Lightly Documented Features: Difference between revisions

Revision as of 20:39, 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[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.

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

`In[4]:=`	`Total[AlternatingQ /@ AllKnots[{0,11}]]`
`Out[4]=`	`238 False + 564 True`

@@ Line 8: / Line 8: @@
 n  = 1 |
 in = <nowiki>NumberOfKnots</nowiki> |
-out= <nowiki>NumberOfKnots[type] return the number of knots of a given type.</nowiki>}}
+out= <nowiki>NumberOfKnots[n] returns the number of knots with n crossings.
+NumberOfKnots[n, Alternating&#124;NonAlternating] returns the number of knots of the specified type.</nowiki>}}
 <!--END-->
@@ Line 22: / Line 23: @@
 <!--Robot Land, no human edits to "END"-->
 {{HelpLine|
-n  = 1 |
+n  = 3 |
-in = <nowiki>NumberOfKnots</nowiki> |
+in = <nowiki>AlternatingQ</nowiki> |
-out= <nowiki>NumberOfKnots[type] return the number of knots of a given type.</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>}}
 <!--END-->
@@ Line 32: / Line 33: @@
 <!--Robot Land, no human edits to "END"-->
 {{InOut|
-n  = 2 |
+n  = 4 |
-in = <nowiki>NumberOfKnots[16, NonAlternating]</nowiki> |
+in = <nowiki>Total[AlternatingQ /@ AllKnots[{0,11}]]</nowiki> |
-out= <nowiki>1008906</nowiki>}}
+out= <nowiki>238 False + 564 True</nowiki>}}
 <!--END-->