Birational type method

The proof route(s) behind birational_type, joined by +:

• free_presentation: the chart has no equations, so it is rational.
• rigid: a single-point space over $\mathbb Z$.
• linear_elimination: coordinates were eliminated linearly until the space became a projective space.
• point_field: zero-dimensional core; its field is identified by a minimal polynomial.
• curve_genus: one-dimensional core; geometric genus of a birational plane model. With +weierstrass_riemann_roch, a genus-1 Weierstrass model was obtained by Riemann–Roch.
• surface_conic_bundle: conic bundle over $\mathbb P^1$, so the surface is rational.
• surface_elliptic_fibration_chi: genus-1 fibration. The value of $\chi$ decides between rational, K3, properly elliptic and ruled.
• surface_ruled_over_curve: ruled over a genus-1 curve.
• hypersurface_double_cover: double-cover and conic reductions of a higher-dimensional hypersurface.
• threefold_elliptic_canonical_class: elliptic threefold whose canonical class was computed (e.g. Calabi–Yau).
• empty_char0: no characteristic-0 points.
• surface_undetermined, higher_undetermined, timeout, error: not settled.

Full details: docs/birational_type.md.