passagemath-homfly

10.8.4 verified Mon Apr 27 auth: no python

passagemath-homfly provides computation of Homfly polynomials for knots and links using libhomfly, integrated with the passagemath ecosystem. Current version 10.8.4, requiring Python ≥3.11 and <3.15. Follows passagemath release cadence; stable maintenance.

pip install passagemath-homfly

Common errors

error ImportError: cannot import name 'link_homfly_polynomial' from 'passagemath.homfly' ↓

cause Incorrect import path or passagemath-homfly not installed.

fix

Run 'pip install passagemath-homfly' then use 'from passagemath.homfly import link_homfly_polynomial'

error TypeError: expected a Sage knot or link, got str ↓

cause Passing a string (e.g., '3_1') directly to link_homfly_polynomial.

fix

Create a Knot object: Knot('3_1') before passing.

error ModuleNotFoundError: No module named 'sage' ↓

cause SageMath environment not installed or not activated.

fix

Install passagemath-sage or full SageMath, or run within a SageMath environment (e.g., 'sage -python').

Warnings

deprecated Direct import from 'passagemath.homfly' may be deprecated in future releases. Use full import path as shown in quickstart. ↓

fix Always use 'from passagemath.homfly import link_homfly_polynomial'

gotcha Knot/link must be a SageMath Knot or Link object, not a string. Common mistake: passing a knot name as string directly. ↓

fix Wrap knot name in Knot('3_1') or Link().

breaking Python 3.11+ required. Versions prior to 10.8 may fail on Python 3.12+ due to C library incompatibility. ↓

fix Upgrade to 10.8.4 and use Python 3.11-3.14.

Imports

link_homfly_polynomial
wrong
```
from sage.knots import homfly_polynomial
```
correct
```
from passagemath.homfly import link_homfly_polynomial
```
Old SageMath import path may not include libhomfly; use passagemath namespace
Knot
```
from sage.knots.knot import Knot
```
Knot class is in sage.knots; passagemath-homfly uses this for input

Quickstart

Compute the Homfly polynomial of a trefoil knot. Requires SageMath environment.

from sage.knots.knot import Knot
from passagemath.homfly import link_homfly_polynomial

# Create a trefoil knot (3_1)
trefoil = Knot('3_1')
# Compute Homfly polynomial
poly = link_homfly_polynomial(trefoil)
print(poly)