# An idea to use algebra in to variable definition
**URL:** https://discourse.julialang.org/t/an-idea-to-use-algebra-in-to-variable-definition/121616
**Category:** General Usage
**Created:** [October 22, 2024, 10:21pm UTC](https://discourse.julialang.org/t/an-idea-to-use-algebra-in-to-variable-definition/121616 "2024-10-22T22:21:12Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@xiaodai](https://discourse.julialang.org/u/xiaodai)
#### Post date: [October 22, 2024, 10:21pm UTC](https://discourse.julialang.org/t/an-idea-to-use-algebra-in-to-variable-definition/121616/1 "2024-10-22T22:21:13Z")
If I know that `c^2=a^2+b^2` and I know the values of `a` and `c` but want to find `b` then I have to manually rearrange the equation and do
`b = sqrt(c^2 - a^2)`
For complicated cases, it may be hard to decipher what was the intent.
With the current packages available in Julia, is it possible to do something like this
`@define b: c^2 = a^2 + b^2`
and have the macro do the algebra for me?
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### Author:  [@heliosdrm](https://discourse.julialang.org/u/heliosdrm)
#### Post date: [October 22, 2024, 10:40pm UTC](https://discourse.julialang.org/t/an-idea-to-use-algebra-in-to-variable-definition/121616/2 "2024-10-22T22:40:43Z")
Symbolics.jl may not be exactly what you ask for, but it is related and perhaps useful for the problem that you want to address. Specially the symbolic solver:
> **[Solver · Symbolics.jl](https://docs.sciml.ai/Symbolics/stable/manual/solver/#Symbolics.symbolic_solve)**
>
> Documentation for Symbolics.jl.
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### Author:  [@xiaodai](https://discourse.julialang.org/u/xiaodai)
#### Post date: [October 22, 2024, 11:33pm UTC](https://discourse.julialang.org/t/an-idea-to-use-algebra-in-to-variable-definition/121616/3 "2024-10-22T23:33:25Z")
Cool. I don’t want it solve it at run time but want it to have done it algebraically at compile time. But I suspect we may be able to wrangle it and put that in a macro
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### Author:  [@nsajko](https://discourse.julialang.org/u/nsajko)
#### Post date: [October 22, 2024, 11:38pm UTC](https://discourse.julialang.org/t/an-idea-to-use-algebra-in-to-variable-definition/121616/4 "2024-10-22T23:38:47Z")
> [@xiaodai](#):
>
> If I know that `c^2=a^2+b^2` and I know the values of `a` and `c` but want to find `b` then I have to manually rearrange the equation and do
>
> `b = sqrt(c^2 - a^2)`
The second equation doesn’t follow from the first on its own, though, it’s not known whether b is positive or negative. So it’s not enough to work with a single equation, rather I guess the implementation of the feature you desire would need to solve systems of polynomial inequalities. Which is very demanding.
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### Author:  [@xiaodai](https://discourse.julialang.org/u/xiaodai)
#### Post date: [October 23, 2024, 12:55am UTC](https://discourse.julialang.org/t/an-idea-to-use-algebra-in-to-variable-definition/121616/5 "2024-10-23T00:55:34Z")
> [@nsajko](#):
>
> The second equation doesn’t follow from the first on its own
Hmmm…… ok…..