The Take Home Database
All knot data on the Knot Atlas is now available as a take-home database file in compressed RDF (Resource Description Framework) format. Load it and use it as follows.
Loading
Pick up the full untreated unsorted monster katlas.rdf.gz and save it somewhere where you have a lot of space; it is almost 50MB compressed and almost 400MB uncompressed.
Alternatively, pick up one of the sorted smaller pieces from our Data directory:
- Rolfsen.rdf.gz (1MB/5MB) - Data from The Rolfsen Knot Table.
- Knots11.rdf.gz (0.5MB/5MB) - Data from The Hoste-Thistlethwaite Table of 11 Crossing Knots.
- Knots12.rdf.gz (0.7MB/4MB) - Data for 12 crossing knots.
- Knots13.rdf.gz (3MB/17MB) - Data for 13 crossing knots.
- Knots14.rdf.gz (11MB/73MB) - Data for 14 crossing knots.
- Knots15.rdf.gz (31MB/220MB) - Data for 15 crossing knots.
- Links.rdf.gz (0.6MB/6MB) - Data from The Thistlethwaite Link Table.
- TorusKnots.rdf.gz (0.04MB/0.5MB) - Data from 36 Torus Knots.
Using the Take Home Database from a Linux Shell
The examples in this section assume that you have downloaded all the "small pieces" from the previous section and placed them in your working directory, but that you did not bother to uncompress them.
The Jones polynomial of 10_71:
[drorbn@katlas ~/Data]$ zgrep 10_71 Rolfsen.rdf.gz | grep Jones_Polynomial
<knot:10_71> <invariant:Jones_Polynomial> "<math>-q^5+3 q^4-6 q^3+10 q^2-12 q+13-12 q^{-1} +10 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5} </math>" .
The first few invariants (lexicographically) of 10_71:
[drorbn@katlas ~/Data]$ zgrep knot:10_71 Rolfsen.rdf.gz | head
<knot:10_71> <invariant:2nd_AlexanderIdeal> "<math>\\{1\\}</math>" .
<knot:10_71> <invariant:3-Genus> "3" .
<knot:10_71> <invariant:Alexander_Polynomial> "<math>-t^3+7 t^2-18 t+25-18 t^{-1} +7 t^{-2} - t^{-3} </math>" .
<knot:10_71> <invariant:BraidIndex> "5" .
<knot:10_71> <invariant:BraidWord> "<math>\\textrm{BR}(5,\\{-1,-1,2,-1,-3,2,2,4,-3,4\\})</math>" .
<knot:10_71> <invariant:Bridge_Index> "3" .
<knot:10_71> <invariant:ConcordanceGenus> "<math>3</math>" .
<knot:10_71> <invariant:Conway_Notation> "[22,21,2+]" .
<knot:10_71> <invariant:ConwayNotation> "[22,21,2+]" .
<knot:10_71> <invariant:Conway_Polynomial> "<math>-z^6+z^4+z^2+1</math>" .
The Alexander Polynomials of the last few knots in the Rolfsen table:
[drorbn@katlas ~/Data]$ zgrep Alexander_Polynomial Rolfsen.rdf.gz | tail
<knot:10_156> <invariant:Alexander_Polynomial> "<math>t^3-4 t^2+8 t-9+8 t^{-1} -4 t^{-2} + t^{-3} </math>" .
<knot:10_157> <invariant:Alexander_Polynomial> "<math>-t^3+6 t^2-11 t+13-11 t^{-1} +6 t^{-2} - t^{-3} </math>" .
<knot:10_158> <invariant:Alexander_Polynomial> "<math>-t^3+4 t^2-10 t+15-10 t^{-1} +4 t^{-2} - t^{-3} </math>" .
<knot:10_159> <invariant:Alexander_Polynomial> "<math>t^3-4 t^2+9 t-11+9 t^{-1} -4 t^{-2} + t^{-3} </math>" .
<knot:10_160> <invariant:Alexander_Polynomial> "<math>-t^3+4 t^2-4 t+3-4 t^{-1} +4 t^{-2} - t^{-3} </math>" .
<knot:10_161> <invariant:Alexander_Polynomial> "<math>t^3-2 t+3-2 t^{-1} + t^{-3} </math>" .
<knot:10_162> <invariant:Alexander_Polynomial> "<math>-3 t^2+9 t-11+9 t^{-1} -3 t^{-2} </math>" .
<knot:10_163> <invariant:Alexander_Polynomial> "<math>t^3-5 t^2+12 t-15+12 t^{-1} -5 t^{-2} + t^{-3} </math>" .
<knot:10_164> <invariant:Alexander_Polynomial> "<math>3 t^2-11 t+17-11 t^{-1} +3 t^{-2} </math>" .
<knot:10_165> <invariant:Alexander_Polynomial> "<math>-2 t^2+10 t-15+10 t^{-1} -2 t^{-2} </math>" .
11 crossings knots with determinant equal to 1:
[drorbn@katlas ~/Data]$ zgrep Determinant Knots11.rdf.gz | grep \"1\" <knot:K11n34> <invariant:Determinant> "1" . <knot:K11n42> <invariant:Determinant> "1" . <knot:K11n49> <invariant:Determinant> "1" . <knot:K11n116> <invariant:Determinant> "1" .
Creating the database
If you have access to the katlas command line, you can follow these instructions for Creating the take home database.
