Multivalued Elementary Functions in Computer-Algebra Systems

Abstract

An implementation (in Maple) of the multivalued elementary inverse functions is described. The new approach addresses the difference between the single-valued inverse function defined by computer systems and the multivalued function which represents the multiple solutions of the defining equation. The implementation takes an idea from complex analysis, namely the branch of an inverse function, and defines an index for each branch. The branch index then becomes an additional argument to the (new) function. A benefit of the new approach is that it helps with the general problem of correctly simplifying expressions containing multivalued functions.