zero-sum-sequences

zero-sum-sequences provides immutable finite additive sequences and algorithms for factoring them into minimal zero-sum sequences. It runs in ordinary Python with NetworkX and optionally integrates with additive groups supplied by SageMath.

For a sequence over an additive group , the zero-sum condition is

The package computes sets of factorization lengths, minimum and maximum lengths, witnesses, and complete factorizations. It also supports atom catalogues, factorization relations, and automorphism orbits. The ambient group and an upper bound for its Davenport constant are supplied explicitly by the caller.

For example, over , the minimal zero-sum sequences , , and satisfy the factorization relation .

An executable tutorial introduces the API with small examples; the repository also includes benchmarks.