A constructor as defined in Axiom is called an abstract datatype in the computer science literature. Abstract datatypes separate ``specification'' (what operations are provided) from ``implementation'' (how the operations are implemented). The Exports (specification) part of a constructor is said to be ``public'' (it provides the user interface to the package) whereas the Implementation part is ``private'' (information here is effectively hidden---programs cannot take advantage of it).
The Exports part specifies what operations the package provides to users. As an author of a package, you must ensure that the Implementation part provides a function for each operation in the Exports part.The DrawComplex package enhances the facility described in Chapter ugIntProgCompFuns by allowing a complex function to have arrows emanating from the surface to indicate the direction of the complex argument.
An important difference between interactive programming and the use of packages is in the handling of global variables such as and . In interactive programming, you simply change the values of variables by assignment. With packages, such variables are local to the package---their values can only be set using functions exported by the package. In our example package, we provide two functions setRealSteps and setImagSteps for this purpose.
Another local variable is which can be changed using the exported operation setClipValue. This value is referenced by the internal function clipFun that decides whether to use the computed value of the function at a point or, if the magnitude of that value is too large, the value assigned to (with the appropriate sign).