Hi Stephan,
just try it, https://knotplot.com/dowker/dowker.html has a knot with 36
crossings
In[6]:= TimeConstrained[
DrawPD[DTCode[40, 24, 10, 30, 22, 52, 32, 64, 46, 12, 6, 42,
60, 2,
8, 50, 66, 16, 62, 58, 28, 4, 54, 34, 14, 20, 68, 36, 72,
26, 70,
56, 48, 18, 44, 38], {Gap -> 0.025}], 180]
KnotTheory::credits: The GaussCode to PD conversion was written by
Siddarth Sankaran at the University of Toronto in the summer of 2005.
resulting in a planar diagram, a shot into to wild shows potential to
check the input
In[8]:= TimeConstrained[
DrawPD[DTCode[2 RandomInteger[{1, 32}, {36}]], {Gap -> 0.025}], 180]
During evaluation of In[8]:= Part::partw: Part {1,9} of {True} does not
exist. >>
During evaluation of In[8]:= Part::partw: Part {1,12} of {True} does not
exist. >>
During evaluation of In[8]:= Part::partw: Part 1 of {} does not exist. >>
During evaluation of In[8]:= General::stop: Further output of Part::partw
will be suppressed during this calculation. >>
During evaluation of In[8]:= Part::pkspec1: The expression {}[[1]] cannot
be used as a part specification. >>
During evaluation of In[8]:= Part::pkspec1: The expression {}[[2]] cannot
be used as a part specification. >>
During evaluation of In[8]:= Part::pkspec1: The expression {}[[1]] cannot
be used as a part specification. >>
During evaluation of In[8]:= General::stop: Further output of
Part::pkspec1 will be suppressed during this calculation. >>
During evaluation of In[8]:= Set::shape: Lists
{{KnotTheory`GaussCode`c1$6630,KnotTheory`GaussCode`c2$6630,KnotTheory`GaussCode`s}}
and {} are not the same shape. >>
During evaluation of In[8]:= Set::shape: Lists
{{KnotTheory`GaussCode`c1$6630,KnotTheory`GaussCode`c2$6630,KnotTheory`GaussCode`s}}
and {} are not the same shape. >>
During evaluation of In[8]:= Set::shape: Lists
{{KnotTheory`GaussCode`c1$6630,KnotTheory`GaussCode`c2$6630,KnotTheory`GaussCode`s}}
and {} are not the same shape. >>
During evaluation of In[8]:= General::stop: Further output of Set::shape
will be suppressed during this calculation. >>
Out[8]= $Aborted
just this reference
https://pyknotid.readthedocs.io/en/latest/sources/catalogue/index.html#downloading-the-database
goes systematically with up to 15 crossings. There are of course pretzel
knots and torus knots with potentially any number of crossings.
Before you can burn calculation time you need something to calculate which
might be not so obviously to find. One rather exterior approach could be
to classify - you could even try to use Mathematicas machine learning
capabilities - the given systematic data collections to find out pattern
for existing knots (or links) and use that to guess or construct similar
knots, but with higher crossing number, by combining the patterns found in
a meaningful way. Look around.
Best regards
Udo.
On Wed, 29 Aug 2018 11:27:12 +0200, Stephan Rosebrock
<rosebrock@XXXXXXX.de> wrote:
Hi Udo,
thanks for your answer. Your suggestion only works for knots and links
for which there are already tables implemented, right? >What, if I want
to have a link with more crossings (about 22 or even more). There are no
tables for them, right? Since this is part of >a very long going project
(years) I don't mind long calculation time.
Best wishes
Stephan
Quoting Udo und Susanne Krause <su.krause@XXXXXXX.ch>:
Hello Stephan,you shouldn't, period. The manual help once again
http://katlas.org/wiki/DT_(Dowker-Thistlethwaite)_Codes
saysDTCode also acts as a "type caster", so for example, DTCode[K]
where K is is a named knot or link returns the DT code of K.
<snip>
*********************************************************
Dr. Stephan Rosebrock
Paedagogische Hochschule Karlsruhe
Bismarckstr. 10
76133 Karlsruhe
Deutschland / Germany
e-mail: rosebrock@XXXXXXX.de
Homepage: http://www.rosebrock.ph-karlsruhe.de/
Tel: 0721-925-4275
Fax: 0721-925-4249
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