Guides

Explore the full functionality of HomotopyContinuation.jl

Get started

Installing HomotopyContinuation.jl

Up and running in under a minute

Problem formulation

Learn how to formulate your problem

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?

Solving many systems in a loop

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

Overdetermined systems

How to solve systems with more equations than variables.

Composite systems

How to construct and solve composite systems

Data analysis of solutions

Analysing arrays of vectors

Solutions in a product of projective spaces

Solving systems over a product of projective spaces

Total Degree Homotopy

The total degree start system