Most of the techniques presented in this paper cannot be easily and efficiently implemented within major existing CA system. This is especially true of honest plotting, direct manipulation, and Chains of Recurrences.
     Interval arithmetic, for example, requires a robust interval arithmetic extension for all functions which is usually not provided by existing CA systems. In addition, systems allowing addition of new functions by users should also allow users to specify the interval arithmetic extension of these user-defined functions. This is essential as honest plotting fails when the function to be plotted includes operators whose interval arithmetic extension is unknown.
     Direct manipulation requirements are twofold. Firstly, the representation used to display curves and surfaces should allow usual interactive manipulations such as moving, scaling, and rotating. Using Postscript, for instance, at this level (like Mathematica does) prevents such interactive manipulations. Then, allowing interactive study of family of surfaces requires a communication scheme between the CAS system and the graphics package which is both two-ways and efficient enough. Most system fail in these respects.
     The Chains of Recurrences method guarantees more efficient evaluations for expressions containing polynomials or trigonometric functions. Unlike evaluation methods based on interval arithmetic, the CR evaluation method can be used even with user-defined operators whose properties are unknown (although it might not be effective in those cases). However, to take fully advantage of the CR method it is necessary that a system either providers built-in primitives for evaluating CRs or allows user-programs to be compilable. Above all, it is essential that possibly large arrays of floats can be manipulated efficiently. Unfortunately, most CA system fail with respect to these criteria.
     On one other hand, these techniques could all immediately apply to mathematical assistants which only deal with a limited number of mathematical functions, and to larger CA system willing to systematically enforce support for interval arithmetic extensions and efficient manipulation of large arrays of floats.