Lightly Documented Features: Difference between revisions

Latest revision as of 17:24, 21 February 2013

(For In[1] see Setup)

In[2]:=	?NumberOfKnots
NumberOfKnots[n] returns the number of knots with n crossings. NumberOfKnots[n, Alternating\|NonAlternating] returns the number of knots of the specified type.

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

In[4]:=	?AlternatingQ
AlternatingQ[D] returns True iff the knot/link diagram D is alternating.

Among the knots with up to 11 crossings, 564 are alternating and 238 are not:

`In[5]:=`	`Total[AlternatingQ /@ AllKnots[{0,11}]]`
`Out[5]=`	`238 False + 564 True`

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-n  = 1 |
+n  = 2 |
 in = <nowiki>NumberOfKnots</nowiki> |
 out= <nowiki>NumberOfKnots[n] returns the number of knots with n crossings.
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 in = <nowiki>NumberOfKnots[16, NonAlternating]</nowiki> |
 out= <nowiki>1008906</nowiki>}}
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-n  = 3 |
+n  = 4 |
 in = <nowiki>AlternatingQ</nowiki> |
-out= <nowiki>AlternatingQ[K] tries to decide if the knot K is alternating. This function is extremely incomplete; it only works for named knots from the tables, or torus knots.</nowiki>}}
+out= <nowiki>AlternatingQ[D] returns True iff the knot/link diagram D is alternating.</nowiki>}}
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 {{InOut|
-n  = 4 |
+n  = 5 |
 in = <nowiki>Total[AlternatingQ /@ AllKnots[{0,11}]]</nowiki> |
 out= <nowiki>238 False + 564 True</nowiki>}}