XPost: sci.math   
   From: hrubin@skew.stat.purdue.edu   
      
   On 2014-08-28, IV  wrote:   
   > "Richard Fateman"  wrote in news:ltg6uo$28p$1@speranza.aioe.org...   
   >>>> No.   
   >>> How we do it by hand: If we use the inverse operation (inverse function)   
   >>> of the outer function in each step. (The roots of algebraic functions   
   >>> can be determined numerically or symbolically - e.g. by the Buchberger   
   >>> algorithm.)   
   >>> How is that realized in computer algebra systems, and how   
   >>> powerful/complete are this methods/algorithms?   
   >> How does your method work for solving for x in    exp(x)=log(x) ?   
   > With LambertW.   
   > I see, the inverse function of a Real Elementary function somehow composed   
   > from the Real Elementary Standard functions is not necessarily an Elementary   
   > function.   
   > One must define previously all inverse functions that are required. Is this   
   > possible? Are there studies on this? Or is it nonsense?   
      
   The inverse of an elementary function is an elementary function.   
      
   The solution of an equation expressed with elementary functions   
   is not, in general, an elementary function.   
      
      
   --   
   This address is for information only.  I do not claim that these views   
   are those of the Statistics Department or of Purdue University.   
   Herman Rubin, Department of Statistics, Purdue University   
   hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558   
      
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