# 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?

Looking in the code via

`??implicit_plot`

we get the relevant lines...and it is hard to arrange $f<0$ passing a square to the

`region_plot`

...This leads one to investigate a similar phenomenon:

produces a line on the coordinate y-axis, but

produces an empty plot.