When working with symbolic equations in Julia, it is often necessary to simplify them for better understanding or further calculations. In this article, we will explore three different ways to simplify a symbolic equation whose right-hand side (rhs) is zero.

## Option 1: Using the simplify function

The first option is to use the simplify function provided by the Symbolics.jl package. This function attempts to simplify the given expression by applying various algebraic rules and transformations.

```
using Symbolics
@variables x
eq = x^2 - x - x + x - x^2
simplified_eq = simplify(eq)
println(simplified_eq)
```

In this code snippet, we define a symbolic equation `eq`

and then use the `simplify`

function to simplify it. The resulting simplified equation is stored in the `simplified_eq`

variable, which is then printed to the console.

## Option 2: Using the simplify_zero function

If we know that the rhs of the equation is zero, we can use the `simplify_zero`

function provided by the Symbolics.jl package. This function simplifies the equation by assuming that the rhs is zero, which allows for more aggressive simplifications.

```
using Symbolics
@variables x
eq = x^2 - x - x + x - x^2
simplified_eq = simplify_zero(eq)
println(simplified_eq)
```

In this code snippet, we define a symbolic equation `eq`

and then use the `simplify_zero`

function to simplify it. The resulting simplified equation is stored in the `simplified_eq`

variable, which is then printed to the console.

## Option 3: Using the simplify_zero! function

If we want to modify the original equation in-place, we can use the `simplify_zero!`

function provided by the Symbolics.jl package. This function simplifies the equation by assuming that the rhs is zero and modifies the equation object directly.

```
using Symbolics
@variables x
eq = x^2 - x - x + x - x^2
simplify_zero!(eq)
println(eq)
```

In this code snippet, we define a symbolic equation `eq`

and then use the `simplify_zero!`

function to simplify it in-place. The modified equation is then printed to the console.

After exploring these three options, it is clear that the best option depends on the specific use case. If you want to keep the original equation unchanged, Option 1 using the `simplify`

function is the way to go. However, if you want to aggressively simplify the equation assuming the rhs is zero, Option 2 using the `simplify_zero`

function is more suitable. Finally, if you want to modify the original equation in-place, Option 3 using the `simplify_zero!`

function is the best choice.