Orientable

A matroid is orientable if it admits an orientation: a chirotope $\chi: E^r \to \{-1,0,+1\}$ that is alternating, is nonzero exactly on (orderings of) bases, and satisfies the chirotope exchange axiom. Every matroid realizable over $\mathbb R$ is orientable.

The question is encoded as a SAT problem, with one Boolean variable per basis for the sign of $\chi$, and decided by a SAT solver. A non-simple matroid gets the value of its simplification.

Full details: docs/is_orientable.md.