This is of degree 8 in the coefficients, and degree 6 in the variables, and, for the canonical form, has the expression -9m 6 (x 3 +y 3 +z 3) 2 - (2m +5m 4 +20m 7) (x3 +y3+z3)xyz - (15m 2 +78m 5 -12m 8) Passing on to the ternary quartic we find that the number of ground forms is apparently very great.
Successive triangles in the diagram of forces may be constructed in the order XYZ, ZXA, AZB.
The Hessian is symbolically (abc) 2 azbzcz = H 3, and for the canonical form (1 +2m 3)xyz-m 2 (x 3 +y 3 +z 3).
How would you define XYZ? Add your definition here.