# How to get subtree from symbolic expression? in ModelingToolkit.jl
**URL:** https://discourse.julialang.org/t/how-to-get-subtree-from-symbolic-expression-in-modelingtoolkit-jl/117070
**Category:** Modelling & Simulations
**Created:** [July 15, 2024, 8:04pm UTC](https://discourse.julialang.org/t/how-to-get-subtree-from-symbolic-expression-in-modelingtoolkit-jl/117070 "2024-07-15T20:04:56Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@jogama](https://discourse.julialang.org/u/jogama)
#### Post date: [July 15, 2024, 8:04pm UTC](https://discourse.julialang.org/t/how-to-get-subtree-from-symbolic-expression-in-modelingtoolkit-jl/117070/1 "2024-07-15T20:04:56Z")
My apologies if this has already been addressed.
Let’s say we have
```julia
using ModelingToolkit
@variables t x(t) y(t) z(t)
ex = x * y + z
```
How should I extract the sub-expression `x * y` from `ex`? It’s not clear to me how I’d traverse the expression tree in the documentation, nor did I see any way to do this via filtering.
I don’t seek to build a function. I’m fine with the output being an expression or string `x * y`. I want to extract products to populate nodes in a graph later on. For now, all the expressions would just have sums and products, and I’d want to get all the products.
I could do `split(string(ex), ['+', '-'])`, and use this result, and am currently working on this route. I still wonder if I’m not seeing a better way.
---
### Author:  [@contradict](https://discourse.julialang.org/u/contradict)
#### Post date: [July 15, 2024, 11:34pm UTC](https://discourse.julialang.org/t/how-to-get-subtree-from-symbolic-expression-in-modelingtoolkit-jl/117070/2 "2024-07-15T23:34:47Z")
ModelingToolkit is built on Symbolics and SymbolicUtils, that is the place to look for low-level expression manipulation like this. Here is an example (not complete and minimally tested).
```julia
using Symbolics
function products(expr)
ex = Symbolics.unwrap(expr)
terms = arguments(ex)
products = filter(terms) do t
istree(t) && ((operation(t) == *) || (operation(t) == ^))
end
end
```
```julia
julia> ex = x * y + z + z*x + y*y
z(t) + x(t)*y(t) + x(t)*z(t) + y(t)^2
julia> products(ex)
3-element Vector{Any}:
x(t)*y(t)
x(t)*z(t)
y(t)^2
```
---
### Author:  [@jogama](https://discourse.julialang.org/u/jogama)
#### Post date: [July 16, 2024, 9:42pm UTC](https://discourse.julialang.org/t/how-to-get-subtree-from-symbolic-expression-in-modelingtoolkit-jl/117070/3 "2024-07-16T21:42:07Z")
Thank you; this is helpful. I hadn’t seen `Symbolics.unwrap` in the symbolics documentation, and I would have never thought of using `filter` with `operation` that way!