var('u v')
x1 = u * cos(v)
y1 = u * sin(v) / 2
x = (x1 + y1)
y = (x1 - y1)
z = x^4 + y^4 - 4 * x * y + 1
parametric_plot3d([x, y, z], (u, 0, 1.5), (v, 0, 2 * pi)) + \
point([(1, 1, -1), (-1, -1, -1)], pointsize = 100, rgbcolor = "green") + \
point((0, 0, 1), pointsize = 100, rgbcolor = "red")
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z = u^4 + v^4 - 4 * u * v + 1
contour_plot(z, (u, -2, 2), (v, -2, 2), contours = (-1, -0.5, 0.5, 0.9, 1, 1.1, 1.5, 2, 2.5, 3), plot_points = 100, fill = False) + \
point([(1, 1), (-1, -1)], pointsize = 30, rgbcolor = "green") + \
point((0, 0), pointsize = 30, rgbcolor = "red")
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