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# Homotopy Continuation in Julia
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This is a project for the "Laboratorio Computazionale" exam at the University of Pisa
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## Implemented
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- Total-degree Homotopy with "Roots of unity" start system
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- Euler-Newton predictor-corrector method with adaptive step size
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- Homotopy Continuation for all roots of the target system
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## TODO
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- Projective coordinates
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- Parallelization
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- Extract functions in separate modules(?)
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## Example system
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$$
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\begin{align*}
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x^2 + y^2 - 4 &= 0 \\
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xy - 1 &= 0 \\
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\end{align*}
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$$
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Plot of the approximate solutions:
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