The Take Home Database: Difference between revisions
From Knot Atlas
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==Using From a Linux Shell== |
==Using From a Linux Shell== |
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The examples in this section assume that you have downloaded all the "small pieces" from the previous section and places them in your working directory, but that you did not bother to uncompress them. |
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The Jones polynomial of [[10_71]]: |
The Jones polynomial of [[10_71]]: |
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<knot:10_71> <invariant:ConwayNotation> "<nowiki>[22,21,2+]</nowiki>" . |
<knot:10_71> <invariant:ConwayNotation> "<nowiki>[22,21,2+]</nowiki>" . |
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<knot:10_71> <invariant:Conway_Polynomial> "<math>-z^6+z^4+z^2+1</math>" . |
<knot:10_71> <invariant:Conway_Polynomial> "<math>-z^6+z^4+z^2+1</math>" . |
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</pre> |
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The [[The Alexander-Conway Polynomial|Alexander Polynomials]] of the last few knots in the Rolfsen table: |
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<pre> |
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[drorbn@katlas ~/TakeHomeDatabase]$ zgrep Alexander_Polynomial Rolfsen.rdf.gz | tail |
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<knot:10_156> <invariant:Alexander_Polynomial> "<math>t^3-4 t^2+8 t-9+8 t^{-1} -4 t^{-2} + t^{-3} </math>" . |
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<knot:10_157> <invariant:Alexander_Polynomial> "<math>-t^3+6 t^2-11 t+13-11 t^{-1} +6 t^{-2} - t^{-3} </math>" . |
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<knot:10_158> <invariant:Alexander_Polynomial> "<math>-t^3+4 t^2-10 t+15-10 t^{-1} +4 t^{-2} - t^{-3} </math>" . |
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<knot:10_159> <invariant:Alexander_Polynomial> "<math>t^3-4 t^2+9 t-11+9 t^{-1} -4 t^{-2} + t^{-3} </math>" . |
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<knot:10_160> <invariant:Alexander_Polynomial> "<math>-t^3+4 t^2-4 t+3-4 t^{-1} +4 t^{-2} - t^{-3} </math>" . |
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<knot:10_161> <invariant:Alexander_Polynomial> "<math>t^3-2 t+3-2 t^{-1} + t^{-3} </math>" . |
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<knot:10_162> <invariant:Alexander_Polynomial> "<math>-3 t^2+9 t-11+9 t^{-1} -3 t^{-2} </math>" . |
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<knot:10_163> <invariant:Alexander_Polynomial> "<math>t^3-5 t^2+12 t-15+12 t^{-1} -5 t^{-2} + t^{-3} </math>" . |
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<knot:10_164> <invariant:Alexander_Polynomial> "<math>3 t^2-11 t+17-11 t^{-1} +3 t^{-2} </math>" . |
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<knot:10_165> <invariant:Alexander_Polynomial> "<math>-2 t^2+10 t-15+10 t^{-1} -2 t^{-2} </math>" . |
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</pre> |
</pre> |
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Revision as of 10:20, 18 July 2007
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:
- Rolfsen.rdf.gz (1MB/5MB) - Data from The Rolfsen Knot Table.
Using From a Linux Shell
The examples in this section assume that you have downloaded all the "small pieces" from the previous section and places them in your working directory, but that you did not bother to uncompress them.
The Jones polynomial of 10_71:
[drorbn@katlas ~/TakeHomeDatabase]$ 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 ~/TakeHomeDatabase]$ 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 ~/TakeHomeDatabase]$ 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>" .
