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SymbolicUtils is a practical symbolic programming utility in Julia. It lets you create, rewrite and simplify symbolic expressions, and generate Julia code from them. SymbolicUtils.jl provides various utilities for symbolic computing. SymbolicUtils.jl is what one would use to build a Computer Algebra System (CAS). If you're looking for a complete CAS, similar to SymPy or Mathematica, see Symbolics.jl. If you want to build a crazy CAS for your weird Octonian algebras, you've come to the right place. ...

...It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration. Physical measures are typically reported with an error, a quantification of the uncertainty of the accuracy of the measurement. Whenever you perform mathematical operations involving these quantities you have also to propagate the uncertainty, so that the resulting number will also have an attached error to quantify the confidence about its accuracy. Measurements.jl relieves you from the hassle of propagating uncertainties coming from physical measurements, when performing mathematical operations involving them. ...

This module provides a Julia-language interface to the free/open-source NLopt library for nonlinear optimization. NLopt provides a common interface for many different optimization algorithms.

...The implemented manifolds are accompanied by their mathematical formulae. The manifolds are implemented using the interface for manifolds given in ManifoldsBase.jl. You can use that interface to implement your own software on manifolds, such that all manifolds based on that interface can be used within your code.

DynamicalSystems.jl is an award-winning Julia software library for nonlinear dynamics and nonlinear time series analysis. To install DynamicalSystems.jl, run import Pkg; Pkg.add("DynamicalSystems"). To learn how to use it and see its contents visit the documentation, which you can either find online or build locally by running the docs/make.jl file. DynamicalSystems.jl is part of JuliaDynamics, an organization dedicated to creating high-quality scientific software. All implemented algorithms provide a high-level scientific description of their functionality in their documentation string as well as references to scientific papers. ...

JuliaImages (source code) hosts the major Julia packages for image processing. Julia is well-suited to image processing because it is a modern and elegant high-level language that is a pleasure to use, while also allowing you to write "inner loops" that compile to efficient machine code (i.e., it is as fast as C). Julia supports multithreading and, through add-on packages, GPU processing. JuliaImages is a collection of packages specifically focused on image processing. It is not yet as complete as some toolkits for other programming languages, but it has many useful algorithms. ...