---
id: passagemath-homfly
version: "10.8.9"
license: GPL-2.0-or-later
license_treatment: copyleft
maintenance: active
---

# passagemath-homfly — passagemath: Homfly polynomials of knots/links with libhomfly

License: copyleft · Maintenance: active · Downloads: 82.3K/mo

## What it is and what it does

passagemath-homfly wraps libhomfly, a C library for computing Homfly polynomials—a key invariant in knot theory. It exposes a Cython interface allowing Python developers to compute polynomial invariants for knots and links. The package is part of the passagemath ecosystem, a modularized fork designed for pip-installable distribution and integration with the scientific Python ecosystem.

The library accepts knot and link diagrams in a specific string format and returns polynomial coefficients as dictionaries. It is actively maintained with recent releases and broad platform support including macOS, Linux, and Windows. The package depends on cysignals for signal handling and requires Python 3.11 or later.

Use it for:

- Compute Homfly polynomial invariants for knot diagrams in research or educational settings.
- Integrate knot invariant computation into larger mathematical software pipelines.
- Verify knot equivalence or distinguish non-equivalent knots using polynomial invariants.
- Analyze topological properties of links in computational geometry or topology projects.

## Worth the install?

AI-flagged interpretation of the facts above — verify before relying.

Provides a Python interface to libhomfly for computing Homfly polynomials of knots and links.

Yes, if you need to compute Homfly polynomials for knots and links. The package is actively maintained, supports current Python versions, has no known vulnerabilities, and provides convenient pip installation with pre-built wheels. The copyleft GPL-2.0-or-later license requires that derivative works remain open-source. Install friction is moderate but manageable for the specialized mathematical use case.

## Install

pip install passagemath-homfly
uv add passagemath-homfly
poetry add passagemath-homfly

## Installing passagemath-homfly

Before you install: Medium install friction due to compiled wheel dependencies. Package is actively maintained with releases within days, supports Python 3.11–3.14, and provides pre-built wheels across macOS, Linux, and Windows platforms.

License in practice: Licensed under GPL-2.0-or-later (copyleft). Use requires compliance with GPLv2+ terms; derivative works and distributions must be released under compatible open-source licenses.

Quickstart:

pip install passagemath-homfly

from sage.libs.homfly import homfly_polynomial_dict
trefoil = '1 6 0 1  1 -1  2 1  0 -1  1 1  2 -1 0 1 1 1 2 1'
result = homfly_polynomial_dict(trefoil)

Requires Python 3.11–3.14; depends on cysignals runtime library.

Verify before relying:

- Exact API surface and supported knot/link representation formats beyond the example shown.
- Performance characteristics and scalability limits for large or complex knot diagrams.
- Compatibility details with different cysignals versions.

## Package facts

- License: GPL-2.0-or-later (copyleft)
- Python support: supports_current
- Install friction: medium
- Maintenance: active
- Downloads: 82.3K/month (top 15,000 on PyPI)
- Known vulnerabilities: none known

## Tags

homfly polynomial knot, knot invariant computation, link polynomial libhomfly, knot theory python, homfly invariant calculator, knot-theory, topology, mathematical-software

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