Spherogram

2.4.1 verified Fri May 01 auth: no python

A Python library for spherical diagrams in 3-manifold topology, including links, knots, braids, tangles, and planar diagrams. Current version 2.4.1 supports ribbon concordance tools, bridge number bounds, and knot Floer homology. Release cadence is irregular, with major features in even-numbered versions.

pip install spherogram

Common errors

error ModuleNotFoundError: No module named 'spherogram' ↓

cause spherogram not installed or installed in wrong environment.

fix

Run pip install spherogram in the target Python environment.

error ImportError: cannot import name 'Link' from 'spherogram.links' ↓

cause Using incorrect submodule import path. The correct symbol is at top level.

fix

Change to from spherogram import Link.

error ValueError: Unrecognized knot name ↓

cause Knot name not in the internal database or string malformed.

fix

Use standard notation like 'K11n34' (K = knot, 11 crossings, n = non-alternating, 34th in table). Check spherogram's knot_table for available names.

Warnings

breaking Version 2.0 changed the sign convention for knot signature (positive knots now have negative signature) and braid generator signs (positive generators give positive crossings). Older code expecting old signs will produce wrong results. ↓

fix Update any code relying on signature signs or braid generator orientation.

breaking The function `Link.simplify()` was significantly improved in 2.1 but may change the diagram representation; do not depend on stable crossing order after simplification. ↓

fix Do not assume crossing indices or ordering remain constant after simplify().

deprecated Automatic import of `snappy_16_knots` in 2.4.1 may be removed in future; always import explicitly if needed. ↓

fix Use `from snappy_16_knots import ...` explicitly.

gotcha Many functions return `Link` objects that may have duplicate crossings or be non-minimal; always call `simplify()` before computing invariants if diagram size matters. ↓

fix After constructing a Link, call L.simplify() for a reduced diagram.

Imports

Link
wrong
```
from spherogram.links import Link
```
correct
```
from spherogram import Link
```
Top-level import is correct; submodule imports may break
Knot
```
from spherogram import Knot
```

Tangle

wrong

from spherogram.tangles import Tangle

correct

from spherogram import Tangle

Submodule path may not be stable

Quickstart

Creates a link from a named knot (e.g. 'K11n34') and computes its bridge number and Jones polynomial.

from spherogram import Link
L = Link('K11n34')
print(L.bridge_number())
print(L.jones_polynomial())