Guides

Explore the full functionality of HomotopyContinuation.jl

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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