Stanley-Reisner-Ring/Rechnung/1/Aufgabe

Berechne in ${}\mathbb {Q} [X,Y,Z]/(XY,XZ)$ das Produkt

{\left(3+3X-5X^{2}-4Y-2Y^{2}+3Z-Z^{3}+YZ-Y^{2}Z+2YZ^{3}\right)}\cdot {\left(-2+3X-X^{3}+Y+Z+5Y^{3}-Z^{2}-2YZ+Y^{2}Z^{2}\right)}.