Homotopy Continuation in Julia

Implemented

• Total-degree Homotopy
• Roots of unity start 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: