Ternary quartic
In mathematics, a ternary quartic form is a degree 4 homogeneous polynomial in three variables. Hilbert's theorem

 showed that a positive semi-definite ternary quartic form over the reals  can be written as a sum of three squares of quadratic forms. Invariant theory

The ring of invariants is generated by 7 algebraically independent invariants of degrees 3, 6, 9, 12, 15, 18, 27 (discriminant) , together with 6 more invariants of degrees 9, 12, 15, 18, 21, 21, as conjectured by . discussed the invariants of order up to about 15. The Salmon invariant is a degree 60 invariant vanishing on ternary quartics with an
inflection bitangent. Catalecticant

The catalecticant of a ternary quartic is the resultant of its 6 second partial derivatives. It vanishes when the ternary quartic can be written as a sum of five 4th powers of linear forms. See also

Ternary cubic
Invariants of a binary form

References

. External links

Invariants of the ternary quartic

Invariant theory