Catalecticant

Meicatalecticizant would more completely express the meaning of that which, for the sake of brevity, I denominate the catalecticant.

For binary quartics the catalecticant vanishes when the form is a sum of two 4th powers.

For a ternary quartic the catalecticant vanishes when the form is a sum of five 4th powers.

For quaternary quartics the catalecticant vanishes when the form is a sum of nine 4th powers.

For quinary quartics the catalecticant vanishes when the form is a sum of fourteen 4th powers.