Mathscape and molecular integrals

I have used mathematica to solve several problems that relate to the symbolic calculation of the ‘molecular integrals’ that are a mainstay of computational chemistry. This work has provided many new results of chemical and mathematical interest, and it has led to a powerful programming methodology that I call mathscape that uses a novel open ended set of macros. Some further work on molecular integrals is presented here, largely as an introduction to mathscape. I discuss (1) the immediate mathematical problem of the ‘J’ integrals, (2) the key features of mathscape, (3) a novel reduction of the J integrals, (4) the chemical context of this work, and (5) the computer science context.