Abstract
We discuss the effective symbolic computation of operators under composition. We analyse data structures consisting of formal linear combinations of rooted labelled trees. We define a multiplication on rooted labelled trees, thereby making the set of these data structures into an associative algebra. We then define an algebra homomorphism from the original algebra of operators into this algebra of trees. The cancellation which occurs when non-commuting operators are expressed in terms of commuting ones occurs naturally when the operators are represented using this data structure. This leads to an algorithm which, for operators which are derivations, speeds up the computation exponentially in the degree of the operator.
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