Editing Invariant theory (section)

== Examples ==
Simple examples of invariant theory come from computing the invariant [[monomial]]s from a group action. For example, consider the <math>\mathbb{Z}/2\mathbb{Z}</math>-action on <math>\mathbb{C}[x,y]</math> sending
:<math>
\begin{align}
x\mapsto -x && y \mapsto -y
\end{align}
</math>
Then, since <math>x^2,xy,y^2</math> are the lowest degree monomials which are invariant, we have that
:<math>\mathbb{C}[x,y]^{\mathbb{Z}/2\mathbb{Z}} \cong \mathbb{C}[x^2,xy,y^2] \cong \frac{\mathbb{C}[a,b,c]}{(ac - b^2)}</math>
This example forms the basis for doing many computations.