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Re: [Dmug] knot theory package

 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.
   
So one looks to the link table in the case of links (http://katlas.org/wiki/The_Thistlethwaite_Link_Table), all links KnotTheory knows about are listed. No need for iteration on integer lists (that might take a very very very long time if the list is an n-tupel with n > 1).
   
  First get the DTCodes[] out of the list 
   
  In[13]:= DTCode[Link[8, Alternating, 1]]
During evaluation of In[13]:= KnotTheory::loading: Loading precomputed data in PD4Links`.
Out[13]= DTCode[{6, 8}, {10, 14, 12, 16, 2, 4}]

In[14]:= DTCode[Link[8, NonAlternating, 1]]
Out[14]= DTCode[{6, -8}, {-10, 14, -12, -16, -2, 4}]
   
if for example a link with 8 crossings (http://katlas.org/wiki/The_Thistlethwaite_Link_Table_L8n1-L8n8) has the name 'L8n1' than this is Link[8, NonAlternating, 1], and if it has the name 'L8a19' in the table, then it is Link[8,Alternating, 19]. This can be plotted without actually realizing the DTCode[]:
   
  In[17]:= DrawPD[DTCode[Link[8, Alternating, 1]], {Gap -> 0.025}]

In[18]:= DrawPD[DTCode[Link[8, NonAlternating, 1]], {Gap -> 0.025}]

In[19]:= DrawPD[DTCode[Link[8, Alternating, 19]], {Gap -> 0.025}]
   
if you really want to iterate, here is a linear opportunity (may be you meant that):
   
  In[53]:= Clear[howManyLinks]
howManyLinks[k_Integer, a_Integer] := Block[{o = 1},
   If[a == 1,
   While[Depth[DTCode[Link[k, Alternating, o]]] == 3, o += 1];
   Print["There are ", o - 1, " alternating links with ", k, " crossings in KnotTheory."], (* else *)
   While[Depth[DTCode[Link[k, NonAlternating, o]]] == 3, o += 1];
   Print["There are ", o - 1, " non-alternating links with ", k, " crossings in KnotTheory."]
 ]
] /; k > 1 && k != 3 && k < 12 && (a == 0 || a == 1)

In[56}:= howManyLinks[11, 0]
There are 459 non-alternating links with 11 crossings in KnotTheory.

In[58]:= howManyLinks[11, 1]
There are 548 alternating links with 11 crossings in KnotTheory.
   
   
  Mit den besten grüssen
  Udo.
   
   
On Mon, 06 Aug 2018 18:23:13 +0200, Stephan Rosebrock <rosebrock@XXXXXXX.de> wrote:

Hi Udo and Peter, it is possible, to draw a knot or a link by giving its Dowker notation: Show[DrawPD[DTCode[{6, -8}, {-10, 12, -14, 2, -4}], {Gap -> 0.025}]] Since I am interested to draw knots and links with many crossings, this is interesting to me. I would like to write a small mathematica program which takes as input some dowker notation and a number n. As output I would like to have the pictures of the next n exisiting knots or links, where the program makes the dowker notation bigger in lexicographic order. I think I might be able to do this by myself up to one point which I don't know: If I come to a dowker notation of a link which does not exist, I want the program just to forget about it and go on to the next link. How can I do this? Best wishes Stephan

 
 *********************************************************
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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