Describing texts for algorithms: how they prescribe operations and integrate cases. Reflections based on ancient Chinese mathematical sources

Résumé En

An algorithm has two facets. It has a text —a written text—, which usually appears to be an enumerated list of operations. In addition, whenever an algorithm is applied to a specific set of numerical values, practitioners derive from its text a sequence of actions, or operations, to be carried out. In the execution of the algorithm, these actions generate events that constitute a flow of computations eventually yielding numerical results. This chapter aims mainly to develop some reflections on the relationship between these two facets: the text and the different sequences of actions that practitioners derive from it. Two tools prove useful in developing the argumentation. Firstly, the author uses the description of textual enumerations, as developed by Jacques Virbel, to find out how enumerations of operations were carried out in the text of algorithms and how these enumerations were used. This approach deals with the text of the algorithm as text. Then the chapter focuses on the language acts carried out in some of the sentences composing the texts, since, when prescribing operations, the texts of the algorithms differ in that they use distinct ways of carrying out directives.