Invariant of a binary form

In mathematical invariant theory, 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 the special linear group acting on the variables x and y. == Terminology == A binary form (of degree n) is a homogeneous polynomial ∑ i = 0 n ( n i ) a n − i x n − i y i = a n x n + ( n 1 ) a n − 1 x n − 1 y + ⋯ + a 0 y n {\displaystyle \sum _{i=0}^{n}{\binom {n}{i}}a_{n-i}x^{n-i}y^{i}=a_{n}x^{n}+{\binom {n}{1}}a_{n-1}x^{n-1}y+\cdots +a_{0}y^{n}} .

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