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...If you want to build a crazy CAS for your weird Octonian algebras, you've come to the right place. Symbols in SymbolicUtils carry type information. Operations on them propagate this information. A rule-based rewriting language can be used to find subexpressions that satisfy arbitrary conditions and apply arbitrary transformations on the matches. The library also contains a set of useful simplification rules for expressions of numeric symbols and numbers. These can be remixed and extended for special purposes.

PromptingTools.jl is a Julia-based toolkit designed to simplify prompt engineering and unify interactions with multiple large language model providers through a consistent interface. It focuses on reducing the complexity of prompt creation by introducing templating systems, macros, and reusable functions that standardize how prompts are constructed and executed. The library provides a family of ai* functions that handle tasks such as generation, embeddings, classification, and data extraction, all following a consistent structure. ...

...It is part of the JuliaStats ecosystem and is tightly integrated with StatsModels.jl for formula handling, and Distributions.jl for specifying error families. The package supports modeling through both formula-based (e.g. @formula) and matrix-based interfaces, allowing both high-level convenience and low-level control. Under the hood, GLM.jl separates the linear predictor and response objects, allowing flexible combinations of link functions, variance structures, and fitting methods.

...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.

This package provides Julia bindings to the FFTW library for fast Fourier transforms (FFTs), as well as functionality useful for signal processing. These functions were formerly a part of Base Julia. Users with a build of Julia based on Intel's Math Kernel Library (MKL) can use MKL for FFTs by setting a preference in their top-level project by either using the FFTW.set_provider!() method, or by directly setting the preference using Preferences.jl. Note that this choice will be recorded for the current project, and other projects that wish to use MKL for FFTs should also set that same preference. ...

Metatheory.jl is a general purpose term rewriting, metaprogramming and algebraic computation library for the Julia programming language, designed to take advantage of the powerful reflection capabilities to bridge the gap between symbolic mathematics, abstract interpretation, equational reasoning, optimization, composable compiler transforms, and advanced homoiconic pattern matching features. The core features of Metatheory.jl are a powerful rewrite rule definition language, a vast library...

NFFT is a software library, written in C, for computing non-equispaced fast Fourier transforms and related variations.