Symbolics.jl
Symbolics.jl is a fast and modern Computer Algebra System (CAS) for a fast and modern programming language (Julia). The goal is to have a high-performance and parallelized symbolic algebra system that is directly extendable in the same language as that of the users.
Installation
To install Symbolics.jl, use the Julia package manager:
using Pkg
Pkg.add("Symbolics")Citation
If you use Symbolics.jl, please cite this paper
@article{gowda2021high,
title={High-performance symbolic-numerics via multiple dispatch},
author={Gowda, Shashi and Ma, Yingbo and Cheli, Alessandro and Gwozdz, Maja and Shah, Viral B and Edelman, Alan and Rackauckas, Christopher},
journal={arXiv preprint arXiv:2105.03949},
year={2021}
}Feature Summary
Because Symbolics.jl is built into the Julia language and works with its dispatches, generic functions in Base Julia will work with symbolic expressions! Make matrices of symbolic expressions and multiply them: it will just work. Take the LU-factorization. Etc. Thus, see the Julia Documentation for a large list of functionality available in Symbolics.jl.
A general list of the features is:
- Symbolic arithmetic with type information and multiple dispatch
- Symbolic polynomials and trigonometric functions
- Pattern matching, simplification and substitution
- Differentiation
- Symbolic linear algebra (factorizations, inversion, determinants, eigencomputations, etc.)
- Discrete math (representations of summations, products, binomial coefficients, etc.)
- Logical and Boolean expressions
- Symbolic equation solving and conversion to arbitrary precision
- Support for non-standard algebras (non-commutative symbols and customizable rulesets)
- Special functions (list provided by SpecialFunctions.jl)
- Automatic conversion of Julia code to symbolic code
- Generation of (high performance and parallel) functions from symbolic expressions
- Fast automated sparsity detection and generation of sparse Jacobians and Hessians
and much more.
Extension Packages
Below is a list of known extension packages. If you would like your package to be listed here, feel free to open a pull request!
- ModelingToolkit.jl: Symbolic representations of common numerical systems
- Ordinary differential equations
- Stochastic differential equations
- Partial differential equations
- Nonlinear systems
- Optimization problems
- Optimal Control
- Causal and acausal modeling (Simulink/Modelica)
- Automated model transformation, simplification, and composition
- Catalyst.jl: Symbolic representations of chemical reactions
- Symbolically build and represent large systems of chemical reactions
- Generate code for ODEs, SDEs, continuous-time Markov Chains, and more
- Simulate the models using the SciML ecosystem with O(1) Gillespie methods
- DataDrivenDiffEq.jl: Automatic identification of equations from data
- Automated construction of ODEs and DAEs from data
- Representations of Koopman operators and Dynamic Mode Decomposition (DMD)
- SymbolicRegression.jl: Distributed High-Performance symbolic regression
- Parallelized generic algorithms for finding equations from data
- Pareto frontier-based scoring
- ReversePropagation.jl: Source-to-source reverse mode automatic differentiation
- Automated tracing of code and construction of backpropagation equations
- Composes with symbolic transformation and simplification functionality
Reproducibility
The documentation of this SciML package was built using these direct dependencies,
Status `~/work/Symbolics.jl/Symbolics.jl/docs/Project.toml`
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[d1185830] SymbolicUtils v3.7.2
[0c5d862f] Symbolics v6.22.0 `~/work/Symbolics.jl/Symbolics.jl`and using this machine and Julia version.
Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 4 × AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
JULIA_DEBUG = DocumenterA more complete overview of all dependencies and their versions is also provided.
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[de0858da] Printf v1.11.0
[9abbd945] Profile v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.11.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[781609d7] GMP_jll v6.3.0+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[3a97d323] MPFR_jll v4.2.1+0
[c8ffd9c3] MbedTLS_jll v2.28.6+0
[14a3606d] MozillaCACerts_jll v2023.12.12
[4536629a] OpenBLAS_jll v0.3.27+1
[05823500] OpenLibm_jll v0.8.1+2
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.7.0+0
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`You can also download the manifest file and the project file.