Invariant of a binary form
In mathematics, an invariant of a binary form is a polynomial in the coefficients of a binary form in two variables x and y that remains invariant under unimodular transformations of the variables x and y.
The invariants of a binary form are a graded algebra, and Gordan (1868) proved that this algebra is finitely generated if the base field is the complex numbers.
The ring of invariants
The structure of the ring of invariants has been worked out for small degrees as follows:
- The only invariants are constants.
- The ring of invariants is a polynomial ring in 1 variable generated by the discriminant
- Classical
- Classical
- Classical
- Classical
- von Gall (1888) Dixmier & Lazard (1986)
- von Gall (1880), Shioda (1967)
- Brouwer & Popoviciu (2009)
- Brouwer & Popoviciu (2010) Generated by 106 invariants