Introduction to the Symbolic Integration System

Symbolic integration is an important module of a typical Computer Algebra System. As for now, Mathematica, Matlab, Maple and Sage are all mainstream CAS. They share the same framework for symbolic integration at some points. In this book first we review the state of the art in the field of CAS. Then we focus on typical frameworks of the current symbolic integration systems and summarize the main mathematical theories behind these frameworks. Based on the open-source computer algebra system maTHmU developed by our team in our university, we propose a potential framework to improve the performance of the current symbolic integration system.