Calculating the distance of objects using the Gaia DR1 The Gaia DR1 was released middle of September with ~1.1 billion objects. The schema contains right ascension, declination and parallax, which could be used to calculate Cartesian co-ordinates (xyz).

The overwhelming majority (>99.998%) of objects do not contain an entry for parallax. I suspect this needs to be computed using other columns (e.g. phot_g_mean_mag?).

How do you compute the parallax for an object when its not included?

The data model is documented here .
The early 1990s Hipparcos mission
yielded parallaxes for 118000 stars (Hipparcos catalog) and positions without parallax for another 2.4 million (Tycho-2 catalog).
The Tycho-Gaia astrometric solution (TGAS) combines those data with preliminary Gaia observations to get 2 million parallaxes, "only" 17 times as many as Hipparcos, with better precision.
If this is a small fraction of the total number of star positions, it's not a deficiency; it's just easier to get a position than a parallax.
Lindegren et al. 2016 explain what they could or could not do with the first 14 months of Gaia observations.
Future Gaia data releases should have still more parallaxes.