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9 Lightly Documented Features

In[1]

In[2]:= ?NumberOfKnots
NumberOfKnots[type] return the number of knots of a given type.

In[3]:=	NumberOfKnots[16, NonAlternating]
Out[3]=	1008906

In[4]:= ?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[5]:= MorseLink::about
MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005.

In[6]:=	MorseLink[Knot[3, 1]]
Out[6]=	MorseLink[1 \[Cup] 2, 4 \[Cup] 3, X[2, Under, Up, Up], X[2, Under, Up, Up], > X[2, Under, Up, Up], 2 \[Cap] 1, 1 \[Cap] 2]

In[7]:= ?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[8]:=	Show[DrawMorseLink[Link[11, Alternating, 548]]]
Out[8]=	-Graphics-