation employing ellipses in order to expose homogeneous regions present in a matrix. We furthermore extend that procedure to allow for generalisations of concrete matrices to an abstract form that enables us to determine the generic type of a given matrix. The presented algorithms employ artificial intelligence techniques such as pattern recognition and constraint solving.

MSC:

68W30 Symbolic computation and algebraic computation
68T10 Pattern recognition, speech recognition
15A99 Basic linear algebra

Software:

Maple; Mathematica
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Almomen, R.: Abstracting symbolic matrices. Master’s thesis, School of Computer Science, University of Birmingham (2010)
[2] Maplesoft: Maple User Manual. Maplesoft (2011)
[3] Murdoch, D.J., Chow, E.D.: A graphical display of large correlation matrices. Amer. Statist. 50, 178–180 (1996)
[4] Plotkin, G.D.: A note on inductive generalization. In: Proc. of the Fifth Annual Machine Intelligence Workshop, Machine Intelligence 5, pp. 153–163, Edinburgh University Press (1970) · Zbl 0219.68045
[5] Sexton, A.P., Sorge, V.: Abstract matrices in symbolic computation. In: Proceedings of ISSAC 2006, pp. 318–325. ACM Press (2006) · Zbl 1151.68674
[6] Sexton, A.P., Sorge, V., Watt, S.M.: Computing with abstract matrix structures. In: Proc. of ISSAC’2009, pp. 325–332. ACM Press (2009) · Zbl 1237.68261
[7] Sexton, A.P., Sorge, V., Watt, S.M.: Reasoning with generic cases in the arithmetic of abstract matrices. In: Proc. of Calculemus 2009. LNAI, vol. 5625, pp. 138–153. Springer (2009) · Zbl 1247.68327
[8] Wolfram Research, Inc.: Mathematica Edition: Version 8.0. Wolfram Research, Inc. (2010)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.