### Requirements

If you have not yet installed HomotopyContinuation.jl, please consider the installation guide.

### Solve your first system of equations

Consider the following simple system of two polynomials in two variables.

$$ f=\begin{bmatrix}x^2+2y \\ y^2-2 \end{bmatrix} $$

Solving the equation $f=0$ can be accomplished as follows

```
using HomotopyContinuation # load the package into the current Julia session
@polyvar x y; # declare the variables x and y
f = [x^2 + 2y, y^2 - 2]
result = solve(f) # solve f
```

After the computation has finished, you should see the following output.

```
Result with 4 solutions
==================================
• 4 non-singular solutions (2 real)
• 0 singular solutions (0 real)
• 4 paths tracked
• random seed: 902575
```

We see that $f$ has two real zeros. They are

```
julia> realsolutions(result)
2-element Array{Array{Float64,1},1}:
[1.68179, -1.41421]
[-1.68179, -1.41421]
```

It is possible to interrupt the computations using `control+c`

. All solutions that have been computed before the interruption will be returned.

### Understanding the output of your computation

A detailed explanation of the output of `solve(f)`

is described in the next guide.

### Solving many systems of equations

`solve(f)`

works nicely for single systems. If you have to solve many systems in a loop, you should read this guide.

### What else should I know?

HomotopyContinuation.jl provides many more features. Check our detailed Guides for learning more about the full power of homotopy continuation.

You should also consult our API Docs, where all options of `solve(f)`

are listed.