Computing Tropical Curves Using Homotopy Continuation
summary
Numeric method computes tropical curves by tracing amoeba tentacles with homotopy continuation, sampling parallel log-slices, and recovering primitive integer rays and tentacle multiplicities from endpoint differences and Puiseux-series counts. Implementation chains polyhedral homotopies (PHCpack), Bertini for high precision, and a Macaulay2 interface (Gfan for small cases), runs on knot-complement examples where symbolic prevarieties fail, produces candidate rays and multiplicities, and succeeds on many tested instances though witness-set generation remains the bottleneck.
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