>In 2D,
> r = 4, -1<x<3 does not display a slice of a circle, although
> r^2 = 25, -1<x<3 works.
>
>And in 3D,
> r = 4 + 0*phi, -1<z<3 cuts off the bottom of the sphere,
>but doesn't display a slice of the sphere.
>
>I'm using Graphing Calculator 3.5.

Hello,

These are both bugs in the software.

The difference between the first two is because implicit curves in 2D
are graphed using a completely different method than parametric curves.

To work around the first problem, writing the equation differently,
to force it being interpreted as an implicit equation, will recognize
the constraints. In this case, the simplest way to re-write it would be as
r + 0 = 4, -1<x<3 which should do what you expect.

In the last example, the problem is a bug in how the condition is parsed.
If you change it so that the equation is not linear in x, y, or z, that
will avoid the bug. For example r=4+0*phi,-1<z+0*x^2<3 will graph correctly.

I will work on correcting both of these for the next update.

Best regards,

Ron Avitzur