Hi Udo,
thanks, so I know now where to start working.
Best wishes
Stephan
Quoting Udo und Susanne Krause <su.krause@XXXXXXX.ch>:
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
says
DTCode 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
*********************************************************
*********************************************************
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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