Fluctuation expansion is a method used for finding the matrix representation of functions. The approach is to truncate the infinite dimensional representation of a function at some dimension n, and then gradually add the contributions of the residual terms that are formed because of the truncation. The Fluctuationless-ness Theorem states that the truncated matrix representation of a function may be approximated by the image of the matrix representation of the operator multiplying its operand with its independent variable, under the function. This approximation may be improved by adding residual terms. The residual terms are operator-argumented contour integrals and are also called fluctuation terms. The simplification of the terms rely heavily on operator algebra. The geometric series expansions of the inverse of the operators and factorization schemes enable us to perform the contour integral and acquire simpler formulae. These symbolic simplifications motivate us to create a new algebra for the simplifications and design an algorithm to find the compact form of the residual terms via symbolic programming.