CAS: Computer Algebra systems

ModelingToolkit.jl

• Symbolics.jl Symbolic programming for the next generation of numerical software
• ModelingToolkit.jl An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations

AbstractAlgebra / Nemo

• AbstractAlgebra.jl
• Nemo.jl

OSCAR

• Oscar.jl
• Singular.jl
• GAP.jl

CatLab / AlgebraicJulia

• Catlab.jl A framework for applied category theory in the Julia language
• AlgebraicDynamics.jl
• AlgebraicPetri.jl
• Semagrams.jl

Calculus

• Calculus.jl Calculus functions in Julia. Unmaintained
• ChainRulesCore.jl AD-backend agnostic system defining custom forward and reverse mode rules. Maintainer needed

Gröbner Bases

• Groebner.jl Groebner bases in (almost) pure Julia
• ParametricGroebnerBases.jl An implementation of the Suzuki-Sato algorithm for computing Gröbner systems and comprehensive/parametric Gröbner bases

Geometry

• JuliaManifolds Organization
• Manifolds.jl Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation.
• LieGroups.jl Lie groups and Lie algebras

Graphs

• JuliaGraphs Organization
• Graphs.jl An optimized graphs package for the Julia programming language
• SimpleWeightedGraphs.jl Edge-weighted graphs compatible with Graphs.jl
• GraphPlot.jl Graph visualization for Julia.
• MetaGraphsNext.jl A package for graphs with vertex labels and metadata in Julia
• MetaGraphs.jl Graph data structures with multiple heterogeneous metadata for Graphs.jl.
• GraphDataFrameBridge.jl Tools for interoperability between DataFrame objects and LightGraphs and MetaGraphs objects
• https://github.com/CameronBieganek/GraphInterface.jl Proposal for Graphs 2.0. See RFC
• NamedGraphs.jl Extension of Graphs.jl to graphs with named vertices.