A package for symbolic solution of real functional equations of real variables (Q1364863)

The authors describe a Mathematica package for the solution of functional equations. Solving functional equations is a tricky business. Most people working in the field have a bagful of equations whose solution is known and a bag of tricks (methods to reduce to these and thus solve other equations), nobody knows everything. Computers have better memories, so they can help if well programmed. The authors start with a database of ``the most important functional equations and their solutions for different domains and classes''. They also list ten methods of solution. While their names sound pretty general, in this reviewer's opinion this is an aspect which may need strengthening and considerably more work. At several places, e.g. p. 185, the authors speak about the ``same'' equation on different domains. This concept would have to be defined exactly. Another approach would be to ``computerize'' known solution methods for very large classes of equations. Several of these are algebraic or functional analytic, so there would be no need to restrict oneselves to real functions as the authors do. Examples of such methods are those of \textit{E. Vincze} [Publ. Math. 9, 149-163, 314-323 (1962); 10, 191-202, 283-318 (1963; Zbl 0125.35803)] and of \textit{L. Székelyhidi} [Convolution type functional equations on topological abelian groups (1991; Zbl 0748.39003)]. The first steps towards computerization of a generalization of the latter (in Maple) were made by \textit{A. Gilányi} [Charakterisierung von monomialen Funktionen und Lösung von Funktionalgleichungen mit Computern, Univ. Karlsruhe (1995)].