Simplification in Maple and the Risch Structure Theorem

			      (Abstract)

		    Petr Lisonek, Michael Monagan

		   CECM Colloqium, October 22, 1997



This talk is concerned with methods of simplification of algebraic expressions
and with the implementation of these methods.  In the first part 
of the talk we explain how simplification is currently done in Maple
and we point to limitations of this approach and its design flaws.  
In the second part we propose a different approach and discuss it
on examples of specific classes of expressions (functions).
In particular, we recall the Risch Structure Theorem for the elementary
functions and explain how it can be used for simplification of expressions
containing elementary functions.  (The Risch Structure Theorem
is an important part of the Risch Integration Procedure for the indefinite
integration of elementary functions.)