General algorithms in asymptotics II: common operations


We continue the study of automatic transseries, which has been started in the previous paper on general algorithms. We start by giving algorithms for expanding solutions to polynomial equations and then proceed with differentiation, integration, functional composition and inversion. Functions, constructed by a succession of these operations can also be handled.

Keywords: asymptotic expansion, transseries, algorithm, real field, differential calculus, composition, inversion

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