Examples

Polynomial equations appear in a wide variety of topics.

Applications in the Sciences

Polynomial systems arising from Nash equilibria

A story about how game theory meets multilinear systems and product of simplices.

Alt's problem

A classical problem from robotics

Computer vision

Triangulation of a dinosaur

Bacillus Subtilis

environmental and energy stress response of the bacterium Bacillus subtilis

Cyclooctane

The conformation space of cyclooctane

The 6R-serial link robot

Using HomotopyContinuation.jl for a problem in kinematics

Energy minimization

Computing a macroscopic configuration

Mathematics of Data

The reach of a plane curve

Computing the reach

Sampling and Homology via Bottlenecks

Sampling an algebraic variety and computing its homology

Computing a logarithmic Voronoi cell

An adventure at the intersection of statistics and nonlinear algebra.

Sampling a probability distribution on a variety

By intersecting with linear spaces

Method of moments

For mixtures of three Gaussians

Monte Carlo integration

Integrating functions on a variety

Algebraic Geometry

When do two ellipses meet?

Let two ellipses grow until they intersect

Symmetroids

Computing the degree of a cubic symmetroid

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