Lightly Documented Features: Difference between revisions
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{{Help1|n=1|s=NumberOfKnots}} |
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NumberOfKnots[type] return the number of knots of a given type. |
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{{Help2}} |
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<!--$$NumberOfKnots[16, NonAlternating]$$--> |
<!--$$NumberOfKnots[16, NonAlternating]$$--> |
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{{InOut1|n=2}} |
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<pre style="color: red; border: 0px; padding: 0em"><nowiki>NumberOfKnots[16, NonAlternating]</nowiki></pre> |
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{{InOut2|n=2}}<pre style="border: 0px; padding: 0em"><nowiki>1008906</nowiki></pre> |
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{{InOut3}} |
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<!--$$?MorseLink$$--> |
<!--$$?MorseLink$$--> |
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{{HelpAndAbout1|n=3|s=MorseLink}} |
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MorseLink[K] returns a presentation of the oriented link K, composed, in successive order, of the following 'events': Cup[m,n] is a directed creation, starting at strand position n, towards position m, where m and n differ by 1. X[n,a = {Over/Under}, b = {Up/Down}, c={Up/Down}] is a crossing with lower-left edge at strand n, a determines whether the strand running bottom-left to top-right is over/under the crossing, b and c give the directions of the bottom-left and bottom-right strands respectively through the crossing. Cap[m,n] is a directed cap, from strand m to strand n. |
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{{HelpAndAbout2|n=4|s=MorseLink}} |
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MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005. |
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{{HelpAndAbout3}} |
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<!--$$MorseLink[Knot[3, 1]]$$--> |
<!--$$MorseLink[Knot[3, 1]]$$--> |
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{{InOut1|n=5}} |
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<pre style="color: red; border: 0px; padding: 0em"><nowiki>MorseLink[Knot[3, 1]]</nowiki></pre> |
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{{InOut2|n=5}}<pre style="border: 0px; padding: 0em"><nowiki>MorseLink[1 ? 2, 4 ? 3, X[2, Under, Up, Up], X[2, Under, Up, Up], |
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X[2, Under, Up, Up], 2 ? 1, 1 ? 2]</nowiki></pre> |
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{{InOut3}} |
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<!--$$?DrawMorseLink$$--> |
<!--$$?DrawMorseLink$$--> |
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{{HelpAndAbout1|n=6|s=DrawMorseLink}} |
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DrawMorseLink[L] returns a drawing of the knot or link L as a "Morse Link". For diagrams with a large number of crossings, it may be helpful to use one or both of the options as in DrawMorseLink[L, Gap -> g, ArrowSize -> as ], with 0 < as, g < 1, where g controls the amount of white space at each crossing, and as controls the size of the orientation arrows. |
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{{HelpAndAbout2|n=7|s=DrawMorseLink}} |
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DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005. |
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{{HelpAndAbout3}} |
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<!--$$Show[DrawMorseLink[Link[11, Alternating, 548]]]$$--> |
<!--$$Show[DrawMorseLink[Link[11, Alternating, 548]]]$$--> |
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{{Graphics1|n=8}} |
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<pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Link[11, Alternating, 548]]]</nowiki></pre> |
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{{Graphics2|n=8|imagename=Lightly_Documented_Features_Out_8.gif}} |
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Revision as of 08:53, 30 August 2005
(For In[1] see Setup)
In[1]:= ?NumberOfKnots
NumberOfKnots[type] return the number of knots of a given type. |
| In[2]:= |
NumberOfKnots[16, NonAlternating] |
| Out[2]= | 1008906 |
In[3]:= ?MorseLink
MorseLink[K] returns a presentation of the oriented link K, composed, in successive order, of the following 'events': Cup[m,n] is a directed creation, starting at strand position n, towards position m, where m and n differ by 1. X[n,a = {Over/Under}, b = {Up/Down}, c={Up/Down}] is a crossing with lower-left edge at strand n, a determines whether the strand running bottom-left to top-right is over/under the crossing, b and c give the directions of the bottom-left and bottom-right strands respectively through the crossing. Cap[m,n] is a directed cap, from strand m to strand n. |
In[4]:= MorseLink::about
MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005. |
| In[5]:= |
MorseLink[Knot[3, 1]] |
| Out[5]= | MorseLink[1 ? 2, 4 ? 3, X[2, Under, Up, Up], X[2, Under, Up, Up], X[2, Under, Up, Up], 2 ? 1, 1 ? 2] |
In[6]:= ?DrawMorseLink
DrawMorseLink[L] returns a drawing of the knot or link L as a "Morse Link". For diagrams with a large number of crossings, it may be helpful to use one or both of the options as in DrawMorseLink[L, Gap -> g, ArrowSize -> as ], with 0 < as, g < 1, where g controls the amount of white space at each crossing, and as controls the size of the orientation arrows. |
In[7]:= DrawMorseLink::about
DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005. |
| In[8]:= |
Show[DrawMorseLink[Link[11, Alternating, 548]]] |
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| Out[8]= | -Graphics- |
