Examples

Polynomial equations appear in a wide variety of topics.

Sampling

Sampling from a variety

Cyclooctane

The conformation space of cyclooctane

Method of Moments

For mixtures of three Gaussians

Minimizing a function over the sphere

Using HomotopyContinuation.jl for a problem in optimization

The 6R-serial link robot

Using HomotopyContinuation.jl for a problem in kinematics

When do two ellipses meet?

Let two ellipses grow until they intersect

Monte Carlo Integration

Integrating measurable functions on a variety

Tensor decomposition and homotopy continuation

Using homotopy continuation for computing the CPD of a tensor

Tritangents

Using HomotopyContinuation.jl for computing tritangents of sextic curves

Curvature of plane curves

How to compute curvature

3264 conics tangent to five conics

All of them can be real.

The number of circles that are tangent to 3 given conics

Using HomotopyContinuation.jl for a problem in enumerative geometry

Do It Yourself

3264 conics in a second.