Homotopy Continuation in Julia

This is a project for the "Laboratorio Computazionale" exam at the University of Pisa

Implemented

• Total-degree Homotopy with "Roots of unity" start system
• Euler-Newton predictor-corrector method with adaptive step size
• Homotopy Continuation for all roots of the target system

TODO

• Projective coordinates
• Parallelization
• Extract functions in separate modules(?)

Example system

\begin{align*}
x^2 + y^2 - 4 &= 0 \\
xy - 1 &= 0 \\
\end{align*}

Plot of the approximate solutions: