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

点击翻译按钮获取中文摘要

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 theycan be large. This project aims to simplify large equations, reducing themwhen 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 formulasor 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 foreach of these types of equations is that in order to simplify them, a key step is atechnical analysis of their singularities.Computer algebra systems can automatically find exact solutions for various typesof equations. They are an important part of the infrastructure for researchand 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.