# Guides

Explore the full functionality of HomotopyContinuation.jl

## Get started

#### Installing HomotopyContinuation.jl

Up and running in under a minute

#### How to solve a system of polynomial equations

For this guide, we're going to walk through an illustrative example

#### An introduction to the numerical solution of polynomial systems

The basics of the theory and techniques behind HomotopyContinuation.jl

#### Choosing a start system

What start system should I choose?

## Feature guides

#### Systems with parameters

How to track parametrized systems of equations

#### Monodromy

How to solve polynomial system by using the monodromy method.

#### Polyhedral homotopy

A start system from polyhedral geometry

#### Using HomotopyContinuation.jl from Macaulay2

How do I solve my ideal from Macaulay2 with HomotopyContinuation.jl?

#### Groups of variables

Declaring additional structure for homotopy continuation

#### Solving many systems in a loop

What to do, if you have to solve system in a loop

#### Overdetermined systems

How to track solutions of systems with more equations than variables.

#### Composite systems

How to construct and solve composite systems

#### Custom Homotopies

How to construct your own custom homotopy.

#### Data analysis of solutions

Analysing arrays of vectors

#### Solutions at infinity

Let solve return the outcomes of all paths

#### Solutions in a product of projective spaces

Solving systems over a product of projective spaces

#### Solutions in projective space

Solving systems defined over projective space

#### Total Degree Homotopy

The totaldegree start system

#### Tracking in affine space or in projective space

Define the space for the paths that are tracked