Symbolic expressions, rewriting and simplification
For information on using the package, see the stable documentation. Use the in-development documentation 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. 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.
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.
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