Abstract
We apply FORM, a computer algebra (CA) program for fast processing of very large expressions, to decide if perturbative quantum gravity yields a finite S matrix or not. This requires a difficult ‘two-loop’ computation. The extreme complexity of this calculation makes it an excellent testing ground for CA programs. In 1985 Goroff and Sagnotti wrote programs for this task in C and showed that the theory is no longer finite at two loops. In 1992 we confirmed their result with an independent calculation. The first lecture discusses our method, which keeps general coordinate invariance manifest and simplifies the Feynman rules, thus reducing the complexity of the task considerably. The second lecture gives a complete and annotated FORM program for two-loop Yang-Mills computations. Some aspects of our analogous gravity program follow.
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