Symbolic method for binary-form invariants
= Symbolic method for binary-form invariants
Replace a degree-$d$ <binary form> by the formal power $(a_0x+a_1y)^d$ and recover its coefficients with the linear rule $a_0^{d-i}a_1^i\mapsto f_i$. For a coefficient invariant of degree $r$, use $r$ symbolic letters, each of degree $d$, polarize and then apply this rule to each letter. Products of brackets $(ab)=a_0b_1-a_1b_0$ generate the invariant expressions before the final coefficient substitution.