The hyperelliptic locus $V_{hyp}$ in $Q \subset \mathbb{P}^{11}$ is is birational to a product of a Hirzebruch surface $F$ with 3 copies of $\mathbb{P}^{1}$. The procedure returns a ring map corresponding to the rational map $$ \phi: F \ \times \ \mathbb{P}^1 \ \times \ \mathbb{P}^1 \ \times \ \mathbb{P}^1 \ \rightarrow \ V_{hyp} \ \subset \ \mathbb{P}^{11}.$$ This function prints the commands which check that the assertion of Thm 2.9 in [F.-O. Schreyer and I. Stenger, Marked Godeaux surfaces with special bicanonical fibers. https://arxiv.org/pdf/2201.12065.pdf] are true.
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The object verifyThmHypLocus is a method function.