Creating a Database of Yang-Mills Solutions for the Differential Geometry Package in Maple

Using non-Abelian Lie groups, Yang-Mills theory describes the behavior of elementary particles. This system of geometric PDEs successfully unifies the electromagnetic and weak forces and accurately describes quantum chromodynamics. Because of this, it is vital for understanding the standard model of particle physics. The main goal of this project is to make solutions to the Yang-Mills equations easily accessible. We did this by creating a database of solutions and their properties. This database will be available as a free addition to the differential geometry package in Maple. Initially, the database will have 37 solutions from a review paper by Alfred Actor, but we plan to continue adding to this database in the future. The solutions are first input into Maple to find the connection one-form for each solution and add it to the database. Various properties presented in the paper for each solution are then tested and cataloged alongside the connection one-form. From the entries in the database, these Yang-Mills solutions can be called up in a format that can be manipulated in Maple lending a great deal of readily available computing power to studies about these solutions.