database-knotinfo 2026.3.1

The KnotInfo and LinkInfo databases as lists of dictionaries

Database KnotInfo

This repository contains a snapshot of the complete content of the KnotInfo and LinkInfo databases. Each database is provided as a Python list of Python dictionaries. The data are from the corresponding Excel spreadsheets available on the KnotInfo and LinkInfo homepages on the date of release.

Please note that the databases contain columns that are not visible on the web pages (see also the Release Notes 2023.4.8). The validity of the information in such columns cannot be guaranteed. Also, there are plans to remove them in the future.

This repository was created as a part of the SageMath interface to these databases (see the corresponding section of the SageMath reference manual or this tutorial) but can also be used independently.

In Python, it can be used as follows:

>>> from database_knotinfo import link_list
>>> k = link_list()
>>> len(k)
2979
>>> names_k = k[0]
>>> type(names_k)
<type 'dict'>
>>> names_k['braid_index']
'Braid Index'
>>> k2 = k[2]
>>> k2['name']
'3_1'
>>> k2['braid_index']
'2'
>>> k2['homfly_polynomial']
'(2*v^2-v^4)+(v^2)*z^2'

>>> l = link_list(proper_links=True)
>>> len(l)
4189
>>> names_l = l[0]
>>> type(names_l)
<type 'dict'>
>>> names_l['braid_notation']
'Braid Notation'
>>> l2 = l[2]
>>> l2['name']
'L2a1{1}'
>>> l2['homflypt_polynomial']
'v/z-v^3/z + v*z'

To build a new release, the CSV files can be upgraded with the create_knotinfo_csv.py script. A cronjob executes it on the first day of every month and creates a new release if differences are detected.

Installation

Python

pip install database_knotinfo

or

pip install database_knotinfo==2021.9.1

if you want to install a former version.

SageMath

Since Release 9.4, the database can be installed in Sage by:

sage -i database_knotinfo

This will contain integration with the knot and link functionality of Sage. Sage 9.4 ships the PyPI release 0.7 of the database. To use a more recent one you have to execute

sage -package update database_knotinfo <version>

before the installation command above, for example:

sage -package update database_knotinfo 2021.9.1

This procedure can be used to upgrade to the next version, as well. But note that there is a bug in 9.4 concerning such upgrades which will be fixed in SageMath 9.5 (see Trac ticket #32099). A workaround for 9.4 can be perfomed in a Sage session as follows:

sage: from sage.databases.knotinfo_db import KnotInfoDataBase
sage: KnotInfoDataBase().reset_filecache()

If you upgrade to a version of the database which is ahead of the version the SageMath release is build on, you should keep in mind, that the examples shown in the Sage reference manual may be outdated.

In case the installation via sage -i is failing on your system you can try:

sage -pip install database_knotinfo

or

sage -pip install database_knotinfo==0.7

for the version compatible the the current Sage release.

Versioning

Version numbers are automatically generated every month if differences to the original databases are detected. They follow the scheme

<year>.<month>.<day>

Help

If you note a divergence between this repository and the original data in case the current release is older than a month please create an issue about that.

Credits

Many thanks to Chuck Livingston and Allison Moore for making the data available. For further acknowledgments see the corresponding homepages.