AF: Small: Solving and Simplifying Algebraic, Differential, and Difference Equations.

Florida State University, Tallahassee FL

Investigators

Abstract

Problems in science are often reduced to mathematical equations. There are many computer programs for solving various types of equations. The equations themselves often come from computer computation, so they can be large. This project aims to simplify large equations, reducing them when possible to smaller ones that can be solved more easily. When computers construct formulas and equations to tackle problems in science, their first expressions need not be the simplest ones. It is likely that simpler formulas or equations exist. Finding them makes subsequent computations easier and faster. The types of equations that this project aims to simplify are differential equations, recurrence relations, and algebraic equations in two variables. A common theme for each of these types of equations is that in order to simplify them, a key step is a technical analysis of their singularities. Computer algebra systems can automatically find exact solutions for various types of equations. They are an important part of the infrastructure for research and education. However, they often produce unnecessarily complicated answers. The techniques developed in this project will help to simplify not only equations, but solutions as well, making them more useful for research and teaching. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.