Abstract
This chapter highlights the problems and difficulties currently faced in the area of mathematical software. These problems cover the broad range from a lack of fundamental knowledge and scientific know-how to organizational problems and low professional status. Part of the reason for a shortage of good mathematical software is that the creation of such programs has not been identified as a high-status activity that requires expert and professional talent. It has not been identified as a separate, independent activity. The chapter describes the objectives of algorithm construction and discusses some of the problems that arise in this scenario. There are nine desirable characteristics of mathematical software: reliability, flexibility, simplicity of use, modularity, reasonable diagnostics, common sense, good documentation, efficiency, and transportability. There are direct conflicts between some of these objectives. The essence of mathematical software construction is to achieve a reasonable balance while optimizing with respect to two or three of these objectives.
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