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I'm not sure how easy this is. The problem is that Sage doesn't actually do anything with this until it's requested to be shown as a figure.

The magic is done by contourf in matplotlib. You may find this question or this one helpful, though no guarantees. You can create a Matplotlib object from a Sage one by doing something C = implicit_plot(...) and then c = C.matplotlib(). But you'd still have to extract stuff from it and I'm not an mpl expert, here one exits Sage territory since mpl thinks differently about plots - data, not functions.