But the catalecticant of the biquadratic function of x, y was first brought into notice as an invariant by Mr Boole; and the discriminant of the quadratic function of x, y is identical with its catalecticant, as also with its Hessian. Meicatalecticizant would more completely express the meaning of that which, for the sake of brevity, I denominate the catalecticant.
In mathematical invariant theory, the catalecticant of a binary form of degree 2n is a polynomial in its coefficients that vanishes when the binary form is a sum of at most n powers Sturmfels (1993). It was introduced by Sylvester (1852); see (Miller 2010). The word catalectic refers to an incomplete line of verse, lacking a syllable at the end or ending with an incomplete foot.
The catalecticant can be given as the determinant of a catalecticant matrix (Eisenbud 1988), also called a Hankel matrix, that is a square matrix with constant (positive sloping) skew-diagonals, such as