  A spectral scan of the circumstellar environment of the asymptotic giant
branch (AGB) star R~Doradus was taken with ALMA in cycle 2 at frequencies
between 335 and 362 GHz and with a spatial resolution of $\sim$150
milliarcseconds. Many molecular lines show a spatial offset between the blue
and red shifted emission in the innermost regions of the wind. The
position-velocity diagrams of this feature, in combination with previous SPHERE
data and theoretical work point towards the presence of a compact
differentially rotating disk, orientated nearly edge-on. We model the $^{\rm
28}$SiO ($v=1,~J=8\to7$) emission with a disk model. We estimate the disk mass
and angular momentum to be $3 \times 10^{-6}$ Solar masses and $5 \times
10^{40}\ {\rm m^2 kg/s}$. The latter presents an `angular momentum problem'
that may be solved by assuming that the disk is the result of wind-companion
interactions with a companion of at least 2.5 earth masses, located at 6 AU,
the tentatively determined location of the disk's inner rim. An isolated clump
of emission is detected to the south-east with a velocity that is high compared
to the previously determined terminal velocity of the wind. Its position and
mean velocity suggest that it may be associated with a companion planet,
located at the disk's inner rim.
