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Normal forms for homogeneous cubic polynomials in $\mathbb{R}[x_1, x_2, x_3]$
Hi, Jeanne! It may help to have some geometric explanation of the normal forms over $\mathbb{R}$. The standard account is this:
If the projective cubic curve $F(x_1,x_2,x_3)=0$ is nonsingular (the …