# 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

#### The point on a variety that minimizes the distance to a given point

Computing critical points

#### 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.