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2021-07-27 14:08:00 +0200	received badge	● Popular Question (source)
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2017-08-19 17:33:59 +0200	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 19:30:48 +0200	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 19:30:47 +0200	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?