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Many functions in combinatorics follow simple recursive relations of the type F (n, k) = a n−1,k F (n − 1, k) + b n−1,k−1 F (n − 1, k − 1). Treating such functions as (infinite) triangular matrices and calling a n,k and b n,k generators of F , our paper will study the following question: Given two triangular arrays and their generators, how can we give(More)
Financial companies, engineering firms and even scientistscreate increasingly larger spreadsheets and spreadsheetprograms. The creators of large spreadsheets makeerrors and must track them down. One common class oferrors concerns unit errors, because spreadsheets often employformulas with physical or monetary units.In this paper, we describe XeLda, our tool(More)
The use of electronic spreadsheets as the primary software tool for teaching management science modeling techniques and quantitative methods in economics and finance undoubtedly played a key role in the increasing impact of quantitative lectures given in graduate programs. Researchers suggest that the ability to extract data from various sources and embed(More)
Many educational programming environments (e.g. Imagine) have facilities to enrich programs with music. In most cases, this programming constructs allow to play simple melodies. It is not easily possible to play more complex music either containing chords or polyphonic structures. On the other hand, some tools (like MSWLogo and FMSLogo) implement low level(More)
We present a new package which allows R to produce sound from data. The packages uses Csound, an extremely powerful and freely available multi platform program for sound creation. Sonification is a relatively new branch of data analysis, so even the basic set of concepts is still in flux. Our toolkit hopefully makes research into different options for(More)