An Implementation of Unary Pairfunctions Using the Reverse Polish Notation
by
Predrag V. Krtolica
University of Nis, Nis, Yugoslavia
Coauthors: Predrag S. Stanimirovic (University of Nis)

In [6] the semigroup of unary pairfunctions is defined and implemented using MAPLE . In this paper, an implementation of these unary pairfunctions is described using the symbolic manipulations based on reverse Polish notation. Appropriate extensions of the known algorithms (see [1], [5]) for the transformation of the input expression to the corresponding reverse Polish presentation and vice versa are introduced. Also, the algorithm for direct transformation of the reverse Polish notation of the input expression into the reverse Polish notation of the resulting expression is developed. This algorithm is based on the properties of the reverse Polish notation investigated in [4].

[1]

Gries, D., Compiler Construction for Digital Computers, John Wiley & Sons, Inc., New York, London, Sydney, Toronto, 1971.

[2]

Iri, M., History of Automatic Differentiation and Rounding Error Estimation, Automatic Differentiation of Algorithms: Theory, Implementation, and Application , Proceedings of the first SIAM Workshop on Automatic Differentiation, Breckenridge, Colorado, January 6-8, eds. Andreas Griewank and George F. Corliss, 1991; 3-16.

[3]

Iri, M. and Kubota, K., Norms, Rounding Errors, Partial Derivatives and Fast Automatic Differentiation, IEICE transactions E 74 no. 3 (1991), 463-471.

[4]

Krtolica, P. V. and Stanimirovi\'c, P. S., On Some Properties of Reverse Polish Notation, FILOMAT 13 (1999), to appear.

[5]

Tremblay, J.-P. and Sorenson, P.G., The Theory and Practice of Compiler Writing , McGraw-Hill Book Company, New York, 1985.

[6]

Wald, B., The Semigroup of Unary Pairfunctions, Verification of the Group Relations, MapleTech 4 (1997), 51-54.

Date received: March 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caec-03.