Lightly Documented Features: Difference between revisions

Revision as of 20:56, 12 December 2007

(For In[1] see Setup)

In[1]:=	?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[2]:=`	`NumberOfKnots[16, NonAlternating]`
`Out[2]=`	`1008906`

In[3]:=	?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[4]:=`	`Total[AlternatingQ /@ AllKnots[{0,11}]]`
`Out[4]=`	`239 False + 563 True`

@@ Line 25: / Line 25: @@
 n  = 3 |
 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>}}
 <!--END-->
@@ Line 35: / Line 35: @@
 n  = 4 |
 in = <nowiki>Total[AlternatingQ /@ AllKnots[{0,11}]]</nowiki> |
-out= <nowiki>238 False + 564 True</nowiki>}}
+out= <nowiki>239 False + 563 True</nowiki>}}
 <!--END-->