Given a so-called Wronski-system, i.e. \(d\) polynomials in \(d\) variables such that

all polynomials have the same Newton polytope

the Newton polytope has a regular triangulation whose dual graph is bipartite,
which implies that the vertices are \(d+1\) colorable and the facet are 2 colorable
(say black and white), and the coefficients are constant on the \(d+1\) vertex colors.

This is done by constructing a special map whose degree is the signature,
which yields that many zeroes.

The goal is to find a algorithm to compute exactly those solutions, given a Wronski-system,
for the case \(d=2\). This can be regarded as a real homotoy algorithm.

## Comments¶

## Comments by Michael Joswig:¶

Given a so-called Wronski-system, i.e. \(d\) polynomials in \(d\) variables such that

## Example¶

Two polynomials of the form \(a(1+xy)+b(x+y^2)+c(y+x^2)\), whose Newton polytope is a simplex of side length 2.

Then Soprunova and Sotile (2006) showed that the number of real solutions to that system is at least the signature of that coloring

This is done by constructing a special map whose degree is the signature, which yields that many zeroes.

The goal is to find a algorithm to compute exactly those solutions, given a Wronski-system, for the case \(d=2\). This can be regarded as a real homotoy algorithm.