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Symbolic Asymptotics : Functions of Two Variables, Implicit Functions

Bruno Salvy 1 John Shackell
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : A number of recent papers have been concerned with algorithms to decide the limiting behaviour of functions of a single variable. Here we make a corresponding study of a class of functions of two variables, namely the exp-log functions. As in the one-variable case, we need to make certain assumptions regarding the handling of constants. Two of the main tools in the one-variable case are Hardy fields and nested forms. Here, we show how to compute some asymptotic estimates for two-variable exp-log functions (modulo a constant oracle). This method is then used to give an algorithm for computing the nested forms of real implicit functions.
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Submitted on : Wednesday, May 24, 2006 - 1:47:30 PM
Last modification on : Friday, February 4, 2022 - 3:10:17 AM
Long-term archiving on: : Thursday, March 24, 2011 - 1:02:39 PM


  • HAL Id : inria-00073807, version 1



Bruno Salvy, John Shackell. Symbolic Asymptotics : Functions of Two Variables, Implicit Functions. [Research Report] RR-2883, INRIA. 1996. ⟨inria-00073807⟩



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