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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
as
infinite module over
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].

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