Bug in diff and inverting variable in rings over a fraction field

```m2
i1 : R = frac(QQ[x,y])[z];

i2 : 1/x

1
o2 = -
x

o2 : frac(QQ[x..y])

i3 : 1/x_R
stdio:3:2:(3): error: not implemented yet: fraction fields of polynomial rings over rings other than ZZ, QQ, or a finite field

i4 : x_R^-1

1
o4 = -
x

o4 : R
```

Start by reproducing the transcript in a Macaulay2 session, comparing 1/x, 1/x_R, and x_R^-1 for R = frac(QQ[x,y])[z]. Then trace the fraction-field and ring-inversion handling implicated by the not-implemented error. Done means the reproduced forms behave consistently without that error, with regression coverage for the case.

Written by the indexing model from the issue text.