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The purpose of the TaylorSeries.jl package is to provide a framework to exploit Taylor polynomials in one and several variables in the Julia programming language (Bezanson, Edelman, Karpinski, & Shah, 2017). It can be thought of as providing a primitive CAS (computer algebra system), which works numerically and not symbolically. The package allows the user to define dense polynomials p(x) of one variable and p(x) of several variables with a specified maximum degree, and perform operations on them, including powers and composition, as well as series expansions for elementary functions of polynomials, for example exp[p(x)], where techniques of automatic differentiation are used (Haro, Canadell, Figueras, Luque, & Mondelo, 2016; Tucker, 2011). Differentiation and integration are also implemented.

TaylorSeries.jl: Taylor expansions in one and several variables in Julia