Lightly Documented Features - Revision history

ScottDataRobot at 22:24, 21 February 2013

2013-02-21T22:24:33Z

← Older revision		Revision as of 18:24, 21 February 2013
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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{HelpLine\|		{{HelpLine\|
	n = 1 \|		n = 2 \|
	in = <nowiki>NumberOfKnots</nowiki> \|		in = <nowiki>NumberOfKnots</nowiki> \|
	out= <nowiki>NumberOfKnots[n] returns the number of knots with n crossings.		out= <nowiki>NumberOfKnots[n] returns the number of knots with n crossings.
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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{InOut\|		{{InOut\|
	n = 2 \|		n = 3 \|
	in = <nowiki>NumberOfKnots[16, NonAlternating]</nowiki> \|		in = <nowiki>NumberOfKnots[16, NonAlternating]</nowiki> \|
	out= <nowiki>1008906</nowiki>}}		out= <nowiki>1008906</nowiki>}}
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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{HelpLine\|		{{HelpLine\|
	n = 3 \|		n = 4 \|
	in = <nowiki>AlternatingQ</nowiki> \|		in = <nowiki>AlternatingQ</nowiki> \|
	out= <nowiki>AlternatingQ[D] returns True iff the knot/link diagram D is alternating.</nowiki>}}		out= <nowiki>AlternatingQ[D] returns True iff the knot/link diagram D is alternating.</nowiki>}}
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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{InOut\|		{{InOut\|
	n = 4 \|		n = 5 \|
	in = <nowiki>Total[AlternatingQ /@ AllKnots[{0,11}]]</nowiki> \|		in = <nowiki>Total[AlternatingQ /@ AllKnots[{0,11}]]</nowiki> \|
	out= <nowiki>238 False + 564 True</nowiki>}}		out= <nowiki>238 False + 564 True</nowiki>}}

DrorsRobot at 02:04, 13 December 2007

2007-12-13T02:04:25Z

← Older revision		Revision as of 22:04, 12 December 2007
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	n = 4 \|		n = 4 \|
	in = <nowiki>Total[AlternatingQ /@ AllKnots[{0,11}]]</nowiki> \|		in = <nowiki>Total[AlternatingQ /@ AllKnots[{0,11}]]</nowiki> \|
	out= <nowiki>~~239~~ False + ~~563~~ True</nowiki>}}		out= <nowiki>238 False + 564 True</nowiki>}}
	<!--END-->		<!--END-->

DrorsRobot at 01:56, 13 December 2007

2007-12-13T01:56:40Z

← Older revision		Revision as of 21:56, 12 December 2007
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	n = 3 \|		n = 3 \|
	in = <nowiki>AlternatingQ</nowiki> \|		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-->		<!--END-->

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

DrorsRobot at 01:39, 13 December 2007

2007-12-13T01:39:17Z

← Older revision		Revision as of 21:39, 12 December 2007
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	n = 1 \|		n = 1 \|
	in = <nowiki>NumberOfKnots</nowiki> \|		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\|NonAlternating] returns the number of knots of the specified type.</nowiki>}}
	<!--END-->		<!--END-->

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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{HelpLine\|		{{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-->		<!--END-->

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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{InOut\|		{{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-->		<!--END-->

Drorbn at 01:38, 13 December 2007

2007-12-13T01:38:59Z

@@ Line 12: / Line 12: @@
 <!--$$NumberOfKnots[16, NonAlternating]$$-->
 <!--Robot Land, no human edits to "END"-->
 {{InOut|

Siddarth: MorseLink stuff doc'ed elsewhere

2005-09-06T17:19:35Z

MorseLink stuff doc'ed elsewhere

@@ Line 17: / Line 17: @@
 in = <nowiki>NumberOfKnots[16, NonAlternating]</nowiki> |
 out= <nowiki>1008906</nowiki>}}
 <!--END-->

DrorsRobot at 18:23, 30 August 2005

2005-08-30T18:23:54Z

← Older revision		Revision as of 14:23, 30 August 2005
Line 5:		Line 5:
	<!--$$?NumberOfKnots$$-->		<!--$$?NumberOfKnots$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
			{{HelpLine\|
	{{Help1\|n=1\|s=NumberOfKnots}}
			n = 1 \|
⚫	NumberOfKnots[type] return the number of knots of a given type.
			in = <nowiki>NumberOfKnots</nowiki> \|
	{{Help2}}
		⚫	out= <nowiki>NumberOfKnots[type] return the number of knots of a given type.</nowiki>}}
	<!--END-->		<!--END-->

	<!--$$NumberOfKnots[16, NonAlternating]$$-->		<!--$$NumberOfKnots[16, NonAlternating]$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{~~InOut1~~\|~~n=2}}~~		{{InOut\|
			n = 2 \|
	~~<pre~~ ~~style~~=~~"color:~~ ~~red; border: 0px; padding: 0em">~~<nowiki>NumberOfKnots[16, NonAlternating]</nowiki>~~</pre>~~		in = <nowiki>NumberOfKnots[16, NonAlternating]</nowiki> \|
	{{InOut2\|n=2}}<pre style="border: 0px; padding: 0em"><nowiki>1008906</nowiki></pre>
			out= <nowiki>1008906</nowiki>}}
	{{InOut3}}
	<!--END-->		<!--END-->

	<!--$$?MorseLink$$-->		<!--$$?MorseLink$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
			{{HelpAndAbout\|
	{{HelpAndAbout1\|n=3\|s=MorseLink}}
			n = 3 \|
⚫	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.
			n1 = 4 \|
	{{HelpAndAbout2\|n=4\|s=MorseLink}}
			in = <nowiki>MorseLink</nowiki> \|
⚫	MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005.
		⚫	out= <nowiki>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.</nowiki> \|
	{{HelpAndAbout3}}
		⚫	about= <nowiki>MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005.</nowiki>}}
	<!--END-->		<!--END-->

	<!--$$MorseLink[Knot[3, 1]]$$-->		<!--$$MorseLink[Knot[3, 1]]$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{~~InOut1~~\|~~n=5}}~~		{{InOut\|
			n = 5 \|
	~~<pre~~ ~~style~~=~~"color:~~ ~~red; border: 0px; padding: 0em">~~<nowiki>MorseLink[Knot[3, 1]]</nowiki>~~</pre>~~		in = <nowiki>MorseLink[Knot[3, 1]]</nowiki> \|
	~~{{InOut2\|n~~=~~5}}<pre~~ ~~style="border: 0px; padding: 0em">~~<nowiki>MorseLink[1 ? 2, 4 ? 3, X[2, Under, Up, Up], X[2, Under, Up, Up],		out= <nowiki>MorseLink[1 ? 2, 4 ? 3, X[2, Under, Up, Up], X[2, Under, Up, Up],

	X[2, Under, Up, Up], 2 ? 1, 1 ? 2]</nowiki>~~</pre>~~		X[2, Under, Up, Up], 2 ? 1, 1 ? 2]</nowiki>}}
	{{InOut3}}
	<!--END-->		<!--END-->

	<!--$$?DrawMorseLink$$-->		<!--$$?DrawMorseLink$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
			{{HelpAndAbout\|
	{{HelpAndAbout1\|n=6\|s=DrawMorseLink}}
			n = 6 \|
⚫	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.
			n1 = 7 \|
	{{HelpAndAbout2\|n=7\|s=DrawMorseLink}}
			in = <nowiki>DrawMorseLink</nowiki> \|
⚫	DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
		⚫	out= <nowiki>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.</nowiki> \|
	{{HelpAndAbout3}}
		⚫	about= <nowiki>DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.</nowiki>}}
	<!--END-->		<!--END-->

	<!--$$Show[DrawMorseLink[Link[11, Alternating, 548]]]$$-->		<!--$$Show[DrawMorseLink[Link[11, Alternating, 548]]]$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
			{{Graphics\|
	{{Graphics1\|n=8}}
			n = 9 \|
	~~<pre~~ ~~style~~=~~"color:~~ ~~red; border: 0px; padding: 0em">~~<nowiki>Show[DrawMorseLink[Link[11, Alternating, 548]]]</nowiki>~~</pre>~~		in = <nowiki>Show[DrawMorseLink[Link[11, Alternating, 548]]]</nowiki> \|
	~~{{Graphics2\|n=8\|imagename~~=Lightly_Documented_Features_Out_8.gif}}		img= Lightly_Documented_Features_Out_8.gif \|
			out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->		<!--END-->

DrorsRobot at 13:53, 30 August 2005

2005-08-30T13:53:34Z

← Older revision		Revision as of 09:53, 30 August 2005
Line 4:		Line 4:

	<!--$$?NumberOfKnots$$-->		<!--$$?NumberOfKnots$$-->
			<!--Robot Land, no human edits to "END"-->
			{{Help1\|n=1\|s=NumberOfKnots}}
			NumberOfKnots[type] return the number of knots of a given type.
			{{Help2}}
	<!--END-->		<!--END-->

	<!--$$NumberOfKnots[16, NonAlternating]$$-->		<!--$$NumberOfKnots[16, NonAlternating]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut1\|n=2}}
			<pre style="color: red; border: 0px; padding: 0em"><nowiki>NumberOfKnots[16, NonAlternating]</nowiki></pre>
			{{InOut2\|n=2}}<pre style="border: 0px; padding: 0em"><nowiki>1008906</nowiki></pre>
			{{InOut3}}
	<!--END-->		<!--END-->

	<!--$$?MorseLink$$-->		<!--$$?MorseLink$$-->
			<!--Robot Land, no human edits to "END"-->
			{{HelpAndAbout1\|n=3\|s=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.
			{{HelpAndAbout2\|n=4\|s=MorseLink}}
			MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005.
			{{HelpAndAbout3}}
	<!--END-->		<!--END-->

	<!--$$MorseLink[Knot[3, 1]]$$-->		<!--$$MorseLink[Knot[3, 1]]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut1\|n=5}}
			<pre style="color: red; border: 0px; padding: 0em"><nowiki>MorseLink[Knot[3, 1]]</nowiki></pre>
			{{InOut2\|n=5}}<pre style="border: 0px; padding: 0em"><nowiki>MorseLink[1 ? 2, 4 ? 3, X[2, Under, Up, Up], X[2, Under, Up, Up],

			X[2, Under, Up, Up], 2 ? 1, 1 ? 2]</nowiki></pre>
			{{InOut3}}
	<!--END-->		<!--END-->

	<!--$$?DrawMorseLink$$-->		<!--$$?DrawMorseLink$$-->
			<!--Robot Land, no human edits to "END"-->
			{{HelpAndAbout1\|n=6\|s=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.
			{{HelpAndAbout2\|n=7\|s=DrawMorseLink}}
			DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
			{{HelpAndAbout3}}
	<!--END-->		<!--END-->

	<!--$$Show[DrawMorseLink[Link[11, Alternating, 548]]]$$-->		<!--$$Show[DrawMorseLink[Link[11, Alternating, 548]]]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{Graphics1\|n=8}}
			<pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Link[11, Alternating, 548]]]</nowiki></pre>
			{{Graphics2\|n=8\|imagename=Lightly_Documented_Features_Out_8.gif}}
	<!--END-->		<!--END-->

Drorbn at 13:53, 30 August 2005

2005-08-30T13:53:26Z

← Older revision		Revision as of 09:53, 30 August 2005
Line 18:		Line 18:
	<!--END-->		<!--END-->

	<!--$$?Show[DrawMorseLink[Link[11, Alternating, 548]]]$$-->		<!--$$Show[DrawMorseLink[Link[11, Alternating, 548]]]$$-->
	<!--END-->		<!--END-->

Drorbn at 13:51, 30 August 2005

2005-08-30T13:51:04Z

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