An extension to MACSYMA's concept of functional differentiation

ABSTRACT

An important attribute that any symbolic mathematics program should have is that the user should be able to differentiate an arbitrary function of arbitrary arguments, and do so in a manner that is natural to him or her. Obtaining solutions to many types of problems does not require a complete implementation of this concept, but there will always be applications which will be difficult or even impossible to perform if some feature is missing. In this paper, we shall discuss some of the limitations of the implementation of symbolic differentiation in MACSYMA [2]. In particular, we shall consider some major weaknesses in the functional dependencies approach employed by the MACSYMA differentiator, and then present a method (in the form of a simple modification to the DIFF function) of how we attempted to eliminate these difficulties. Finally, we shall include a set of applications that can be done more naturally with our modifications than was possible in the current version of MACSYMA.

REFERENCES

• 1: G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Springer-Verlag, New York, 1974.
• 2: MACSYMA Reference Manual, Version Ten, The Math-Lab Group, Laboratory for Computer Science, MIT, 1983.
• 3: S. Steinberg, Symmetry operators, Proceedings of the 1979 MACSYMA Users's Conference, edited by V. Ellen Lewis, Washington, DC, 408--444.
• 4: S. Steinberg and P. J. Roache, Symbolic manipulation in computational fluid dynamics, To appear in the Journal of Computational Physics.
• 5: S. Steinberg, Change of variables in partial differential equations, in preparation.