A term rewriting system for the calculus of moving surfaces

Authors:
Mark Boady;Pavel Grinfeld;Jeremy Johnson
Affiliations:
Drexel University, Philadelphia, PA, USA;Drexel University, Philadelphia, PA, USA;Drexel University, Philadelphia, PA, USA
Venue:
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Year:
2013

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Abstract

The calculus of moving surfaces (CMS) is an analytic framework that extends the tensor calculus to deforming manifolds. We have applied the CMS to a number of boundary variation problems using a Term Rewrite System (TRS). The TRS is used to convert the initial CMS expression into a form that can be evaluated. The CMS produces expressions that are true for all coordinate spaces. This makes it very powerful but applications remain limited by a rapid growth in the size of expressions. We have extended results on existing problems to orders that had been previously intractable. In this paper, we describe our TRS and our method for evaluating CMS expressions on a specific coordinate system. Our work has already provided new insight into problems of current interest to researchers in the CMS.