Zero-sum sequences
zero-sum-sequences computes with sequences over finite additive groups:
minimal zero-sum sequences (atoms), factorizations and their length sets,
automorphism orbits, and zero-sum constants. It runs in ordinary Python; SageMath is optional.
Installation
Requires Python 3.12 or newer:
python -m pip install zero-sum-sequences
A small example
Over C₂ ⊕ C₄, take an atom A of length five and its negative B = -A.
Sequences are written multiplicatively. The product A * B has
factorization lengths 2, 4, and 5, but not 3:
from zero_sum_sequences import AdditiveSequenceSpace, FiniteAdditiveGroup
G = FiniteAdditiveGroup.cyclic_product(2, 4)
S = AdditiveSequenceSpace(G)
A = S((0, 1)) ** 3 * S((1, 0), (1, 1))
B = -A
A.is_atom(), B.is_atom() # (True, True)
sorted((A * B).length_set()) # [2, 4, 5]
Documentation — installation options, tutorial, definitions, and API reference.
1 maintainer
Metadata
1 maintainer
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