  Let F denote a homogeneous degree 4 polynomial in 3 variables, and let s be
an integer between 1 and 5. We would like to know if F can be written as a sum
of fourth powers of s linear forms (or a degeneration). We determine necessary
and sufficient conditions for this to be possible. These conditions are
expressed as the vanishing of certain concomitants of F for the natural action
of SL_3.
