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https://github.com/JuliaSymbolics/SymbolicUtils.jl

Symbolic expressions, rewriting and simplification
https://github.com/JuliaSymbolics/SymbolicUtils.jl

julia pattern-matching symbolic-manipulation symbolic-math

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Symbolic expressions, rewriting and simplification

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# SymbolicUtils.jl 



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## Tutorials and Documentation



For information on using the package,

[see the stable documentation](https://symbolicutils.juliasymbolics.org/stable/). Use the

[in-development documentation](https://symbolicutils.juliasymbolics.org/dev/) for the version of

the documentation, which contains the unreleased features.



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](https://github.com/JuliaSymbolics/Symbolics.jl). If you want to build a crazy CAS for your weird

Octonian algebras, you've come to the right place.



[Symbols in SymbolicUtils](https://symbolicutils.juliasymbolics.org/#creating_symbolic_expressions) carry type information. Operations on them propagate this information. [A rule-based rewriting language](https://symbolicutils.juliasymbolics.org/rewrite/#rule-based_rewriting) 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](https://juliasymbolics.github.io/SymbolicUtils.jl/#simplification) rules for expressions of numeric symbols and numbers. These can be remixed and extended for special purposes.



If you are a Julia package developer in need of a rule rewriting system for your own types, have a look at the [interfacing guide](https://symbolicutils.juliasymbolics.org/interface/).



### "I don't want to read your manual, just show me some cool code"

```julia

julia> using SymbolicUtils



julia> SymbolicUtils.show_simplified[] = true



julia> @syms x::Real y::Real z::Complex f(::Number)::Real

(x, y, z, f(::Number)::Real)



julia> 2x^2 - y + x^2

(3 * (x ^ 2)) + (-1 * y)



julia> f(sin(x)^2 + cos(x)^2) + z

f(1) + z



julia> r = @rule sinh(im * ~x) => sin(~x)

sinh(im * ~x) => sin(~x)



julia> r(sinh(im * y))

sin(y)



julia> simplify(cos(y)^2 + sinh(im*y)^2, RuleSet([r]))

1

```



# Citations



- The pattern matcher is an adaption of the one by Gerald Jay Sussman (as seen in [6.945](https://groups.csail.mit.edu/mac/users/gjs/6.945/) at MIT), his use of symbolic programming in the book [SICM](https://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/book.html) inspired this package.

- [Rewrite.jl](https://github.com/HarrisonGrodin/Rewrite.jl) and [Simplify.jl](https://github.com/HarrisonGrodin/Simplify.jl) by [Harrison Grodin](https://github.com/HarrisonGrodin) also inspired this package.