X and Y values of plot points using implicit_plot

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See contour_plot. The returned object from that has an attribute xy_data_array from contains the values at the grid points used to make the plot. Sage doesn't construct the contour lines itself. Matplotlib does that. See matplotlib.pyplot.contour for the relevant routine. You'd have to look there to see if matplotlib makes the computed data easily available.

I noticed Sage plot inner structure posted on the sidebar and after some time puzzling through the details came up with the following code to work off of:

x,y = var('x,y')
gridDim = 300
xmin = -2
xmax = 2
deltax = (xmax-xmin)/(gridDim-1)
ymin = -2
ymax = 2
deltay = (ymax-ymin)/(gridDim-1)
xvals = []
yvals = []
f(x,y)=x^2+y^2-2
P=implicit_plot(f, (x,xmin,xmax), (y,ymin,ymax),plot_points=gridDim)
C = P._objects[0]
for i in range(0,gridDim):
    for j in range(0,gridDim):
        if abs(C.xy_data_array[i][j])<.02:
            xvals += [xmin+j*deltax]
            yvals += [ymin+i*deltay]

To look at the points on the curve add these 2 lines:

for i in range(0,len(xvals)):
    print "(%f,%f),"%(xvals[i],yvals[i])

As the link showed, the default number of points is a grid of 150 by 150. I found it necessary to have a bigger grid size and the plot_points=200 makes a 200 by 200 grid of 40,000 points. The comment "Then you get the points by looking at sign changes, or values close to zero." refers to the fact that most of those points aren't plotted. The actual points that end up getting plotted from the grid are just those where f(x,y) is close to 0--I chose abs(C.xy_data_array[i][j])<.02 and have been getting expected results.