  Comets formed in the outer and cold parts of the disk which eventually
evolved into our Solar System. Assuming that the comets have undergone no major
processing, studying their composition provides insight in the pristine
composition of the Solar Nebula. We derive production rates for a number of
volatile coma species and explore how molecular line ratios can help constrain
the uncertainties of these rates. We analyse observations obtained with the
Atacama Large Millimetre/Submillimetre Array of the volatile composition of the
comae of comets C/2012 F6 (Lemmon) and C/2012 S1 (ISON) at heliocentric
distances of ~1.45 AU and ~0.56 AU, respectively. Assuming a Haser profile with
constant outflow velocity, we model the line intensity of each transition using
a 3D radiative transfer code and derive molecular production rates and parent
scale lengths. We report the first detection of CS in comet ISON obtained with
the ALMA array and derive a parent scale length for CS of ~200 km. Due to the
high spatial resolution of ALMA, resulting in a synthesised beam with a size
slightly smaller than the derived parent scale length, we are able to
tentatively identify CS as a daughter species, i.e., a species produced in the
coma and/or sublimated from icy grains, rather than a parent species. In
addition we report the detection of several CH3OH transitions and confirm the
previously reported detections of HCN, HNC and H2CO as well as dust in the coma
of each comet, and report 3sigma upper limits for HCO+. We derive molecular
production rates relative to water of 0.2% for CS, 0.06-0.1% for HCN,
0.003-0.05% for HNC, 0.1-0.2% for H2CO and 0.5-1.0% for CH3OH, and show that
the modelling uncertainties due to unknown collision rates and kinematic
temperatures are modest and can be mitigated by available observations of
different transitions of HCN.
