Let $S = \mathbb{Q}[x,y,z]$ and $I = (x^3 - y, x^4 - z)$, a monomial space curve.
(a) Compute the reduced Groebner basis of $I$ and list its elements.
(b) Compute a minimal free resolution of $S/I$ and display its Betti table.
(c) State $\dim(S/I)$.
Do not answer anything you have not seen in a tool output.
