At the moment Sage offers just a small set of 250 named knots (src/sage/knots/knot_table.py) taken form the Rolfsen table. Proper named links aren't available at all.

Nowadays, larger databases for knots and links are available at the Knot Atlas pages in RDF-format and at KnotInfo as XLS / XLSX -files. Since parsing of CSV files is already supported by Sage, this is a good start to produce a Sage packages from these files containing about 3000 knots and 4000 proper links together with a lot of their properties and invariants.

Such a package has a couple of advantages:

1. Perform cross-checks for about 7000 links of alternative implementations of certain methods.
2. Do cross-checks against results listed in the KontInfo database.
3. Provide properties for these links that are not provided by Sage, yet.
4. Implement a link identification method for our link class (like KnotFinder).
5. Launch webpages containing additional information for a link or alternate graphical representations.

The aim of this ticket is to have the databases accessible in Sage together with conversion methods for the most important properties and invariants.

Many thanks to Allison Moore and Chuck Livingston for their kind permission to have this interface implemented and their offer to support us.

Having checked out the ticket for the first time, you have to run

./configure --enable-download-from-upstream-url
sage -i database_knotinfo

in order to have the databases installed. If you like to run all relevant doctests on the installation use:

sage -i -c database_knotinfo

CC: @miguelmarco @mkoeppe @kiwifb

Component: algebraic topology

Keywords: knot, link

Author: Sebastian Oehms

Branch: 9cde996

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/30352