3.4 The algorithm of Traverso/Caboara

This algorithm is a clever way to put all the different computations of standard bases of ideals and modules and of their syzygies in a common hull. The main point is to think of an algebra $k[\underline{x}][\underline{y}]$ as infinite module over $k[\underline{x}]$ and to handle all computations in that context. Of course, module components are not variables and so one has to rewrite the normal form procedure to distinguish the variables. One obtains the advantage of having an ``automatic'' treatment of additional information, such as module components, module indices in resolutions or membership in minimal sets of generators. For a detailed description I would like to refer to [TC].