Invariants from Braid Theory - Revision history

ScottDataRobot at 22:20, 21 February 2013

2013-02-21T22:20:49Z

← Older revision		Revision as of 18:20, 21 February 2013
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	{{HelpLine\|		{{HelpLine\|
	n = 1 \|		n = 2 \|
	in = <nowiki>BraidLength</nowiki> \|		in = <nowiki>BraidLength</nowiki> \|
	out= <nowiki>BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.</nowiki>}}		out= <nowiki>BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.</nowiki>}}
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	{{InOut\|		{{InOut\|
	n = 2 \|		n = 3 \|
	in = <nowiki>K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}</nowiki> \|		in = <nowiki>K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}</nowiki> \|
	out= <nowiki>{11, 11}</nowiki>}}		out= <nowiki>{11, 11}</nowiki>}}
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	{{HelpAndAbout\|		{{HelpAndAbout\|
	n = 3 \|		n = 4 \|
	n1 = 4 \|		n1 = 5 \|
	in = <nowiki>BraidIndex</nowiki> \|		in = <nowiki>BraidIndex</nowiki> \|
	out= <nowiki>BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.</nowiki> \|		out= <nowiki>BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.</nowiki> \|
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	{{InOut\|		{{InOut\|
	n = 5 \|		n = 6 \|
	in = <nowiki>K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}</nowiki> \|		in = <nowiki>K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}</nowiki> \|
	out= <nowiki>{4, 5}</nowiki>}}		out= <nowiki>{4, 5}</nowiki>}}
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	n = 7 \|		n = 7 \|
	in = <nowiki>Show[BraidPlot[BR[K]]]</nowiki> \|		in = <nowiki>Show[BraidPlot[BR[K]]]</nowiki> \|
	img= ~~Invariants_from_Braid_Theory_Out_6~~.gif \|		img= Invariants_from_Braid_Theory_Out_7.gif \|
	out= <nowiki>-Graphics-</nowiki>}}		out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->		<!--END-->

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

2008-12-17T11:43:41Z

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

← Older revision		Revision as of 07:43, 17 December 2008
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	domlilatr
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VitrrAccna: zelvidompa

2008-12-16T16:12:41Z

zelvidompa

← Older revision		Revision as of 12:12, 16 December 2008
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			domlilatr
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Scott: Reverted edits by 217.149.45.68 (Talk); changed back to last version by Drorbn

2007-08-28T23:30:31Z

Reverted edits by 217.149.45.68 (Talk); changed back to last version by Drorbn

← Older revision		Revision as of 19:30, 28 August 2007
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	The ''braid length'' of a knot or a link <math>K</math> is the smallest number of crossings in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid lengths preloaded:		The ''braid length'' of a knot or a link <math>K</math> is the smallest number of crossings in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid lengths preloaded:

217.149.45.68 at 15:09, 28 August 2007

2007-08-28T15:09:36Z

← Older revision		Revision as of 11:09, 28 August 2007
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sprint blast scarpa moda uomo] [http://wedner.info/content/view/testi-canzoni.htm testi canzoni zero assoluto] [http://klohy.info/img/styles/marey-carey.htm marey carey] [http://polex.com.cn/resources/articles/qtek-.htm qtek 8020 gps] [http://klohy.info/img/styles/totti-barzellette.htm totti barzellette] [http://sneck.info/data/un-topolino/ un topolino in gamba] [http://svike.info/view/new/appartamento-firenze.htm appartamento firenze] [http://klohy.info/img/styles/compuprint-toner.htm compuprint toner] [http://budget7i.info/lib/ghost/ ghost 8 0 0 984] [http://xionny.cn/topic/egaxve-sfma/ eg701ax-ve sfma] [http://soler.net.cn/data/scarica-roms.htm scarica roms] [http://funkall.us/images/small/power-dvd/ power dvd software] [http://budget7i.info/lib/hp/ hp 4250] [http://budget7i.info/lib/uomini-alla/ uomini alla ventura] [http://soler.net.cn/data/seder.htm seder] [http://soler.net.cn/data/video-sfilate.htm video sfilate moda] [http://funkall.us/images/small/nortek-recorder/ nortek recorder dvd] [http://veggis.org.cn/resources/articles/date-concerti.htm date concerti dei new trolls] [http://budget7i.info/lib/terapia-del/ terapia del dolore] [http://polex.com.cn/resources/articles/weekend-terme.htm weekend terme benessere] [http://funkall.us/images/small/gelait/ gelait] [http://polex.com.cn/resources/articles/flickman.htm flickman] [http://funkall.us/images/small/mammamia/ mammamia] [http://sneck.info/data/street-of/ street of simcity] [http://svike.info/view/new/indesign.htm indesign 2] [http://xionny.cn/topic/dizionario-della/ dizionario della lingua italiana] [http://primonona.info/content/view/stampanti-per/ stampanti per notebook] [http://manoke.cn/topic/deep-dish/ deep dish flash dance] [http://veggis.org.cn/resources/articles/hosting-condiviso.htm hosting condiviso] [http://joperan.org/data/energizer-a/ energizer a76] [http://sneck.info/data/eligeme-de/ eligeme de luis fonsi] [http://joperan.org/data/atollo-di/ atollo di ari it] [http://sneck.info/data/sido-instrumental/ sido instrumental] [http://soler.net.cn/data/camping-europa.htm camping europa] [http://manoke.cn/topic/audi-a/ audi a3 padova] [http://joperan.org/data/voli-low/ voli low cost alghero venezia] [http://polex.com.cn/resources/articles/novara.htm novara] [http://polex.com.cn/resources/articles/figlio-cognato.htm figlio cognato terzo affine] [http://manoke.cn/topic/asus-kvx/ asus k8vx 754] [http://soler.net.cn/data/acer-.htm acer 17 dvi] [http://manoke.cn/topic/hp-psc/ hp psc 1210] [http://polex.com.cn/resources/articles/ambrosiaster.htm ambrosiaster] [http://funkall.us/images/small/nidi-d/ nidi d arac] [http://funkall.us/images/small/cuba-e/ cuba e lavana] [http://svike.info/view/new/cartuccia-fax.htm cartuccia fax] [http://wedner.info/content/view/rebcca.htm rebcca] [http://xionny.cn/topic/vergassola-dario/ vergassola dario] [http://primonona.info/content/view/braun-sveglia/ braun sveglia] [http://xionny.cn/topic/dvd-cd/ dvd cd pezzi] [http://sneck.info/data/vacanze-a/ vacanze a praga e budapes] [http://sneck.info/data/bodeguita-del/ bodeguita del bito] [http://svike.info/view/new/piedimonte-san.htm piedimonte san germano] [http://funkall.us/images/small/mario-del/ mario del monaco] [http://svike.info/view/new/epson-rx.htm epson rx 600] [http://primonona.info/content/view/celestine/ celestine] [http://polex.com.cn/resources/articles/uefa-euro.htm uefa euro 4] [http://funkall.us/images/small/hp-tom/ hp tom] [http://veggis.org.cn/resources/articles/programma-per.htm programma per scaricare mp3] [http://veggis.org.cn/resources/articles/medea.htm medea] [http://veggis.org.cn/resources/articles/hp.htm hp 9300] [http://sneck.info/data/elvis-costello/ elvis costello - e imposters. club date. live in memphis] [http://svike.info/view/new/www-megan.htm www megan gaige] [http://sneck.info/data/lavatrici-bosch/ lavatrici bosch 1660] [http://funkall.us/images/small/www-liebeskummer/ www liebeskummer ch] [http://wedner.info/content/view/lego-star.htm lego star wars ps2] [http://veggis.org.cn/resources/articles/virus-troian.htm virus troian startpage] [http://joperan.org/data/spartiti-per/ spartiti per pianoforte di tiziano ferro] [http://sneck.info/data/occhiali-da/ occhiali da vista uomo] [http://veggis.org.cn/resources/articles/dance-party.htm dance party winter 2005] [http://svike.info/view/new/online.htm online] [http://primonona.info/content/view/larisa/ larisa] [http://polex.com.cn/resources/articles/milano-manila.htm milano manila biglietti aerei] [http://xionny.cn/topic/tema-d/ tema d attualita] [http://sneck.info/data/personaggi-hamtaro/ personaggi hamtaro] [http://wedner.info/content/view/ram-.htm ram 1024 kingston hyperx] [http://veggis.org.cn/resources/articles/hp-compaq.htm hp compaq server g4] [http://manoke.cn/topic/batteria-canon/ batteria canon nb-1lh] [http://joperan.org/data/blackwood-algernon/ blackwood, algernon] [http://funkall.us/images/small/luana-piovanni/ luana piovanni] [http://budget7i.info/lib/televisore-philips/ televisore philips] [http://klohy.info/img/styles/madonna.htm madonna] [http://wedner.info/content/view/mercato-bici.htm mercato bici da corsa] [http://polex.com.cn/resources/articles/kivi-alexis.htm kivi, alexis] [http://funkall.us/images/small/sceen-savers/ sceen savers] [http://manoke.cn/topic/ps-tray/ ps tray factory 1.94] [http://xionny.cn/topic/carmel-ristorante/ carmel ristorante] [http://funkall.us/images/small/gazzettino-il/ gazzettino, il-] [http://polex.com.cn/resources/articles/ferro-e.htm ferro e fuoco] [http://veggis.org.cn/resources/articles/un-nuovo.htm un nuovo trailer per ultimate spider-man] [http://veggis.org.cn/resources/articles/hotel-napoli.htm hotel napoli centro] [http://funkall.us/images/small/corsi-gratuiti/ corsi gratuiti di restauro] [http://xionny.cn/topic/magic-ppf/ magic ppf 585] [http://primonona.info/content/view/stampante-epson/ stampante epson epl-n7000] [http://manoke.cn/topic/haier-lavatrici/ haier lavatrici] [http://xionny.cn/topic/microsoft-oem/ microsoft oem windows server 2003] [http://primonona.info/content/view/il-promontorio/ il promontorio della paura - cape fear] [http://soler.net.cn/data/manuale-philips.htm manuale philips] [http://polex.com.cn/resources/articles/innocenza-e.htm innocenza e malizia] [http://joperan.org/data/hard-disk/ hard disk con lettori di schede] [http://soler.net.cn/data/rgg.htm rgg] [http://svike.info/view/new/artic-cooling.htm artic cooling] [http://svike.info/view/new/fucecchio.htm fucecchio] [http://wedner.info/content/view/simpatico.htm simpatico] [http://sneck.info/data/orologio-a/ orologio a cucu] [http://soler.net.cn/data/motorola.htm motorola 398] [http://polex.com.cn/resources/articles/subah-ho.htm subah ho gayi] [http://manoke.cn/topic/imitazione-rolex/ imitazione rolex] [http://xionny.cn/topic/il-banco/ il banco dei gelati] [http://sneck.info/data/personaggi-settimo/ personaggi settimo cielo] [http://klohy.info/img/styles/pomas.htm pomas] [http://sneck.info/data/impianti-termici/ impianti termici negli edifici] [http://primonona.info/content/view/mini-cooper/ mini cooper km0] [http://klohy.info/img/styles/george-il.htm george il re della giungla] [http://budget7i.info/lib/drive-flash/ drive flash] [http://veggis.org.cn/resources/articles/preventivi.htm preventivi] [http://xionny.cn/topic/gatitas/ gatitas] [http://sneck.info/data/cinema-monza/ cinema monza] [http://xionny.cn/topic/renzo-arbore/ renzo arbore] [http://manoke.cn/topic/altoparlanti-/ altoparlanti 5 1 wireless] [http://budget7i.info/lib/trick-me/ trick me wav] [http://xionny.cn/topic/sonata-in/ sonata in re maggiore] [http://svike.info/view/new/lettino-mare.htm lettino mare] [http://budget7i.info/lib/nissan-x/ nissan x trail auto] [http://klohy.info/img/styles/vanity-agency.htm vanity agency] [http://wedner.info/content/view/panasonic-fax.htm panasonic fax segreteria] [http://wedner.info/content/view/progetti-architettura.htm progetti architettura] [http://sneck.info/data/profumi-uomo/ profumi uomo armani] [http://veggis.org.cn/resources/articles/bitch.htm bitch] [http://soler.net.cn/data/agp-x.htm agp 8x 256 ddr] [http://manoke.cn/topic/mass-file/ mass file editor] [http://polex.com.cn/resources/articles/apache-in.htm apache in agguato] [http://svike.info/view/new/preve.htm preve] [http://primonona.info/content/view/elekman/ elekman] [http://veggis.org.cn/resources/articles/camionista.htm camionista] [http://xionny.cn/topic/sesso-animal/ sesso animal] [http://funkall.us/images/small/giochi-tim/ giochi tim] [http://joperan.org/data/filmato-di/ filmato di un rapporto sessuale] [http://xionny.cn/topic/the-beat/ the beat - violenza alla deriva] [http://funkall.us/images/small/potatura-piante/ potatura piante] [http://xionny.cn/topic/olivetti-telefono/ olivetti telefono fax] [http://polex.com.cn/resources/articles/sandy-grease.htm sandy grease] [http://primonona.info/content/view/delonghi-deumidificatore/ delonghi deumidificatore] [http://funkall.us/images/small/mp/ mp3 1] [http://soler.net.cn/data/mitsubishi-pick.htm mitsubishi pick up] [http://sneck.info/data/foto-annunci/ foto annunci singole donne amanti anal] [http://veggis.org.cn/resources/articles/produzione-articoli.htm produzione articoli religiosi in metallo torino] [http://sneck.info/data/otello-deve/ otello deve morire] [http://klohy.info/img/styles/annuncio-coppia.htm annuncio coppia sicilia] [http://manoke.cn/topic/tutto-wind/ tutto wind] [http://manoke.cn/topic/supporto-auto/ supporto auto per palmari] [http://soler.net.cn/data/dennis-quaid.htm dennis quaid] [http://manoke.cn/topic/la-peste/ la peste doro] [http://klohy.info/img/styles/centro-america.htm centro america com] [http://svike.info/view/new/i-s.htm i s p e s l] [http://sneck.info/data/video-lesbiche/ video lesbiche gratuiti] [http://xionny.cn/topic/sangre-de/ sangre de grado] [http://xionny.cn/topic/durso/ durso] [http://polex.com.cn/resources/articles/vescovo-bertone.htm vescovo bertone] [http://primonona.info/content/view/www-ciuccia/ www ciuccia billi] [http://sneck.info/data/esecuzione-italiano/ esecuzione italiano in iraq] [http://budget7i.info/lib/nessuna-conferma/ nessuna conferma su out run 2] [http://xionny.cn/topic/oroscopo-anno/ oroscopo anno] [http://svike.info/view/new/dance-mania.htm dance mania] [http://svike.info/view/new/divieto-di.htm divieto di fumare] [http://wedner.info/content/view/vids.htm vids] [http://sneck.info/data/congelatori-verticale/ congelatori verticale ocean] [http://svike.info/view/new/appunti-architettura.htm appunti architettura] [http://primonona.info/content/view/marchesin/ marchesin] [http://funkall.us/images/small/lipsia-citta/ lipsia citta] [http://soler.net.cn/data/tarzan-a.htm tarzan a new york weissmuller thorpe] [http://xionny.cn/topic/imate-pdak/ i-mate pda2k gps] {{Manual TOC Sidebar}}
	{{Manual TOC Sidebar}}

	The ''braid length'' of a knot or a link <math>K</math> is the smallest number of crossings in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid lengths preloaded:		The ''braid length'' of a knot or a link <math>K</math> is the smallest number of crossings in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid lengths preloaded:

Drorbn at 07:30, 3 September 2005

2005-09-03T07:30:23Z

← Older revision		Revision as of 03:30, 3 September 2005
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	out= <nowiki>{11, 11}</nowiki>}}		out= <nowiki>{11, 11}</nowiki>}}
	<!--END-->		<!--END-->

			{{Knot Image Pair\|9_49\|gif\|10_136\|gif}}

	The ''braid index'' of a knot or a link <math>K</math> is the smallest number of strands in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid indices preloaded:		The ''braid index'' of a knot or a link <math>K</math> is the smallest number of strands in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid indices preloaded:

DrorsRobot at 17:11, 30 August 2005

2005-08-30T17:11:51Z

← Older revision		Revision as of 13:11, 30 August 2005
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	<!--$$?BraidLength$$-->		<!--$$?BraidLength$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
			{{HelpLine\|
	{{Help1\|n=1\|s=BraidLength}}
			n = 1 \|
⚫	BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.
			in = <nowiki>BraidLength</nowiki> \|
	{{Help2}}
		⚫	out= <nowiki>BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.</nowiki>}}
	<!--END-->		<!--END-->

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	<!--$$K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}$$-->		<!--$$K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}$$-->
	<!--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>K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}</nowiki>~~</pre>~~		in = <nowiki>K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}</nowiki> \|
	{{InOut2\|n=2}}<pre style="border: 0px; padding: 0em"><nowiki>{11, 11}</nowiki></pre>
			out= <nowiki>{11, 11}</nowiki>}}
	{{InOut3}}
	<!--END-->		<!--END-->

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	<!--$$?BraidIndex$$-->		<!--$$?BraidIndex$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
			{{HelpAndAbout\|
	{{HelpAndAbout1\|n=3\|s=BraidIndex}}
			n = 3 \|
⚫	BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.
			n1 = 4 \|
	{{HelpAndAbout2\|n=4\|s=BraidIndex}}
			in = <nowiki>BraidIndex</nowiki> \|
⚫	The braid index data known to KnotTheory` is taken from Charles Livingston's "Table of Knot Invariants", http://www.indiana.edu/~knotinfo/.
		⚫	out= <nowiki>BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.</nowiki> \|
	{{HelpAndAbout3}}
		⚫	about= <nowiki>The braid index data known to KnotTheory` is taken from Charles Livingston's "Table of Knot Invariants", http://www.indiana.edu/~knotinfo/.</nowiki>}}
	<!--END-->		<!--END-->

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	<!--$$K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}$$-->		<!--$$K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}$$-->
	<!--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>K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}</nowiki>~~</pre>~~		in = <nowiki>K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}</nowiki> \|
	{{InOut2\|n=5}}<pre style="border: 0px; padding: 0em"><nowiki>{4, 5}</nowiki></pre>
			out= <nowiki>{4, 5}</nowiki>}}
	{{InOut3}}
	<!--END-->		<!--END-->

	<!--$$Show[BraidPlot[BR[K]]]$$-->		<!--$$Show[BraidPlot[BR[K]]]$$-->
	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
			{{Graphics\|
	{{Graphics1\|n=6}}
			n = 7 \|
	Show[BraidPlot[BR[K]]]		in = <nowiki>Show[BraidPlot[BR[K]]]</nowiki> \|
	~~{{Graphics2\|n=6\|imagename~~=Invariants_from_Braid_Theory_Out_6.gif}}		img= Invariants_from_Braid_Theory_Out_6.gif \|
			out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->		<!--END-->

69.156.15.171 at 00:43, 28 August 2005

2005-08-28T00:43:11Z

← Older revision		Revision as of 20:43, 27 August 2005
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	<!--$$?BraidLength$$-->		<!--$$?BraidLength$$-->
			<!--Robot Land, no human edits to "END"-->
	<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
	{{Help1\|n=2\|s=BraidLength}}		{{Help1\|n=1\|s=BraidLength}}
	BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.		BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.
	{{Help2}}		{{Help2}}
Line 15:		Line 15:

	<!--$$K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}$$-->		<!--$$K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}$$-->
			<!--Robot Land, no human edits to "END"-->
	<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
	{{InOut1\|n=3}}		{{InOut1\|n=2}}
	K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}		<pre style="color: red; border: 0px; padding: 0em"><nowiki>K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}</nowiki></pre>
	{{InOut2\|n=3}}<pre style="border: 0px; padding: 0em"><nowiki>{11, 11}</nowiki></pre>		{{InOut2\|n=2}}<pre style="border: 0px; padding: 0em"><nowiki>{11, 11}</nowiki></pre>
	{{InOut3}}		{{InOut3}}
	<!--END-->		<!--END-->
Line 25:		Line 25:

	<!--$$?BraidIndex$$-->		<!--$$?BraidIndex$$-->
			<!--Robot Land, no human edits to "END"-->
	<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
	{{HelpAndAbout1\|n=4\|s=BraidIndex}}		{{HelpAndAbout1\|n=3\|s=BraidIndex}}
	BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.		BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.
	{{HelpAndAbout2\|n=5\|s=BraidIndex}}		{{HelpAndAbout2\|n=4\|s=BraidIndex}}
	The braid index data known to KnotTheory` is taken from Charles Livingston's "Table of Knot Invariants", http://www.indiana.edu/~knotinfo/.		The braid index data known to KnotTheory` is taken from Charles Livingston's "Table of Knot Invariants", http://www.indiana.edu/~knotinfo/.
	{{HelpAndAbout3}}		{{HelpAndAbout3}}
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	<!--$$K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}$$-->		<!--$$K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}$$-->
			<!--Robot Land, no human edits to "END"-->
	<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
	{{InOut1\|n=6}}		{{InOut1\|n=5}}
	K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}		<pre style="color: red; border: 0px; padding: 0em"><nowiki>K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}</nowiki></pre>
	{{InOut2\|n=6}}<pre style="border: 0px; padding: 0em"><nowiki>{4, 5}</nowiki></pre>		{{InOut2\|n=5}}<pre style="border: 0px; padding: 0em"><nowiki>{4, 5}</nowiki></pre>
	{{InOut3}}		{{InOut3}}
	<!--END-->		<!--END-->

	<!--$$Show[BraidPlot[BR[K]]]$$-->		<!--$$Show[BraidPlot[BR[K]]]$$-->
			<!--Robot Land, no human edits to "END"-->
	<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
	{{Graphics1\|n=7}}		{{Graphics1\|n=6}}
	Show[BraidPlot[BR[K]]]		Show[BraidPlot[BR[K]]]
	{{Graphics2\|n=7\|imagename=~~Invariants_from_Braid_Theory_Out_7~~.gif}}		{{Graphics2\|n=6\|imagename=Invariants_from_Braid_Theory_Out_6.gif}}
	<!--END-->		<!--END-->

Drorbn at 02:03, 25 August 2005

2005-08-25T02:03:27Z

← Older revision		Revision as of 22:03, 24 August 2005
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	{{Manual TOC Sidebar}}		{{Manual TOC Sidebar}}

	The ``braid length`` of a knot or a link <math>K</math> is the smallest number of crossings in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid lengths preloaded:		The ''braid length'' of a knot or a link <math>K</math> is the smallest number of crossings in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid lengths preloaded:

	{{Startup Note}}		{{Startup Note}}
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	<!--END-->		<!--END-->

	The ``braid index`` of a knot or a link <math>K</math> is the smallest number of strands in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid indices preloaded:		The ''braid index'' of a knot or a link <math>K</math> is the smallest number of strands in a braid whose closure is <math>K</math>. <code>KnotTheory`</code> has some braid indices preloaded:

	<!--$$?BraidIndex$$-->		<!--$$?BraidIndex$$-->

DrorsRobot at 02:02, 25 August 2005

2005-08-25T02:02:18Z

← Older revision		Revision as of 22:02, 24 August 2005
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	<!--$$?BraidLength$$-->		<!--$$?BraidLength$$-->
			<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
			{{Help1\|n=2\|s=BraidLength}}
			BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.
			{{Help2}}
	<!--END-->		<!--END-->

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	<!--$$K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}$$-->		<!--$$K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}$$-->
			<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
			{{InOut1\|n=3}}
			K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}
			{{InOut2\|n=3}}<pre style="border: 0px; padding: 0em"><nowiki>{11, 11}</nowiki></pre>
			{{InOut3}}
	<!--END-->		<!--END-->

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	<!--$$?BraidIndex$$-->		<!--$$?BraidIndex$$-->
			<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
			{{HelpAndAbout1\|n=4\|s=BraidIndex}}
			BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.
			{{HelpAndAbout2\|n=5\|s=BraidIndex}}
			The braid index data known to KnotTheory` is taken from Charles Livingston's "Table of Knot Invariants", http://www.indiana.edu/~knotinfo/.
			{{HelpAndAbout3}}
	<!--END-->		<!--END-->

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	<!--$$K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}$$-->		<!--$$K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}$$-->
			<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
			{{InOut1\|n=6}}
			K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}
			{{InOut2\|n=6}}<pre style="border: 0px; padding: 0em"><nowiki>{4, 5}</nowiki></pre>
			{{InOut3}}
	<!--END-->		<!--END-->

	<!--$$Show[BraidPlot[BR[K]]]$$-->		<!--$$Show[BraidPlot[BR[K]]]$$-->
			<!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
			{{Graphics1\|n=7}}
			Show[BraidPlot[BR[K]]]
			{{Graphics2\|n=7\|imagename=Invariants_from_Braid_Theory_Out_7.gif}}
	<!--END-->		<!--END-->

← Older revision		Revision as of 18:20, 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>BraidLength</nowiki> \|		in = <nowiki>BraidLength</nowiki> \|
	out= <nowiki>BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.</nowiki>}}		out= <nowiki>BraidLength[K] returns the braid length of the knot K, if known to KnotTheory`.</nowiki>}}
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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>K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}</nowiki> \|		in = <nowiki>K = Knot[9, 49]; {BraidLength[K], Crossings[BR[K]]}</nowiki> \|
	out= <nowiki>{11, 11}</nowiki>}}		out= <nowiki>{11, 11}</nowiki>}}
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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{HelpAndAbout\|		{{HelpAndAbout\|
	n = 3 \|		n = 4 \|
	n1 = 4 \|		n1 = 5 \|
	in = <nowiki>BraidIndex</nowiki> \|		in = <nowiki>BraidIndex</nowiki> \|
	out= <nowiki>BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.</nowiki> \|		out= <nowiki>BraidIndex[K] returns the braid index of the knot K, if known to KnotTheory`.</nowiki> \|
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	<!--Robot Land, no human edits to "END"-->		<!--Robot Land, no human edits to "END"-->
	{{InOut\|		{{InOut\|
	n = 5 \|		n = 6 \|
	in = <nowiki>K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}</nowiki> \|		in = <nowiki>K = Knot[10, 136]; {BraidIndex[K], First@BR[K]}</nowiki> \|
	out= <nowiki>{4, 5}</nowiki>}}		out= <nowiki>{4, 5}</nowiki>}}
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	n = 7 \|		n = 7 \|
	in = <nowiki>Show[BraidPlot[BR[K]]]</nowiki> \|		in = <nowiki>Show[BraidPlot[BR[K]]]</nowiki> \|
	img= ~~Invariants_from_Braid_Theory_Out_6~~.gif \|		img= Invariants_from_Braid_Theory_Out_7.gif \|
	out= <nowiki>-Graphics-</nowiki>}}		out= <nowiki>-Graphics-</nowiki>}}
	<!--END-->		<!--END-->