Bio

Rafael G. Gonzalez-Acuña studied Industrial Physics Engineering at the Tecnologico de Monterrey and received a master’s degree in Optomechatronics at the Optics Research Center, A.C. He is currently working toward his PhD at the Tecnologico de Monterrey. His doctoral thesis focuses on the design of free spherical aberration lenses.

Computational Essay: The Cartesian oval collimator

Project: Subexpression identification algorithm for very large symbolic expressions

Goal

When symbolic expressions are very large, they are incomprehensible to most human beings. In this work, we present an algorithm that identifies common subexpressions and replaces them with characteristic variables such that it is easier to grasp the overall structure of the original expression as well as provide insight into the components of the subexpressions. The subexpressions employed are not trivial and themselves may under go this substitution.

Summary of Results

We have tested our algorithm on several large expressions, and we got the expected results. The algorithm divides the expression in several subexpressions, and when subexpressions are substituted into the original expression, this one gets more legible for the reader.

Future Work

The next step in this research is to get an automated intelligent way to choose the level of minimum possible deepness and the minimum reps for the each subexpression to be considered in the substitution of the expression.