Detecting Implicit Indeterminates in Symbolic Computation

In the design of symbolic mathematical computation systems, it is a popular choice to use the same syntax for both mathematical indeterminates and programming variables. While mathematical indeterminates are to be used without specific values, programming variables must be initialized before being used in expressions. A problem occurs when mistakenly uninitialized programming variables are silently taken to be mathematical indeterminates. This article explores how this problem can arise and its consequences. An algorithm to analyze programs for this defect is shown along with a Maple implementation.