Curves are dimension-one objects. One naturally expects curves to be present when the number of variables exceeds the number of equations or constraints by one, and when it does, we call this a complete intersection. When the intersection is complete, the number of equations is at least the number of variables. The twisted cubic is an example of such a curve -- an incomplete intersection.

I have written Matlab code using Bertini to compute tropical curves. You can access it here.

There are some computed examples demonstrating the code in the examples page.