auslander-py

Python bindings for the auslander crate: finite-dimensional basic algebras kQ/I over a checked prime field, where I is an admissible ideal given by forbidden words or by general relations, and finite-dimensional right modules. The v0.9 catalog API builds complete indecomposable catalogs, caches ordered Ext tables, enumerates multiplicities, and replays typed artifacts. classify_derived partitions a finite family up to derived equivalence, and verify_derived_atlas replays its atlas. Paths compose left to right; arrow matrices act on row vectors.

Guides

• Python workbench
• Checkpoints and theorem artifacts
• Compute requests
• Algebra and homological computations
• Representation theory
• Catalog atlas workflow
• Derived classification
• v0.9 migration

Quick start

With a field-bound gentle-tree algebra, catalog.atlas fixes the complete catalog and its inclusive Ext degree bound:

import auslander

field = auslander.PrimeField(5)
quiver = auslander.Quiver(4, [(0, 1), (1, 2), (3, 2)])
algebra = auslander.Algebra(quiver, [[0, 1]], field)
catalog = algebra.catalog()
atlas = catalog.atlas(max_degree=3)
result = atlas.enumerate([1, 1, 1, 1])
assert catalog.provenance == "gentle_tree"
assert result.status == "complete"
assert len(result) == 6

artifact = atlas.export([1, 1, 1, 1])
replayed = auslander.verify_catalog_atlas_artifact(artifact.canonical_json)
assert replayed.verification == "replayed"

The catalog workflow notebook displays the catalog decomposition, ordered Ext cells, materialized modules, artifact replay, and a degree-two obstruction.

The derived classification tour classifies the 77 connected gentle algebras with 3 vertices over F_2. It checks that the gentle trees form the class of A_3, separates a genus-1 pair by the winding class, prints one merge witness, and replays the atlas.

Building

Requires Rust (MSRV 1.88; development is pinned to Rust 1.92 via rust-toolchain.toml), Python >= 3.10, and maturin:

cd crates/auslander-py

# Development install into the active virtualenv:
maturin develop --release

# Or build a wheel (abi3, works on any CPython >= 3.10):
maturin build --release
pip install target/wheels/auslander-*.whl

Testing

python -m pytest tests