Sage plot inner structure

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You can try:

sage: P = implicit_plot(x^2+y^2-2, (x,-3,3), (y,-3,3))
sage: C = P._objects[0]
sage: C
ContourPlot defined by a 150 x 150 data grid
sage: C.xy_data_array

You will get a list of lists, giving evaluated values of the function on the grid row by row (or column by column, i didn't check further).

Then you get the points by looking at sign changes, or values close to zero.

Does this help?

sage: p = implicit_plot(x == y^2, (x, 0, 1), (y, 0, 1))
sage: pc = p._objects[0]
sage: pc.xy_data_array
# Big output here

Similarly for plot

sage: p = plot(x)
sage: pc = p._objects[0]
sage: pc.xdata, pc.ydata