Banff cluster algebras and finite Laurent intersection rings in SageMath

This SageMath extension adds two new algebra classes:

• FiniteLaurentIntersectionRing — a finite intersection of Laurent polynomial rings together with birational change-of-charts data, providing divisor groups, prime divisors, and class group computations.
• BanffClusterAlgebra — a Banff (locally acyclic) cluster algebra realized both as a cluster algebra and as a finite Laurent intersection ring, giving effective algorithms for membership, divisor groups, class groups, and factorization.

These implement the algorithms of Pompili and Smertnig (2026), who introduced FLIRs as a class of rings that contains locally acyclic cluster algebras, full-rank upper cluster algebras, and several other families. The class-group and factoriality algorithms use multivariate polynomial factorization and avoid expensive Gröbner basis calculations.

The code is being added to SageMath via PR #42538 (work in progress) and is licensed under the GNU GPL v2 or later, in line with the rest of SageMath.