JuliaDiff/TaylorSeries.jl

What it solves

It provides a way to perform Taylor polynomial expansions for functions in one or more independent variables, allowing for the automatic generation of series expansions for complex mathematical expressions.

How it works

The package implements Taylor series calculations using a system of variable spaces (JetSpaces). It supports both single-variable and multivariate expansions, and allows users to define multiple co-existing variable spaces with different orders and variable sets. It also provides tools for differential and integral calculus, such as calculating gradients ($\nabla$) and performing integration over specific variables.

Who it’s for

Researchers and mathematicians who need to compute high-order Taylor expansions and perform calculus operations on those expansions within the Julia programming language.

Highlights

• Supports both univariate and multivariate Taylor series expansions.
• Allows for the creation of multiple independent variable spaces with different expansion orders.
• Includes built-in support for differential and integral calculus operations.
• Integrates with standard mathematical functions like exp, log, and sin to automatically generate expansions.