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The [[catalecticant]] is an invariant of a form of even degree.
The [[Jacobian matrix and determinant|Jacobian]]
:<math> \det \begin{bmatrix}
\frac{\partial f}{\partial x} & \frac{\partial f}{\partial y} \\
\frac{\partial g}{\partial x} & \frac{\partial g}{\partial y} \\
\end{bmatrix}.</math>
is a simultaneous invariant of two forms ''f'', ''g''.
==The ring of invariants==
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