Hi There,

I have a couple of example questions that I'm trying to get my head around, a bit of guidance would be fabulous.

$\displaystyle S:=\{f\in\mathcal{Q}[X,Y]\mid f(X,Y)=f(Y,X) \mbox{ and } \deg(f)\geq 0\}$

1a: Give two polynomials that belong to $\displaystyle S$.

1b: Find a finite basis of the ideal $\displaystyle (S)$ of $\displaystyle \mathcal{Q}[X,Y]$ and justify your answer.

I then have the question where the questions are the same but based on this

$\displaystyle S:=\{f\in\mathcal{Q}[X,Y]\mid f(X,Y)=-f(Y,X)\}$.