Symbolic algebra in quantum chemistry

Complex symbolic algebra, such as the manipulation of second-quantized operators, Slater determinants, Feynman diagrams, is inevitable in quantum chemistry. Increasingly, these operations are performed by the computerized systems that can handle higher mathematical constructs than just numbers and simple arithmetic. This article reviews these new algorithms that automate the algebraic transformation and computer implementation of many-body quantum-mechanical methods for electron correlation. They enable a whole new class of highly complex but vastly accurate methods, the manual development of which is no longer practical.