homlab-solver 0.1.0

针对单个无交叉点图的 HomLab 求解算法。

homlab-solver

homlab-solver is a small Python package for solving a single non-intersecting HomLab diagram stored as JSON.

The package currently exposes a Python API. It does not define a command-line entry point yet.

Requirements

• Python 3.10 or newer
• No runtime dependencies outside the Python standard library

Installation

After the package is published to PyPI:

python -m pip install homlab-solver

For local development from this repository:

python -m pip install -e .

Quick Start

import random

from homlab_solver import solve_single_json

rng = random.Random(42)
result = solve_single_json("test.json", rng=rng)

if result.msg:
    raise RuntimeError(result.msg)

print(result.ans)

You can run the same example from a shell:

python - <<'PY'
import random
from homlab_solver import solve_single_json

result = solve_single_json("test.json", rng=random.Random(42))

if result.msg:
    raise SystemExit(result.msg)

print(result.ans)
PY

With the sample test.json in this repository, the output is:

(-A^2-A^(-2)) * C[-1, 1, -2]

API

solve_single_json(filepath, rng, loop_value="(-A^2-A^(-2))", eps=1e-8)

Solves one HomLab JSON file.

Parameters:

• filepath: path to a HomLab JSON file.
• rng: a random.Random instance used for small geometric perturbations and randomized ray tests. Pass a seeded instance when you need reproducible output.
• loop_value: symbolic value used for each free loop.
• eps: floating-point tolerance for geometric predicates.

Returns a SolverObject with:

• ans: the computed symbolic answer, or None if solving failed.
• msg: an empty string on success, or an error message on failure.

Input JSON

The solver expects a JSON object describing a single HomLab diagram. At minimum, the file must include:

{
  "type": "homlab",
  "n": 2,
  "hs": {
    "handle_genus_0000000": {"x": 0.5, "y": 0.35},
    "handle_genus_0000001": {"x": 1.35, "y": 0.35},
    "handle_border_0000000": {"x": 0.5, "y": -0.2},
    "handle_border_0000001": {"x": 1.35, "y": -0.2}
  },
  "ns": {
    "node_0000000": {"x": 0.0, "y": 0.0}
  },
  "es": {
    "edge_0000000": {
      "id_1": "handle_genus_0000000",
      "id_2": "node_0000000"
    }
  }
}

Important constraints:

• type must be "homlab".
• n must be 2.
• The four handle IDs shown above are required by the current solver.
• Normal node IDs should start with node_.
• Handle IDs should start with handle_.
• Edge objects must contain id_1 and id_2.
• IDs starting with # are treated as special metadata and ignored by the solving step.
• Non-handle nodes are expected to have degree 2.
• Handle nodes are expected to have degree 0 or 1.

Building

This project uses poetry-core as its build backend. To build a source distribution and wheel:

python -m pip install --upgrade build
python -m build

The generated artifacts will be written to dist/.

Before uploading to PyPI, check the package metadata:

python -m pip install --upgrade twine
python -m twine check dist/*

Upload to PyPI:

python -m twine upload dist/*

License

This project is licensed under the MIT License. See LICENSE for details.