A program that computes limits using heuristics to evaluate the indeterminate forms

摘要

The object of this work is to find the limit of an expression ƒ(x) as the variable x approaches a value x0, finite or not, and when replacing x by x0 does not allow us to compute this limit. This is a case-study in the fields of theorem-proving and of formula manipulation.Using canonical forms, the program is able to operate on polynomials inside the expression, to use finite MacLaurin's series and to compare powers with exponentials or logarithms. Unfortunately, this is not always sufficient because some expressions have to be transformed one or several times before these methods can succeed. Then the program will use heuristics to find the best transformation to apply to the given expression. The expression will be transformed as many times as necessary until the methods can give the solution.