An explanation rather than a solution:

This is best understood by extrapolation from the <2D case.

```
sage: plot(1/x,(x, -4,4), ymin=-4, ymax=4, axes=False, frame=True)
```

plots a (section of) hyperbola and an almost vertical line around `x=0`

. this is a byproduct of the protting algorithm, hich computes `plot_points`

points of the curve and interpolates a curve between them. The almost vertical line is what remains of the interpolated segment between the lats point with `x<0`

and the first point with `x>0`

after clipping in the plot limits. This artefact can be avoided by requestiong `plot`

's algorithm to fetect the sign changes with the option `detect_poles`

:

```
sage: plot(1/x,(x, -4,4), ymin=-4, ymax=4, axes=False, frame=True, detect_poles=True)
```

Similarly, `plot3d`

(and `implicit_plot3d`

) compute `plot_points^2`

surface points and interpolates surface elements between them. The plane segments you see are the clipped remains of these surface elements around `y=0`

.

Unfortunately, these 3D plot functions do not have a `detect_poles`

option (which would be somewhat nontrivial to write in the 3D case, anyway...). And I am not aware of any easy way to "clip off" these surface elements straddling the discontinuity.

In this specific case, one could work around the difficulty by parametrically plotting the function in cylindrical or spherical coordinates, avoiding the discontinuity region. An approximation can be obtained by :

```
parametric_plot3d([r*cos(theta),r*sin(theta),max_symbolic(-10,min_symbolic(10,r*tan(theta)))],
(r,0,4),(theta,-pi/2+1e-3,pi/2-1e3)) +
parametric_plot3d([r*cos(theta),r*sin(theta),max_symbolic(-10,min_symbolic(10,r*tan(theta)))],
(r,0,4),(theta,-3*pi/2+1e-3,-pi/2-1e-3))
```

which can be clipped off afterwards (I can't remember how ATM, but this exists...).

HTH,

You can restrict the z-range a posteriori like this