Symbolic Asymptotics: Functions of Two Variables, Implicit Functions

This work is part of a global effort to automate the formal aspects of asymptotic expansions. It is possible to mechanize some techniques of asymptotics and build a computer algebra toolbox of these. A lot of work in symbolic asymptotics follows this approach and most existing facilities for asymptotic expansions in computer algebra systems have been obtained in this way. An alternative approach aims at studying the asymptotics of whole classes of problems, investigating all the possible asymptotic scales that may occur. The main tools here are nested forms and expansions, zero-equivalence methods and the theory of Hardy fields. The present paper follows this path. Nested forms and nested expansions were introduced by Shackell (1993a). A formal definition is given in Section 1. An example of a nested form is

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