2017-08-19 10:33:59 -0500 commented question Implicit plot with squaring and absolute value produces empty plot This leads one to investigate a similar phenomenon: region_plot(x==0, (-2, 2), (-2, 2), axes=False)  produces a line on the coordinate y-axis, but region_plot(x^2==0, (-2, 2), (-2, 2), axes=False)  produces an empty plot. 2017-08-18 12:30:48 -0500 asked a question Implicit plot with squaring and absolute value produces empty plot The following code: sage: x,y = var('x y') sage: implicit_plot(x, (x,-2,2), (y,-2,2))  produces a plot of a straight line along the coordinate y-axis as expected (it should plot the curve $x = 0$). However, this very similar code: sage: implicit_plot(x^2, (x,-2,2), (y,-2,2))  produces a plot with nothing on it, even though it should plot the curve $x^2 = 0$ which is clearly the same as the above curve. This problem seems to persist with any function $f(x, y)$, i.e., in the following code, f(x, y) = [some expression involving x and y] sage: implicit_plot(f(x, y), [x scale], [y scale]) sage: implicit_plot(f(x, y)^2, [x scale], [y scale])  the second line produces a nonempty plot while the third line produces an empty plot. Replacing f(x,y)^2 with abs(f(x,y)) or even abs_symbolic(f(x,y)) has the same effect: they all produce empty plots. The problem persists when one replaces implicit_plot with implicit_plot3d. What's going on? Is this a bug? 2017-08-18 12:30:47 -0500 asked a question Implicit plot with squaring and absolute value produces empty plot The following code: sage: x,y = var('x y') sage: implicit_plot(x, (x,-2,2), (y,-2,2))  produces a plot of a straight line along the coordinate y-axis as expected (it should plot the curve $x = 0$). However, this very similar code: sage: implicit_plot(x^2, (x,-2,2), (y,-2,2))  produces a plot with nothing on it, even though it should plot the curve $x^2 = 0$ which is clearly the same as the above curve. This problem seems to persist with any function $f(x, y)$, i.e., in the following code, f(x, y) = [some expression involving x and y] sage: implicit_plot(f(x, y), [x scale], [y scale]) sage: implicit_plot(f(x, y)^2, [x scale], [y scale])  the second line produces a nonempty plot while the third line produces an empty plot. Replacing f(x,y)^2 with abs(f(x,y)) or even abs_symbolic(f(x,y)) has the same effect: they all produce empty plots. The problem persists when one replaces implicit_plot with implicit_plot3d. What's going on? Is this a bug?