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Luis Benet committed Mar 8, 2018
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---
title: 'TaylorSeries.jl: Taylor expansions in Julia'
title: 'TaylorSeries.jl: Taylor expansions in one and many variables in Julia'
tags:
- Taylor series
- Automatic differentiation
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index: 1
- name: Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)
index: 2
date: February 10, 2018
date: February 23, 2018
bibliography: paper.bib
---

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[`TaylorSeries.jl`](https://github.com/JuliaDiff/TaylorSeries.jl)
[@TaylorSeries] provides a framework to use and manipulate
Taylor series polynomials in one and more independent variables
in [Julia](https://julialang.org) [@Julia]. In order to compute
in [Julia](https://julialang.org) [@Julia]. It allows to compute
elementary functions of
polynomials (`Taylor1`- or `TaylorN`-type objects) we
exploit techniques of automatic differentiation
[@Tucker:ValidatedNumerics, @HaroEtAl:ParameterizMeth].
polynomials (`Taylor1`- or `TaylorN`-type objects), where
techniques of automatic differentiation are exploited
[@Tucker:ValidatedNumerics, @HaroEtAl:ParameterizMeth]. Derivation,
integration is also implemented.

The package allows to work with a large number of `Number` formats
The package allows to work with a different `Number` formats
as coefficients of the series, including complex numbers,
the extended precision format `BigFloat` [@MPFR],
the extended precision `BigFloat`s [@MPFR],
`Intervals` [@ValidatedNumerics], `ArbFloats` [@ArbFloats],
as well as `Taylor1` and `TaylorN` objects, which are defined
by the package.
as well as `Taylor1` and `TaylorN` objects.

This package is a core component of
`TaylorSeries.jl` is a core component of
[`TaylorIntegration.jl`](https://github.com/PerezHz/TaylorIntegration.jl)
[@TaylorIntegration], whose aim is to perform precise integration
of ODEs using Taylor's method.
[@TaylorIntegration], whose aim is to perform accurate integration
of ODEs using Taylor's method, including Jet transport techniques.

## Acknowledgements

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