I am trying to see that the localization of ring $A={\mathbb{C}[x,y,z]\over \left<xy, xz, yz \right>}$ on the ideal $\overline{\mathfrak{p}}=\left<\overline{x},\overline{y},\overline{z}\right>$ is a complete intersection. For this I am trying to use Macaulay2 to calculate who is $A_{\mathfrak{p}}$, but I can't find how to define the ideal $\overline{\mathfrak{p}}$ of the quotient ring $A$. Does anyone know how to do it?
Thank you very much!