Drawing Braids - Revision history

ScottDataRobot at 22:20, 21 February 2013

2013-02-21T22:20:17Z

← Older revision		Revision as of 18:20, 21 February 2013
Line 6:		Line 6:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{HelpLine\|		{{HelpLine\|
	n = 1 \|		n = 2 \|
	in = <nowiki>BraidPlot</nowiki> \|		in = <nowiki>BraidPlot</nowiki> \|
	out= <nowiki>BraidPlot[br, opts] produces a plot of the braid br. Possible options		out= <nowiki>BraidPlot[br, opts] produces a plot of the braid br. Possible options are Mode, HTMLOpts, WikiOpts and Images.</nowiki>}}
	are Mode, HTMLOpts, WikiOpts and Images.</nowiki>}}
	<!--END-->		<!--END-->

Line 17:		Line 16:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{In\|		{{In\|
	n = 2 \|		n = 3 \|
	in = <nowiki>br = BR[5, {{1,3}, {-2,-4}, {1, 3}}];</nowiki>}}		in = <nowiki>br = BR[5, {{1,3}, {-2,-4}, {1, 3}}];</nowiki>}}
	<!--END-->		<!--END-->
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	n = 4 \|		n = 4 \|
	in = <nowiki>Show[BraidPlot[br]]</nowiki> \|		in = <nowiki>Show[BraidPlot[br]]</nowiki> \|
	img= ~~Drawing_Braids_Out_3~~.gif \|		img= Drawing_Braids_Out_4.gif \|
	out= <nowiki>-Graphics-</nowiki>}}		out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->		<!--END-->
Line 107:		Line 106:
	n = 9 \|		n = 9 \|
	in = <nowiki>CollapseBraid</nowiki> \|		in = <nowiki>CollapseBraid</nowiki> \|
	out= <nowiki>CollapseBraid[br] groups together commuting generators in the braid		out= <nowiki>CollapseBraid[br] groups together commuting generators in the braid br. Useful in conjunction with BraidPlot to produce compact braid plots.</nowiki>}}
	br. Useful in conjunction with BraidPlot to produce compact braid plots.</nowiki>}}
	<!--END-->		<!--END-->

Line 124:		Line 122:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics\|		{{Graphics\|
	n = 12 \|		n = 11 \|
	in = <nowiki>Show[BraidPlot[br1]]</nowiki> \|		in = <nowiki>Show[BraidPlot[br1]]</nowiki> \|
	img= Drawing_Braids_Out_11.gif \|		img= Drawing_Braids_Out_11.gif \|
Line 133:		Line 131:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{InOut\|		{{InOut\|
	n = 13 \|		n = 12 \|
	in = <nowiki>br2 = CollapseBraid[BR[TorusKnot[5, 4]]]</nowiki> \|		in = <nowiki>br2 = CollapseBraid[BR[TorusKnot[5, 4]]]</nowiki> \|
	out= <nowiki>BR[4, {{1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2},		out= <nowiki>BR[4, {{1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2},
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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics\|		{{Graphics\|
	n = 15 \|		n = 13 \|
	in = <nowiki>Show[BraidPlot[br2]]</nowiki> \|		in = <nowiki>Show[BraidPlot[br2]]</nowiki> \|
	img= ~~Drawing_Braids_Out_14~~.gif \|		img= Drawing_Braids_Out_13.gif \|
	out= <nowiki>-Graphics-</nowiki>}}		out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->		<!--END-->

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

2009-05-28T03:18:15Z

Reverted edits by VidarElbor (Talk); changed back to last version by DrorsRobot

← Older revision		Revision as of 23:18, 27 May 2009
Line 1:		Line 1:
	http://www.textaloloacelrel.com
	{{Manual TOC Sidebar}}		{{Manual TOC Sidebar}}

VidarElbor at 11:34, 22 May 2009

2009-05-22T11:34:36Z

← Older revision		Revision as of 07:34, 22 May 2009
Line 1:		Line 1:
			http://www.textaloloacelrel.com
	{{Manual TOC Sidebar}}		{{Manual TOC Sidebar}}

DrorsRobot at 19:05, 28 September 2007

2007-09-28T19:05:14Z

← Older revision		Revision as of 15:05, 28 September 2007
Line 8:		Line 8:
	n = 1 \|		n = 1 \|
	in = <nowiki>BraidPlot</nowiki> \|		in = <nowiki>BraidPlot</nowiki> \|
	out= <nowiki>BraidPlot[br, opts] produces a plot of the braid br. Possible options ~~are Mode, HTMLOpts and Images.</nowiki>}}~~		out= <nowiki>BraidPlot[br, opts] produces a plot of the braid br. Possible options
			are Mode, HTMLOpts, WikiOpts and Images.</nowiki>}}
	<!--END-->		<!--END-->

Line 38:		Line 39:
	out= <nowiki>{Mode -> Graphics, Images -> {0.gif, 1.gif, 2.gif, 3.gif, 4.gif},		out= <nowiki>{Mode -> Graphics, Images -> {0.gif, 1.gif, 2.gif, 3.gif, 4.gif},

	HTMLOpts -> }</nowiki>}}		HTMLOpts -> , WikiOpts -> }</nowiki>}}
	<!--END-->		<!--END-->

Line 106:		Line 107:
	n = 9 \|		n = 9 \|
	in = <nowiki>CollapseBraid</nowiki> \|		in = <nowiki>CollapseBraid</nowiki> \|
	out= <nowiki>CollapseBraid[br] groups together commuting generators in the braid ~~br. Useful in conjunction with BraidPlot to produce compact braid plots.</nowiki>}}~~		out= <nowiki>CollapseBraid[br] groups together commuting generators in the braid
			br. Useful in conjunction with BraidPlot to produce compact braid plots.</nowiki>}}
	<!--END-->		<!--END-->

Drorbn: Reverted edit of 218.117.68.108, changed back to last version by DrorsRobot

2007-06-19T14:56:19Z

Reverted edit of 218.117.68.108, changed back to last version by DrorsRobot

← Older revision		Revision as of 10:56, 19 June 2007
Line 41:		Line 41:
	<!--END-->		<!--END-->

	The <code>Mode</code> option to <code>BraidPlot</code> defaults to "<code>Graphics</code>", which produces output as above. An alternative is setting <code>Mode -> "HTML"</code>, which produces an HTML <tt>		The <code>Mode</code> option to <code>BraidPlot</code> defaults to "<code>Graphics</code>", which produces output as above. An alternative is setting <code>Mode -> "HTML"</code>, which produces an HTML <tt><table></tt> that can be readily inserted into HTML documents:

			<!--$$BraidPlot[br, Mode -> "HTML"]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 6 \|
			in = <nowiki>BraidPlot[br, Mode -> "HTML"]</nowiki> \|
			out= <nowiki><table cellspacing=0 cellpadding=0 border=0>
			<tr><td><img src=1.gif><img src=0.gif><img src=1.gif></td></tr>
			<tr><td><img src=2.gif><img src=3.gif><img src=2.gif></td></tr>
			<tr><td><img src=1.gif><img src=4.gif><img src=1.gif></td></tr>
			<tr><td><img src=2.gif><img src=3.gif><img src=2.gif></td></tr>
			<tr><td><img src=0.gif><img src=4.gif><img src=0.gif></td></tr>
			</table></nowiki>}}
			<!--END-->

			The table produced contains an array of image inclusions that together draws the braid using 5 fundamental building blocks: a horizontal "unbraided" line (<tt>0.gif</tt> above), the upper and lower halves of an overcrossing (<tt>1.gif</tt> and <tt>2.gif</tt> above) and the upper and lower halves of an underfcrossing (<tt>3.gif</tt> and <tt>4.gif</tt> above).

			Assuming <tt>0.gif</tt> through <tt>4.gif</tt> are [[Image:BraidPart0.gif]], [[Image:BraidPart1.gif]], [[Image:BraidPart2.gif]], [[Image:BraidPart3.gif]] and [[Image:BraidPart4.gif]], the above table is rendered as follows:

			{\| cellspacing=0 cellpadding=0 border=0 align=center
			\|[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]
			\|-
			\|[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]
			\|-
			\|[[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]
			\|-
			\|[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]
			\|-
			\|[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]]
			\|}

			The meaning of the <code>Images</code> option to <code>BraidPlot</code> should be clear from reading its default definition:

			<!--$$Images /. Options[BraidPlot]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 7 \|
			in = <nowiki>Images /. Options[BraidPlot]</nowiki> \|
			out= <nowiki>{0.gif, 1.gif, 2.gif, 3.gif, 4.gif}</nowiki>}}
			<!--END-->

			The <code>HTMLOpts</code> option to <code>BraidPlot</code> allows to insert options within the HTML <tt><img></tt> tags. Thus

			<!--$$BraidPlot[BR[2, {1, 1}], Mode -> "HTML", HTMLOpts -> "border=1"]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 8 \|
			in = <nowiki>BraidPlot[BR[2, {1, 1}], Mode -> "HTML", HTMLOpts -> "border=1"]</nowiki> \|
			out= <nowiki><table cellspacing=0 cellpadding=0 border=0>
			<tr><td><img border=1 src=1.gif><img border=1 src=1.gif></td></tr>
			<tr><td><img border=1 src=2.gif><img border=1 src=2.gif></td></tr>
			</table></nowiki>}}
			<!--END-->

			The above table is rendered as follows:

			<center>[[Image:BraidPlotHTMLExample2.gif]]</center>


			<!--$$?CollapseBraid$$-->
			<!--Robot Land, no human edits to "END"-->
			{{HelpLine\|
			n = 9 \|
			in = <nowiki>CollapseBraid</nowiki> \|
			out= <nowiki>CollapseBraid[br] groups together commuting generators in the braid br. Useful in conjunction with BraidPlot to produce compact braid plots.</nowiki>}}
			<!--END-->

			Thus compare the plots of <code>br1</code> and <code>br2</code> below:

			<!--$$br1 = BR[TorusKnot[5, 4]]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 10 \|
			in = <nowiki>br1 = BR[TorusKnot[5, 4]]</nowiki> \|
			out= <nowiki>BR[4, {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3}]</nowiki>}}
			<!--END-->

			<!--$$Show[BraidPlot[br1]]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{Graphics\|
			n = 12 \|
			in = <nowiki>Show[BraidPlot[br1]]</nowiki> \|
			img= Drawing_Braids_Out_11.gif \|
			out= <nowiki>-Graphics-</nowiki>}}
			<!--END-->

			<!--$$br2 = CollapseBraid[BR[TorusKnot[5, 4]]]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{InOut\|
			n = 13 \|
			in = <nowiki>br2 = CollapseBraid[BR[TorusKnot[5, 4]]]</nowiki> \|
			out= <nowiki>BR[4, {{1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2},

			{3}}]</nowiki>}}
			<!--END-->

			<!--$$Show[BraidPlot[br2]]$$-->
			<!--Robot Land, no human edits to "END"-->
			{{Graphics\|
			n = 15 \|
			in = <nowiki>Show[BraidPlot[br2]]</nowiki> \|
			img= Drawing_Braids_Out_14.gif \|
			out= <nowiki>-Graphics-</nowiki>}}
			<!--END-->

218.117.68.108 at 13:32, 19 June 2007

2007-06-19T13:32:49Z

← Older revision		Revision as of 09:32, 19 June 2007
Line 41:		Line 41:
	<!--END-->		<!--END-->

	The <code>Mode</code> option to <code>BraidPlot</code> defaults to "<code>Graphics</code>", which produces output as above. An alternative is setting <code>Mode -> "HTML"</code>, which produces an HTML <tt>~~<table></tt> that can be readily inserted into HTML documents:~~		The <code>Mode</code> option to <code>BraidPlot</code> defaults to "<code>Graphics</code>", which produces output as above. An alternative is setting <code>Mode -> "HTML"</code>, which produces an HTML <tt>

	<!--$$BraidPlot[br, Mode -> "HTML"]$$-->
	<!--Robot Land, no human edits to "END"-->
	{{InOut\|
	n = 6 \|
	in = <nowiki>BraidPlot[br, Mode -> "HTML"]</nowiki> \|
	out= <nowiki><table cellspacing=0 cellpadding=0 border=0>
	<tr><td><img src=1.gif><img src=0.gif><img src=1.gif></td></tr>
	<tr><td><img src=2.gif><img src=3.gif><img src=2.gif></td></tr>
	<tr><td><img src=1.gif><img src=4.gif><img src=1.gif></td></tr>
	<tr><td><img src=2.gif><img src=3.gif><img src=2.gif></td></tr>
	<tr><td><img src=0.gif><img src=4.gif><img src=0.gif></td></tr>
	</table></nowiki>}}
	<!--END-->

	The table produced contains an array of image inclusions that together draws the braid using 5 fundamental building blocks: a horizontal "unbraided" line (<tt>0.gif</tt> above), the upper and lower halves of an overcrossing (<tt>1.gif</tt> and <tt>2.gif</tt> above) and the upper and lower halves of an underfcrossing (<tt>3.gif</tt> and <tt>4.gif</tt> above).

	Assuming <tt>0.gif</tt> through <tt>4.gif</tt> are [[Image:BraidPart0.gif]], [[Image:BraidPart1.gif]], [[Image:BraidPart2.gif]], [[Image:BraidPart3.gif]] and [[Image:BraidPart4.gif]], the above table is rendered as follows:

	{\| cellspacing=0 cellpadding=0 border=0 align=center
	\|[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]
	\|-
	\|[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]
	\|-
	\|[[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]
	\|-
	\|[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]
	\|-
	\|[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]]
	\|}

	The meaning of the <code>Images</code> option to <code>BraidPlot</code> should be clear from reading its default definition:

	<!--$$Images /. Options[BraidPlot]$$-->
	<!--Robot Land, no human edits to "END"-->
	{{InOut\|
	n = 7 \|
	in = <nowiki>Images /. Options[BraidPlot]</nowiki> \|
	out= <nowiki>{0.gif, 1.gif, 2.gif, 3.gif, 4.gif}</nowiki>}}
	<!--END-->

	The <code>HTMLOpts</code> option to <code>BraidPlot</code> allows to insert options within the HTML <tt><img></tt> tags. Thus

	<!--$$BraidPlot[BR[2, {1, 1}], Mode -> "HTML", HTMLOpts -> "border=1"]$$-->
	<!--Robot Land, no human edits to "END"-->
	{{InOut\|
	n = 8 \|
	in = <nowiki>BraidPlot[BR[2, {1, 1}], Mode -> "HTML", HTMLOpts -> "border=1"]</nowiki> \|
	out= <nowiki><table cellspacing=0 cellpadding=0 border=0>
	<tr><td><img border=1 src=1.gif><img border=1 src=1.gif></td></tr>
	<tr><td><img border=1 src=2.gif><img border=1 src=2.gif></td></tr>
	</table></nowiki>}}
	<!--END-->

	The above table is rendered as follows:

	<center>[[Image:BraidPlotHTMLExample2.gif]]</center>


	<!--$$?CollapseBraid$$-->
	<!--Robot Land, no human edits to "END"-->
	{{HelpLine\|
	n = 9 \|
	in = <nowiki>CollapseBraid</nowiki> \|
	out= <nowiki>CollapseBraid[br] groups together commuting generators in the braid br. Useful in conjunction with BraidPlot to produce compact braid plots.</nowiki>}}
	<!--END-->

	Thus compare the plots of <code>br1</code> and <code>br2</code> below:

	<!--$$br1 = BR[TorusKnot[5, 4]]$$-->
	<!--Robot Land, no human edits to "END"-->
	{{InOut\|
	n = 10 \|
	in = <nowiki>br1 = BR[TorusKnot[5, 4]]</nowiki> \|
	out= <nowiki>BR[4, {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3}]</nowiki>}}
	<!--END-->

	<!--$$Show[BraidPlot[br1]]$$-->
	<!--Robot Land, no human edits to "END"-->
	{{Graphics\|
	n = 12 \|
	in = <nowiki>Show[BraidPlot[br1]]</nowiki> \|
	img= Drawing_Braids_Out_11.gif \|
	out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->

	<!--$$br2 = CollapseBraid[BR[TorusKnot[5, 4]]]$$-->
	<!--Robot Land, no human edits to "END"-->
	{{InOut\|
	n = 13 \|
	in = <nowiki>br2 = CollapseBraid[BR[TorusKnot[5, 4]]]</nowiki> \|
	out= <nowiki>BR[4, {{1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2},

	{3}}]</nowiki>}}
	<!--END-->

	<!--$$Show[BraidPlot[br2]]$$-->
	<!--Robot Land, no human edits to "END"-->
	{{Graphics\|
	n = 15 \|
	in = <nowiki>Show[BraidPlot[br2]]</nowiki> \|
	img= Drawing_Braids_Out_14.gif \|
	out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->

DrorsRobot at 17:09, 30 August 2005

2005-08-30T17:09:30Z

Show changes

DrorsRobot at 03:16, 29 August 2005

2005-08-29T03:16:17Z

← Older revision		Revision as of 23:16, 28 August 2005
Line 22:		Line 22:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics1\|n=3}}		{{Graphics1\|n=3}}
	~~Show[~~Show[BraidPlot[br]]]		<pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[BraidPlot[br]]</nowiki></pre>
	{{Graphics2\|n=3\|imagename=Drawing_Braids_Out_3.gif}}		{{Graphics2\|n=3\|imagename=Drawing_Braids_Out_3.gif}}
	<!--END-->		<!--END-->
Line 118:		Line 118:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics1\|n=10}}		{{Graphics1\|n=10}}
	~~Show[~~Show[BraidPlot[br1]]]		<pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[BraidPlot[br1]]</nowiki></pre>
	{{Graphics2\|n=10\|imagename=Drawing_Braids_Out_10.gif}}		{{Graphics2\|n=10\|imagename=Drawing_Braids_Out_10.gif}}
	<!--END-->		<!--END-->
Line 135:		Line 135:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics1\|n=12}}		{{Graphics1\|n=12}}
	~~Show[~~Show[BraidPlot[br2]]]		<pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[BraidPlot[br2]]</nowiki></pre>
	{{Graphics2\|n=12\|imagename=Drawing_Braids_Out_12.gif}}		{{Graphics2\|n=12\|imagename=Drawing_Braids_Out_12.gif}}
	<!--END-->		<!--END-->

DrorsRobot at 03:13, 29 August 2005

2005-08-29T03:13:02Z

← Older revision		Revision as of 23:13, 28 August 2005
Line 22:		Line 22:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics1\|n=3}}		{{Graphics1\|n=3}}
	Show[BraidPlot[br]]		Show[Show[BraidPlot[br]]]
	{{Graphics2\|n=3\|imagename=Drawing_Braids_Out_3.gif}}		{{Graphics2\|n=3\|imagename=Drawing_Braids_Out_3.gif}}
	<!--END-->		<!--END-->
Line 118:		Line 118:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics1\|n=10}}		{{Graphics1\|n=10}}
	Show[BraidPlot[br1]]		Show[Show[BraidPlot[br1]]]
	{{Graphics2\|n=10\|imagename=Drawing_Braids_Out_10.gif}}		{{Graphics2\|n=10\|imagename=Drawing_Braids_Out_10.gif}}
	<!--END-->		<!--END-->
Line 135:		Line 135:
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{Graphics1\|n=12}}		{{Graphics1\|n=12}}
	Show[BraidPlot[br2]]		Show[Show[BraidPlot[br2]]]
	{{Graphics2\|n=12\|imagename=Drawing_Braids_Out_12.gif}}		{{Graphics2\|n=12\|imagename=Drawing_Braids_Out_12.gif}}
	<!--END-->		<!--END-->

DrorsRobot at 03:12, 29 August 2005

2005-08-29T03:12:42Z

← Older revision		Revision as of 23:12, 28 August 2005
Line 32:		Line 32:
	{{InOut1\|n=4}}		{{InOut1\|n=4}}
	<pre style="color: red; border: 0px; padding: 0em"><nowiki>Options[BraidPlot]</nowiki></pre>		<pre style="color: red; border: 0px; padding: 0em"><nowiki>Options[BraidPlot]</nowiki></pre>
	{{InOut2\|n=4}}<pre style="border: 0px; padding: 0em"><nowiki>{Mode -> Graphics, Images -> {0.gif, 1.gif, 2.gif, 3.gif, 4.gif}, ~~HTMLOpts -> }</nowiki></pre>~~		{{InOut2\|n=4}}<pre style="border: 0px; padding: 0em"><nowiki>{Mode -> Graphics, Images -> {0.gif, 1.gif, 2.gif, 3.gif, 4.gif},

			HTMLOpts -> }</nowiki></pre>
	{{InOut3}}		{{InOut3}}
	<!--END-->		<!--END-->
Line 124:		Line 126:
	{{InOut1\|n=11}}		{{InOut1\|n=11}}
	<pre style="color: red; border: 0px; padding: 0em"><nowiki>br2 = CollapseBraid[BR[TorusKnot[5, 4]]]</nowiki></pre>		<pre style="color: red; border: 0px; padding: 0em"><nowiki>br2 = CollapseBraid[BR[TorusKnot[5, 4]]]</nowiki></pre>
	{{InOut2\|n=11}}<pre style="border: 0px; padding: 0em"><nowiki>BR[4, {{1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2}, ~~{3}}]</nowiki></pre>~~		{{InOut2\|n=11}}<pre style="border: 0px; padding: 0em"><nowiki>BR[4, {{1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2}, {3, 1}, {2},

			{3}}]</nowiki></pre>
	{{InOut3}}		{{InOut3}}
	<!--END-->		<!--END-->