# Where is backslash (\\) implemented?
**URL:** https://discourse.julialang.org/t/where-is-backslash-implemented/104693
**Category:** Numerics
**Tags:** question, package
**Created:** [October 7, 2023, 9:25am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693 "2023-10-07T09:25:42Z")
**Posts on this page:** 10
**Page:** 1
### Author:  [@SupernovaTitanium](https://discourse.julialang.org/u/SupernovaTitanium)
#### Post date: [October 7, 2023, 9:25am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/1 "2023-10-07T09:25:42Z")
Hi, I’m new to Julia. Recently, I’ve used the backslash (\) operator to solve a linear system. However, I don’t know how it is implemented. I wanted to know it so I traced the code.
I am able to locate to line 1110 at [julia/stdlib/LinearAlgebra/src/generic.jl at master · JuliaLang/julia (github.com)](https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/generic.jl)
However, I don’t know what code will do next. For example, what will be done in line 1126? I don’t see any definition of backslash operator (\) there.
---
### Author:  [@abraemer](https://discourse.julialang.org/u/abraemer)
#### Post date: [October 7, 2023, 9:33am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/2 "2023-10-07T09:33:55Z")
To find the specific code run in a function call you can simply use `julia> @edit myfun(arg1, arg2)` and then your favorite editor will pop up at the correct file and line.
Edit: I realized that I may have misunderstood your question. The short answer to “what happens when I do `A\B`?” is “it depends on what `A` and `B` are”. You can see that the function starting in line 1110 starts checking some different cases where better solutions exists or else uses the default fallback of `qr(A)\B` or `lu(A) \ B` for square matrices. So you’ll need to trace the calls further by for example `julia> @edit qr(A)\B`
---
### Author:  [@kellertuer](https://discourse.julialang.org/u/kellertuer)
#### Post date: [October 7, 2023, 9:40am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/3 "2023-10-07T09:40:10Z")
Welcome to the Julia Discourse!
In 1126 the qr decomposition is computed and for that (with multiple dispatch) this method
>
is called.
---
### Author:  [@oheil](https://discourse.julialang.org/u/oheil)
#### Post date: [October 7, 2023, 9:41am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/4 "2023-10-07T09:41:09Z")
Line 1116
```julia
return Diagonal(A) \ B
```
you find in
Line 455 in [https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/diagonal.jl](https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/diagonal.jl)
```julia
julia> @which Diagonal([1 1;2 2])\[2 2 ; 2 2]
\(D::Diagonal, B::AbstractMatrix)
@ LinearAlgebra C:\Users\Oli\.julia\juliaup\julia-1.9.3+0.x64.w64.mingw32\share\julia\stdlib\v1.9\LinearAlgebra\src\diagonal.jl:412
```
Local on my installed version its in line 412.
Just as an example. You find the other implementations/methods in a similar way.
---
### Author:  [@jd-foster](https://discourse.julialang.org/u/jd-foster)
#### Post date: [October 7, 2023, 9:44am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/5 "2023-10-07T09:44:58Z")
In general, a subroutine in a LAPACK library outside julia may ultimately be called to solve the system: the default library that comes with julia is OpenBLAS.
---
### Author:  [@bertschi](https://discourse.julialang.org/u/bertschi)
#### Post date: [October 7, 2023, 11:28am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/6 "2023-10-07T11:28:21Z")
Shameless plug: You can try [TraceFuns.jl](https://github.com/bertschi/TraceFuns.jl) to see which methods are actually hit
```julia
@trace [1 2; 3 4] \ [1, 2] Base.:\
# Or for an even larger picture
import LinearAlgebra
@trace [1 2; 3 4] \ [1, 2] LinearAlgebra
```
---
### Author:  [@SupernovaTitanium](https://discourse.julialang.org/u/SupernovaTitanium)
#### Post date: [October 8, 2023, 8:04am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/7 "2023-10-08T08:04:19Z")
Thank you. I think I know how to trace the code now.
---
### Author:  [@SupernovaTitanium](https://discourse.julialang.org/u/SupernovaTitanium)
#### Post date: [October 8, 2023, 8:05am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/8 "2023-10-08T08:05:00Z")
Thank you. It is an interesting tool.
---
### Author:  [@SupernovaTitanium](https://discourse.julialang.org/u/SupernovaTitanium)
#### Post date: [October 8, 2023, 8:06am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/9 "2023-10-08T08:06:09Z")
Thank you. I know how to find the backslash for qr now.
---
### Author:  [@SupernovaTitanium](https://discourse.julialang.org/u/SupernovaTitanium)
#### Post date: [October 8, 2023, 8:08am UTC](https://discourse.julialang.org/t/where-is-backslash-implemented/104693/10 "2023-10-08T08:08:15Z")
I try to use @edit qr(A)\b. However, it only opens the LinearAlgebra.jl. I still don’t know where I can find the implementation.