3 – Proj | CGS

Let $G_S$ be a gram matrix of $S$.
Let $P_0$ be a known ample class.
Let $m,d$ be integers.

CGS takes this data as input and returns the set

$$ \{ C\in S \mid \langle C,C\rangle_{S}=d, \; \, \langle C,P_0 \rangle_{S}<m\}$$

When $d=-2$, the program $CGS$ acts as SmoothRationalCurves. Thus, it returns the set of classes of square $-2$ that are also classes of smooth rational curves.