Homotopy Continuation in Julia

Implemented

• Total-degree Homotopy
• Roots of unity start system

TODO

• Projective coordinates
• Parallelization
• Endgames(?)

Example system

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

Plot of our approximate solutions: