The Alexander-Conway Polynomial - Revision history

ScottDataRobot at 22:21, 21 February 2013

2013-02-21T22:21:37Z

← Older revision		Revision as of 18:21, 21 February 2013
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	{{HelpAndAbout\|		{{HelpAndAbout\|
	n = 1 \|		n = 2 \|
	n1 = 2 \|		n1 = 3 \|
	in = <nowiki>Alexander</nowiki> \|		in = <nowiki>Alexander</nowiki> \|
	out= <nowiki>Alexander[K][t] computes the Alexander polynomial of a knot K as a function of the variable t. Alexander[K, r][t] computes a basis of the r'th Alexander ideal of K in Z[t].</nowiki> \|		out= <nowiki>Alexander[K][t] computes the Alexander polynomial of a knot K as a function of the variable t. Alexander[K, r][t] computes a basis of the r'th Alexander ideal of K in Z[t].</nowiki> \|
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	{{HelpLine\|		{{HelpLine\|
	n = 3 \|		n = 4 \|
	in = <nowiki>Conway</nowiki> \|		in = <nowiki>Conway</nowiki> \|
	out= <nowiki>Conway[K][z] computes the Conway polynomial of a knot K as a function of the variable z.</nowiki>}}		out= <nowiki>Conway[K][z] computes the Conway polynomial of a knot K as a function of the variable z.</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 4 \|		n = 5 \|
	in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|		in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
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	{{InOut\|		{{InOut\|
	n = 5 \|		n = 6 \|
	in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|		in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
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	{{InOut\|		{{InOut\|
	n = 6 \|		n = 7 \|
	in = <nowiki>Abs[alex /. t -> -1]</nowiki> \|		in = <nowiki>Abs[alex /. t -> -1]</nowiki> \|
	out= <nowiki>45</nowiki>}}		out= <nowiki>45</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 7 \|		n = 8 \|
	in = <nowiki>KnotDet[Knot[8, 18]]</nowiki> \|		in = <nowiki>KnotDet[Knot[8, 18]]</nowiki> \|
	out= <nowiki>45</nowiki>}}		out= <nowiki>45</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 8 \|		n = 9 \|
	in = <nowiki>Coefficient[Conway[Knot[8, 18]][z], z^2]</nowiki> \|		in = <nowiki>Coefficient[Conway[Knot[8, 18]][z], z^2]</nowiki> \|
	out= <nowiki>1</nowiki>}}		out= <nowiki>1</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 9 \|		n = 10 \|
	in = <nowiki>Vassiliev[2][Knot[8, 18]]</nowiki> \|		in = <nowiki>Vassiliev[2][Knot[8, 18]]</nowiki> \|
	out= <nowiki>1</nowiki>}}		out= <nowiki>1</nowiki>}}
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	{{In\|		{{In\|
	n = 10 \|		n = 11 \|
	in = <nowiki>{K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};</nowiki>}}		in = <nowiki>{K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};</nowiki>}}
	<!--END-->		<!--END-->
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	{{InOut\|		{{InOut\|
	n = 11 \|		n = 12 \|
	in = <nowiki>Alexander[K1] == Alexander[K2]</nowiki> \|		in = <nowiki>Alexander[K1] == Alexander[K2]</nowiki> \|
	out= <nowiki>True</nowiki>}}		out= <nowiki>True</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 12 \|		n = 13 \|
	in = <nowiki>Alexander[K1, 2][t]</nowiki> \|		in = <nowiki>Alexander[K1, 2][t]</nowiki> \|
	out= <nowiki>{1}</nowiki>}}		out= <nowiki>{1}</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 13 \|		n = 14 \|
	in = <nowiki>Alexander[K2, 2][t]</nowiki> \|		in = <nowiki>Alexander[K2, 2][t]</nowiki> \|
	out= <nowiki>{3, 1 + t}</nowiki>}}		out= <nowiki>{3, 1 + t}</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 14 \|		n = 15 \|
	in = <nowiki>Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}</nowiki> \|		in = <nowiki>Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}</nowiki> \|
	out= <nowiki>{551, 802}</nowiki>}}		out= <nowiki>{551, 802}</nowiki>}}

Drorbn: Reverted edits by CochiRacde (Talk); changed back to last version by Drorbn

2009-05-27T21:03:13Z

Reverted edits by CochiRacde (Talk); changed back to last version by Drorbn

← Older revision		Revision as of 17:03, 27 May 2009
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CochiRacde at 19:55, 21 May 2009

2009-05-21T19:55:06Z

← Older revision		Revision as of 15:55, 21 May 2009
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Drorbn: Reverted edits by ElchiBocvi (Talk); changed back to last version by Scott

2008-12-17T11:46:07Z

Reverted edits by ElchiBocvi (Talk); changed back to last version by Scott

← Older revision		Revision as of 07:46, 17 December 2008
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ElchiBocvi: chidargetc

2008-12-16T19:37:08Z

chidargetc

← Older revision		Revision as of 15:37, 16 December 2008
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Scott: Reverted edits by 59.77.16.170 (Talk); changed back to last version by Drorbn

2007-08-28T23:33:06Z

Reverted edits by 59.77.16.170 (Talk); changed back to last version by Drorbn

← Older revision		Revision as of 19:33, 28 August 2007
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	{{Startup Note}}		{{Startup Note}}
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	in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|		in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t -- - -- - 10 t 5 t - t		13 - t + -- - -- - 10 t + 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 42:		Line 42:
	in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|		in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t -- - -- - 10 t 5 t - t		13 - t + -- - -- - 10 t + 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 89:		Line 89:
	{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}		{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}

	Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1 t</math>:		Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1+t</math>:

	<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->		<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->
Line 119:		Line 119:
	n = 13 \|		n = 13 \|
	in = <nowiki>Alexander[K2, 2][t]</nowiki> \|		in = <nowiki>Alexander[K2, 2][t]</nowiki> \|
	out= <nowiki>{3, 1 t}</nowiki>}}		out= <nowiki>{3, 1 + t}</nowiki>}}
	<!--END-->		<!--END-->

	Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]		Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]& /@ AllKnots[]]]$--><!--Robot Land, no human edits to "END"-->551<!--END--> values on the <!--$Length[AllKnots[]]$--><!--Robot Land, no human edits to "END"-->802<!--END--> knots known to <code>KnotTheory`</code>:

			<!--$$Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 14 \|
			in = <nowiki>Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}</nowiki> \|
			out= <nowiki>{551, 802}</nowiki>}}
			<!--END-->

59.77.16.170 at 18:25, 28 August 2007

2007-08-28T18:25:24Z

← Older revision		Revision as of 14:25, 28 August 2007
Line 1:		Line 1:
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[http://wedner.info/content/view/nexus.htm nexus 205] [http://polex.com.cn/resources/articles/edge-cellulari.htm edge cellulari bluetooth] [http://veggis.org.cn/resources/articles/ariete-macchina.htm ariete macchina da caffe] [http://wedner.info/content/view/frischmuth-barbara.htm frischmuth, barbara] [http://svike.info/view/new/love-erotic.htm love erotic love] [http://svike.info/view/new/california-download.htm california download] [http://sneck.info/data/rosmarino/ rosmarino] [http://budget7i.info/lib/veloso-caetano/ veloso caetano] {{Manual TOC Sidebar}}
	{{Manual TOC Sidebar}}

	{{Startup Note}}		{{Startup Note}}
Line 31:		Line 31:
	in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|		in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t + -- - -- - 10 t + 5 t - t		13 - t -- - -- - 10 t 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 42:		Line 42:
	in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|		in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t + -- - -- - 10 t + 5 t - t		13 - t -- - -- - 10 t 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 89:		Line 89:
	{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}		{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}

	Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1+t</math>:		Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1 t</math>:

	<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->		<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->
Line 119:		Line 119:
	n = 13 \|		n = 13 \|
	in = <nowiki>Alexander[K2, 2][t]</nowiki> \|		in = <nowiki>Alexander[K2, 2][t]</nowiki> \|
	out= <nowiki>{3, 1 + t}</nowiki>}}		out= <nowiki>{3, 1 t}</nowiki>}}
	<!--END-->		<!--END-->

	Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]& /@ AllKnots[]]]$--><!--Robot Land, no human edits to "END"-->551<!--END--> values on the <!--$Length[AllKnots[]]$--><!--Robot Land, no human edits to "END"-->802<!--END--> knots known to <code>KnotTheory`</code>:		Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]

	<!--$$Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}$$-->
	<!--Robot Land, no human edits to "END"-->
	{{InOut\|
	n = 14 \|
	in = <nowiki>Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}</nowiki> \|
	out= <nowiki>{551, 802}</nowiki>}}
	<!--END-->

Drorbn: Reverted edit of 89.16.161.38, changed back to last version by Drorbn

2007-07-01T19:59:00Z

Reverted edit of 89.16.161.38, changed back to last version by Drorbn

← Older revision		Revision as of 15:59, 1 July 2007
Line 31:		Line 31:
	in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|		in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t -- - -- - 10 t 5 t - t		13 - t + -- - -- - 10 t + 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 42:		Line 42:
	in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|		in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t -- - -- - 10 t 5 t - t		13 - t + -- - -- - 10 t + 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 89:		Line 89:
	{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}		{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}

	Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1 t</math>:		Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1+t</math>:

	<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->		<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->
Line 119:		Line 119:
	n = 13 \|		n = 13 \|
	in = <nowiki>Alexander[K2, 2][t]</nowiki> \|		in = <nowiki>Alexander[K2, 2][t]</nowiki> \|
	out= <nowiki>{3, 1 t}</nowiki>}}		out= <nowiki>{3, 1 + t}</nowiki>}}
	<!--END-->		<!--END-->

	Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]		Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]& /@ AllKnots[]]]$--><!--Robot Land, no human edits to "END"-->551<!--END--> values on the <!--$Length[AllKnots[]]$--><!--Robot Land, no human edits to "END"-->802<!--END--> knots known to <code>KnotTheory`</code>:

			<!--$$Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 14 \|
			in = <nowiki>Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}</nowiki> \|
			out= <nowiki>{551, 802}</nowiki>}}
			<!--END-->

89.16.161.38 at 19:12, 1 July 2007

2007-07-01T19:12:35Z

← Older revision		Revision as of 15:12, 1 July 2007
Line 31:		Line 31:
	in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|		in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t + -- - -- - 10 t + 5 t - t		13 - t -- - -- - 10 t 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 42:		Line 42:
	in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|		in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t + -- - -- - 10 t + 5 t - t		13 - t -- - -- - 10 t 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 89:		Line 89:
	{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}		{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}

	Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1+t</math>:		Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1 t</math>:

	<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->		<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->
Line 119:		Line 119:
	n = 13 \|		n = 13 \|
	in = <nowiki>Alexander[K2, 2][t]</nowiki> \|		in = <nowiki>Alexander[K2, 2][t]</nowiki> \|
	out= <nowiki>{3, 1 + t}</nowiki>}}		out= <nowiki>{3, 1 t}</nowiki>}}
	<!--END-->		<!--END-->

	Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]& /@ AllKnots[]]]$--><!--Robot Land, no human edits to "END"-->551<!--END--> values on the <!--$Length[AllKnots[]]$--><!--Robot Land, no human edits to "END"-->802<!--END--> knots known to <code>KnotTheory`</code>:		Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]

	<!--$$Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}$$-->
	<!--Robot Land, no human edits to "END"-->
	{{InOut\|
	n = 14 \|
	in = <nowiki>Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}</nowiki> \|
	out= <nowiki>{551, 802}</nowiki>}}
	<!--END-->

Drorbn: Reverted edit of 218.74.122.100, changed back to last version by Drorbn

2007-06-18T21:46:31Z

Reverted edit of 218.74.122.100, changed back to last version by Drorbn

← Older revision		Revision as of 17:46, 18 June 2007
Line 31:		Line 31:
	in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|		in = <nowiki>alex = Alexander[Knot[8, 18]][t]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t -- - -- - 10 t 5 t - t		13 - t + -- - -- - 10 t + 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 42:		Line 42:
	in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|		in = <nowiki>Expand[Conway[Knot[8, 18]][Sqrt[t] - 1/Sqrt[t]]]</nowiki> \|
	out= <nowiki> -3 5 10 2 3		out= <nowiki> -3 5 10 2 3
	13 - t -- - -- - 10 t 5 t - t		13 - t + -- - -- - 10 t + 5 t - t
	2 t		2 t
	t</nowiki>}}		t</nowiki>}}
Line 89:		Line 89:
	{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}		{{Knot Image Pair\|K11a99\|gif\|K11a277\|gif}}

	Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1 t</math>:		Sometimes two knots have the same Alexander polynomial but different Alexander ideals. An example is the pair [[K11a99]] and [[K11a277]]. They have the same Alexander polynomial, but the second Alexander ideal of the first knot is the whole ring <math>{\mathbb Z}[t]</math> while the second Alexander ideal of the second knot is the smaller ideal generated by <math>3</math> and by <math>1+t</math>:

	<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->		<!--$${K1, K2} = {Knot[11, Alternating, 99], Knot[11, Alternating, 277]};$$-->
Line 119:		Line 119:
	n = 13 \|		n = 13 \|
	in = <nowiki>Alexander[K2, 2][t]</nowiki> \|		in = <nowiki>Alexander[K2, 2][t]</nowiki> \|
	out= <nowiki>{3, 1 t}</nowiki>}}		out= <nowiki>{3, 1 + t}</nowiki>}}
	<!--END-->		<!--END-->

	Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]		Finally, the Alexander polynomial attains <!--$Length[Union[Alexander[#]& /@ AllKnots[]]]$--><!--Robot Land, no human edits to "END"-->551<!--END--> values on the <!--$Length[AllKnots[]]$--><!--Robot Land, no human edits to "END"-->802<!--END--> knots known to <code>KnotTheory`</code>:

			<!--$$Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 14 \|
			in = <nowiki>Length /@ {Union[Alexander[#]& /@ AllKnots[]], AllKnots[]}</nowiki> \|
			out= <nowiki>{551, 802}</nowiki>}}
			<!--END-->